research article hazmats transportation network design...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 517372 22 pageshttpdxdoiorg1011552013517372

Research ArticleHazmats Transportation Network DesignModel with Emergency Response under ComplexFuzzy Environment

Jiuping Xu12 Jun Gang2 and Xiao Lei3

1 State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan UniversityChengdu 610064 China

2Uncertainty Decision-Making Laboratory Sichuan University Chengdu 610064 China3 China Three Gorges Corporation Yichang 443002 China

Correspondence should be addressed to Jiuping Xu xujiupingscueducn

Received 26 December 2012 Revised 2 February 2013 Accepted 2 February 2013

Academic Editor Valentina E Balas

Copyright copy 2013 Jiuping Xu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A bilevel optimization model for a hazardous materials transportation network design is presented which considers an emergencyresponse teams location problem On the upper level the authority designs the transportation network to minimize totaltransportation risk On the lower level the carriers first choose their routes so that the total transportation cost is minimizedThenthe emergency response department locates their emergency service units so as tomaximize the total weighted arc length covered Incontrast to prior studies the uncertainty associated with transportation risk has been explicitly considered in the objective functionof our mathematical model Specifically our research uses a complex fuzzy variable to model transportation risk An improvedartificial bee colony algorithm with priority-based encoding is also applied to search for the optimal solution to the bilevel modelFinally the efficiency of the proposed model and algorithm is evaluated using a practical case and various computing attributes

1 Introduction

The transportation of hazardous materials (hazmats) hasalways been an important issue because of the risk associatedwith an accidental release of hazardous materials duringtransportation [1] Globally more than 4 billion tons of haz-mat are transported annually [2] withmore than 2 billion tonsof hazmat cargo 6773 companies and over 1164 thousandvehicles in China alone [3] Due to the potential magnitudeof accidents and the risks associated with incidents involvinghazmat shipments the public is very sensitive to the dangersAs a consequence these risks have attracted considerableattention from governments the public and scholars [4ndash6]Today it has been realized that hazmat transportation riskscan be significantly reduced through the design of bettertransportation networks

Hazmat transportation network design has been increas-ingly studied since 2004 Kara and Verter [7] first con-sidered a hazmat transportation network design problem

using a bilevel integer programming model Erkut and Gzara[8] generalized Kara and Verterrsquos model to an undirectednetwork case Bianco et al [9] proposed a bilevel networkflow model which aimed to minimize total risk and toguarantee risk equity Most of the hazmat network designmodels in previous researches considered the governmentsrsquoand carriersrsquo points of view in trying to mitigate the totalrisk However they ignored the effect of the emergencyresponse services When a hazmat incident occurs effectiveemergency response is crucial for mitigating the undesirableincident consequences [10] That is hazmats transportationrisk may be drastically reduced by designing a transportationnetwork which secures a timely and unobstructed provisionof emergency response services [11] Therefore the goal ofnetwork design is not only to encourage carriers to chooseroutes with a lower risk but also to ensure that the chosenroad is close to emergency response service sites

For hazmat transportation network design risk assess-ment is the basis of the decision making There are two types

2 Mathematical Problems in Engineering

Table 1 Comparison among these network design models for transportation of hazardous materials

Author and year Model Decision maker Objective Main contribution

Kara and Verter 2004 [7]Bi-level integernetwork designmodel

Leader localauthorityFollower carriers

Minimum of total riskMinimum of totalcost

The transportation network design isfirst considered as a bi-level modelThe bi-level model is generalized to theundirected caseErkut and Gzara 2008 [8]

Bi-level undirectednetwork designmodel

Bianco et al 2009 [9] Bi-level networkflow model

Leader metalocalauthorityFollower regionalauthority

Risk equityMinimum of total risk

Multiple layers of authorities and riskequity are first considered

Our paperBi-level uncertainnetwork designmodel

Leader localauthorityFollower 1emergency deptFollower 2 carriers

Minimum of total riskMaximum of coverageMinimum of totalcost

Emergency response and uncertaintyof risk are first considered in networkdesign model

Statement

How to model the network design problem withemergency response and complex fuzzy risk

Section 2

Section 3

Section 6

Section 5

Section 4

Conclusion

Case study

Algorithm

Modelling

How to solve the proposed bilevel model

How to apply the model and algorithm in practiceWhat is the performance of the model and algorithm

Conclusion to the paper and future direction

Why is the problem considered as a bilevel modelHow to model the complex fuzzy transportation risk

Figure 1 The structure of the remainder of this paper

of methods for risk assessment One is called quantitative riskanalysis method [12] such as frequency analysis [13] logicaldiagram-based techniques [14] andmodelling of impact area[1 15]They canworkwell when data is sufficient tomodel therisk However in many cases there are no enough availablehistorical data As a result fuzzy approaches [16ndash18] havebeen used to model the risk In these fuzzy approaches fuzzytheory was often used to model only a single parametersuch as accident probability or accident consequence whichtended to lead to a lack of a comprehensive and uniformdescription for risk uncertainty However transportation riskis a complex uncertain parameter which has much imperfectinformation For example both of the accident consequenceand the accident probability may be fuzzy as a result the risksometimes could be stated as ldquoit is about in the interval [119886 119887]dollarsmilerdquoThis is a complex fuzzy problemwhich containstwo fuzzy factors To deal with such complex fuzzy problema number of complex fuzzy theories have been proposedsuch as type-2 fuzzy sets [19] level-2 fuzzy sets [20] bifuzzyvariable [21] and Fu-Fu variable [22] In this paper a Fu-Fuvariable is used to model the risk

By comparison to previous researches (see Table 1) theeffect of the emergency response service is first considered inthis paperThus here a newmodel for hazmat transportation

network design is presented which considers an emergencyresponse teams location problem In this problem there arethree considered actors the authority the carriers and theemergency response department The government authorityhopes to reduce the hazmats transportation risk by designingan effective transportation network However it must alsoconsider the decisions of the carriers and the emergencyresponse department which are closely involved with thetransportation risk Hence this is considered as a bilevelproblem On the upper level the authority designs thetransportation network On the lower level the carriers andemergency response department select the routes and locatesthe emergency service teams respectively In contrast to priorstudies the uncertainty of transportation risk is also explicitlyconsidered in the mathematical modelThe remainder of thispaper is organized as in Figure 1

2 Problem Statement

Every day around the world large quantities of hazmatsare carried by truck Potential dangers from the hazmatstransportation always concern the general public Thereforegovernmental authorities always seek to take measures to

Mathematical Problems in Engineering 3

The upper level The lower level

Leaderauthority

Road network designdecide whether it is used for hazmatshipment to each road section 119910119894119895

Minimizetotal risk Carriers

Selection of routes on thedesigned network 119909119894119895119896

Minimize total cost

Emergencyservice

department

Location emergencyresponse facility 119911119894 ℎ119894119895

Maximize arc covering

119909119894119895119896

119910119894119895

119909119894119895119896

ℎ119894119895

Figure 2 The abstracted structure of the proposed bilevel hazmat transportation network design problem

reduce and mitigate the risks associated with hazmat trans-portation One tool available to authorities is to design atransportation network that restricts hazmat transport tonominated routes [23] At the same time the emergencyresponse service network is also important inmitigating totaltransportation risk Hence a hazmat transportation networkdesign problem which considers the emergency responseservice is discussed in this paper

21 Bilevel Problem Description In the problem presentedhere three actors are considered government authoritiestransportation carriers and emergency response depart-ments The government authority is often the Traffic andTransport Department Their main concern is to control thehazmat transportation risk that may be caused to the generalpopulation and the environmentThis risk is often dependenton both the choice of transportation routes and the avail-able emergency response network After the authority hasdesigned a transportation network transportation carriersselect transportation routes on this network They tend toselect minimum cost routes rather than those of minimumrisk This choice complicates the hazmat network designproblem since the government authority has to consider theglobal problem by taking into account all shipments thatmay pass through its jurisdictional area (Bianco et al [9])Emergency response departments are often a fire-fightingdepartment a first-aid department a police station or theirunion Though they are all public service departments thereare no leader-follower relationships between the transporta-tion department and the emergency response departmentHence the emergency response department is independentof the transportation department and in charge of thedesign of the emergency response network The responsenetwork can be designed by locating accident service teamsto specified sites near the highest risk linksThis can be solvedvia a maximal arc-covering location model [10]

From the above the three actors can be seen to havea special relationship The government authority hopes tomitigate the transportation risk by designing a new network

They know that the risk is dependent on the carriersrsquo selectedroutes and the designed emergency response network How-ever they do not have the right to impose specific routeson individual carriers or to demand specific service teamslocations on emergency response departments and only havethe authority to close certain roads to hazmat vehiclesTherefore the considered problem can be abstracted as abilevel programming problem as in Figure 2 The decisionmaker on the upper level is the government authority whilethe lower level decision makers are the hazmat carriers andthe emergency response departments

22 Modelling of Uncertain Transportation Risk Hazardousmaterials transportation is an important issue in indus-trialized societies because of the inherent dangers Whatdifferentiates hazmat shipments from shipments of othermaterials is the risk associated with an accidental release ofthese materials during transportation

221 Complex Fuzzy Transportation Risk Most peoplewould agree that risk has to do with the probability and theconsequence of an undesirable event Although some authorsdefine risk as only one of these terms (ie probability orconsequence) it ismore common to define risk as the productof both the probability and consequence of an undesirableevent [24]That is the transportation risk on link (119894 119895) is oftenrepresented as

119903119894119895= 119901

119894119895119862119894119895 (1)

where 119901119894119895is the accident probability on link (119894 119895) and 119862

119894119895is

the accident consequencesBased on this equation Erkut and Verter [1] proposed a

risk model that takes into account the dependency on theimpedances of preceding road segments It fact the aboveequation supposes the existence of the probabilities andconsequences of an accident occurring on a route sectionUsually incident probabilities can be estimated using histor-ical frequencies analysis and the logical diagrams methodsAccident consequences are often modelled as a function of


the impact area and population property and environmentalassets within the impact area Erkut et al [12] summarizedthe frequency analysis methods and consequence model indetail The common characteristic of these methods is thedemand for historicalcharacteristic data However it is oftendifficult to calculate this risk because the precise accidentprobability and the consequence of an accident are not knownas a result of insufficient information An accident probabilityis often determined from evidence recorded in past orexperimental data Unfortunately too many factors impactthe probability of an accident such as the volume of trafficthe air exchange rate the type of hazardous material and thedriversrsquo skill so it is difficult to determine the precise accidentprobability in any given road section from experiments orpast records Therefore most often accident probability isbased on subjective management judgment and it is vaguelyexpressed For example it can be said that ldquothe accidentprobability at X place is about 4 times 10minus5 per milerdquo With thisinformation a fuzzy set can be used to describe the uncertainaccident probability The fuzzy probability results in a fuzzyrisk which can be described as ldquoit is about 4 times 10minus5 times 119862dollarsmilerdquo

Let the fuzzy accident probability119901119894119895be given by a domain

119880119901and 119901

119894119895= (119909 120583

119901119894119895(119909)) | 119909 isin 119880

119901 Then the fuzzy risk

can be given as 119903119894119895 120583

119903119894119895(119901

119894119895119862119894119895) = 120583

119901119894j(119901

119894119895) 119901 isin 119880

119901 where

120583119901119894119895

and 120583119903119894119895are the membership functions of fuzzy accident

probability 119901119894119895and fuzzy transportation risk 119903

119894119895119896 respectively

On the other hand one accident may result in a varietyof impacts which need to be factored into the accidentconsequences such as number of fatalities size of economiclosses damage to road network and the effect on thepopulation Most existing research only looks at the effecton the population In many cases such as in constructionproject transportation all consequences which affect projectcost must be considered However for many consequencesit is difficult to give a precise evaluation Manager prefersto give a statement such as ldquothe cost of the consequenceof an accident is between 1 and 2 million dollars and themost likely value is 15 million dollarsrdquo This is an example ofimprecise information in the decision-making process whichcan be translated into a triangular fuzzy number [1 15 2]million dollars Boulmakoul [17] presented a fuzzy approachwhich uses a fuzzy set tomodel uncertain consequences If weconsider accident probability and consequences at the sametime then the risk can be described as ldquoit is possible that thetransportation risk is [4 6 8] dollarsmilerdquo

Assume we consider 119873 types of fuzzy consequence 119862119899119894119895

withmembership function 120583119899

119894119895

119899 = 1 2 119873Then the riskfor a given 119901

119894119895isin 119880

119901will result in fuzzy values

119903119894119895=

119873

sum119899=1

119862119899

119894119895119901119894119895 119901

119894119895isin 119880

119901(2)

with membership function

120583119903119894119895(

119873

sum119899=1

119862119899

119894119895119901119894119895) = 120583

119901119894119895(119901

119894119895) 119901

119894119895isin 119880

119901 (3)

This is a complex fuzzy variable namely a fuzzy variable withfuzzy parameters also called Fu-Fu variable Therefore thisrisk can be modelled as a Fu-Fu variable which means thatit has fuzzy values and there are corresponding membershipdegrees of the risk taking these fuzzy values Actually thistype of complex fuzzy variables has been applied to someimportant fields such as database modelling [25] inventorymanagement [26 27] and vendor selection [28] By com-parison to these quantitative risk analysis methods involvedin Erkut et al [12] the complex fuzzy variables do need lessempirical or historical data

222 Data Fuzzification Method Often there is little his-torical data to describe the accident probability and con-sequences Hence a complex fuzzy variable is proposed tomodel the risk Here how to obtain the complex fuzzytransportation risk from insufficient data using a fuzzificationmethod is introduced The essence of fuzzification is to findan approximate membership function to describe the fuzzynumber [29]

Transportation risk is made up of accident probabilityand accident consequences In order to determine the mem-bership function of the two types of parameters a fuzzyevaluation method is proposed The fuzzy evaluation hasbeen used in many areas such as performance management[30] and studentsrsquo evaluation [31] With accident probabilityfor example it is difficult to assign a determined value toeach link because there are too many influencing factorsHowever it is easy to evaluate these links for a certainimpact factor using some fuzzy linguistic term such aslow or high So an evaluation term set is first given thensome experts are invited to give fuzzy evaluation for eachimpact factor and generate a fuzzy evaluation matrix Andthen the weight for these impact factors is calculated usinganalytic hierarchy process method By a fuzzy operationthe evaluation matrix and the weight can be integratedinto a set of membership grades of the probability Finallyeach linguistic term for accident probability is modelled asa fuzzy number estimated using historical data and thefinal fuzzy result are calculated by the fuzzy product ofthe menbership grades of the probability and the fuzzynumbers associated with these comment terms For examplean interval [119901min

119901max] can be determined from a historical

frequency analysis Based on this interval five differentsubintervals can be defined to describe five linguistic termsvery low low medium high very high Each interval canbe modelled as a fuzzy number such as triangle or a discretefuzzy number An example is given in Figure 3 In conclusionthe main fuzzification steps for accident probability areshown as follows

Main fuzzification steps for accident probability are asfollows

Step 1 Select 119898 impacts as a set 119880 = 1199061 119906

2 119906

119898 Define

a comment linguistic term set for these impacts of accidentprobability 119881 = very low lowmedium high very high

Step 2 Determine the weight of these impacts using analytichierarchy process method119882 = [119908

1 119908

2 119908

119898]

Mathematical Problems in Engineering 5D

egre

e of m

embe

rshi

p

1Very low Low Medium High Very high

Accident probability

119901min 119901max

Figure 3 The fuzzification of accident probability linguistic terms

Step 3 Calculate the fuzzy relationmatrixΨ = (120595119894119895)119898times119899

120595119894119895=

119899119894119895119899

119894 where 119899

119894is the number of experts invited to nominate

their evaluation to a specific term for impact factor 119894 and 119899119894119895

is the nominated number of linguistic terms 119895 for factor 119894

Step 4 Calculate the linguistic evaluation results 119861 = 119882∘Ψwhere ldquo∘rdquo represents the fuzzy operator

Step 5 Describe these linguistic terms with fuzzy numbers119867119875 = [ℎ119901

1 ℎ119901

2 ℎ119901

119869] and calculate the fuzzy results

119901 = 119861 ∘ 119867119875 where ℎ119901119895is the fuzzy number associated with

comment term V119895 which can be derived from historical data

on accident probabilities

In comparison to accident probability accident conse-quences are more difficult to estimate Usually accident con-sequences are composed of injuries and fatalities propertydamage traffic incident delays and environmental damageSome consequences can be estimated easily according toavailable observation data Taking fatalities as an example itis common to assume that fatality consequences are propor-tional to the size of the population in the neighborhood ofthe considered road link Hence the consequences cost canbe obtained directly through the product of population mor-tality rate and unit cost The proportion and unit cost can beestimated from historical information Other consequencessuch as environmental damage are difficult to estimatefrom observation data For this type of consequences thesame method as accident probability is used to evaluatethe consequence for each link Then the sum of all theseconsequences is the final accident consequence

If the accident probability 119901 is modelled using a discretefuzzy number and the consequence 119862119899 is modelled using atriangular fuzzy number119862119899

119894119895= [119862

119899

119897 119862

119899

119898 119862

119899

119903] then the risk can

be described as119903 = 119901 [119862

119897 119862

119898 119862

119903]

=

[1198621198971199011 119862

1198981199011 119862

1199031199011] with membership

grade of 120583119901(119901

1)

[1198621198971199012 119862

1198981199012 119862


grade of 120583119901(119901

2)

[119862119897119901119899 119862

119898119901119899 119862


grade of 120583119901(119901

119899)

(4)

3 Modelling

The hazmat network design problem is a graph theoreticalproblem defined on a directed graph 119866 = (119881119860) where 119881 isthe set of vertices and119860 is the set of arcs on the graphA vertexcorresponds to a road intersection and an arc corresponds toa road segment on the network The network design prob-lem finds a network to transport 119870 commodities betweentheir respective origins and destinations Each commoditycorresponds to an OD pair Let (119904(119896) 119905(119896)) be the OD pair ofcommodity 119896 119896 isin 1 sdot sdot sdot 119870 and let 119889

119896be the corresponding

number of shipmentsThe parameters 119903119894119895119896

and 119888119894119895119896

refer to therisk and cost associated with a unit flow of commodity 119896 onarc (119894 119895) respectively Each link is assumed to be a networksegment

31 Fu-Fu Variable Considering the lack of historical dataused to describe the accident probability and consequencesthe transportation risks are modelled as Fu-Fu variablesSome basic knowledge about Fu-Fu variable is introduced asfollows

Definition 1 (see [22]) A Fu-Fu variable 120585 is a fuzzy variablewith fuzzy parameters

Example 2 Let 1205851 120585

2 120585

119899be triangular fuzzy number and

let 1205831 120583

2 120583

119899be real numbers in [0 1] such that 120583

1or 120583

2or

sdot sdot sdot or 120583119899= 1 Then

120585 =

1205851with membership 120583

1


2


119899

(5)

is a Fu-Fu variable

Example 3 120585 = (119871 120574 119877) with 120574 sim (120574119871 120574

119872 120574

119877) is called Fu-

Fu variable see Figure 4 if the outer-layer and inner-layermembership functions are as follows

120583120585(119909) =

(119909 minus 119871)

120574 minus 119871 if 119871 le 119909 le 120574

(119877 minus 119909)

119877 minus 120574 if 120574 le 119909 le 119877

0 otherwise

120583120574(119909

1015840) =

(119909 minus 120574119871)

120574119872minus 120574

119871

if 120574119871le 119909 le 120574

119872

(120574119877minus 119909)

120574119877minus 120574

119872

if 120574119872le 119909 le 120574

119877

0 otherwise

(6)

where 120574 is the center of 120585 which is a triangular fuzzy variableand 119871 and 119877 are the smallest possible value and the largestpossible value of 120585 120574

119871 120574

119872 and 120574

119877are the smallest possible

value themost promising value and the largest possible valueof 120574 respectively


120583

120583120585

120574119871 120574119872 120574119877

119871

119877

00

1

1

Figure 4 A triangular Fu-Fu variable

Definition 4 (see [22]) The expected value of a Fu-Fu variableis defined by

119864 [120585] = int+infin

0

Cr 120579 isin Θ | 119864 [120585 (120579)] ge 119903 119889119903

minus int0

minusinfin

Cr 120579 isin Θ | 119864 [120585 (120579)] le 119903 119889119903(7)

provided that at least one of the two integrals is finite

Theorem5 (see [22]) Assume that 120585 and 120578 are Fu-Fu variableswith finite expected values If (i) for each 120579 isin Θ the fuzzyvariables 120585(120579) and 120578(120579) are independent and (ii) 119864[120585(120579)] and119864[120578(120579)] are independent fuzzy variables then for any realnumbers 119886 and 119887 one has

119864 [119886120585 + 119887120578] = 119886119864 [120585] + 119887119864 [120578] (8)

Lemma 6 If transportation risk 119903119894119895119896

is a Fu-Fu variablecharacterized as follows (see Figure 5)

119903119894119895119896=

[1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] with membership

grade of 1205831198941198951198961

[1199031

1198941198951198962 119903

2

1198941198951198962 119903

3

1198941198951198962] with membership

grade of 1205831198941198951198962

[1199031

119894119895119896119899 119903

2

119894119895119896119899 119903

3

119894119895119896119899] with membership

grade of 120583119894119895119896119899

(9)

where [1199031119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898] is a triangular fuzzy number 120583

1198941198951198961

is the degree of membership associated with 119903119894119895119896

taking fuzzyvalue [1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] and 1199031

1198941198951198961 1199032

1198941198951198961 and 1199033

1198941198951198961are the smallest

possible value the most promising value and the largestpossible value of the triangular fuzzy number respectively thenthe expected value of 119903

119894119895119896is

119864 [119903119894119895119896] =1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905 (10)

120583119903(119903)

1

0 6 12 18 24 30 119903

119901

120583(119901 = 5) = 02

120583(119901 = 4) = 06

120583(119901 = 3) = 1120583(119901 = 2) = 06

120583(119901 = 1) = 02

Figure 5 An illustration of Fu-Fu fuzzy risk

where the weights 119908119894119895119896119905 119905 = 1 2 119899 are given by

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898

minusmax119897lt119898le119899

120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(11)

Proof For any 119898 = 1 2 119899 119903119894119895119896(119909

119898) = [119903

1

119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898]

is a triangular fuzzy variable It follows from the definition ofexpected value of fuzzy variable that we have

119864 [119903119894119895119896(119909

119898)] =

1

4(119903

1

119894119895119896119898+ 2119903

2

119894119895119896119898+ 119903

3

119894119895119896119898) (12)

From Definition 4 andTheorem 5

119864 [119903119894119895119896] = 119864 [119864 [119903

119894119895119896 (119909)]]

= 119864 [1

4(119903

1

119894119895119896(119909) + 2119903

2

119894119895119896(119909) + 119903

3

119894119895119896(119909))]

=1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

(13)

Here 119903119904119894119895119896(119909) (119904 = 1 2 3) is a discrete fuzzy variable whose

membership function is given by

120583119903119904

119894119895119896(119909) (120579) =

1205831198941198951198961 if 120579 = 119903119904

1198941198951198961

1205831198941198951198962 if 120579 = 119903119904

1198941198951198962

120583119894119895119896119899 if 120579 = 119903119904

119894119895119896119899

(14)

From the definition of expected value of fuzzy variable wehave

119864 [119903119904

119894119895119896] =

119899

sum119905=1

(119903119904

119894119895119896119905119908119894119895119896119905) 119904 = 1 2 3 (15)


where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)

This completes the proof

32 A Network Design Model The problem the governmentauthority on the upper level faces is how to design atransportation network which minimizes the total risk of theshipments in other words they need to decide whether itis to be used to transport the hazardous materials to eachroad sectionWith this in mind the decision variables for theupper level are 119910

119894119895

In most transport planning models the objective is tomove products from the origins to the destinations at mini-mal cost However for hazmat shipments a cost-minimizingobjective is usually not suitable The risk associated withhazmats means that the problems are more complicated (andmore interesting) than many other transport problems Thetotal risk of the network is the sum of the risks of eachlink The risk of each link is dependent on the number ofshipments the unit risk It also relies on whether it is coveredby emergency response teams An emergency response teamis often made up of various emergency response facilitiesand staffs Many tasks such as fire fighting ambulanceand police services and hazmat containment and clean-up involve the emergency response teams These activitiescan have a positive effect on most accident consequencesHence effective emergency response is crucial to contain theimpact on the smallest possible area andmitigate undesirableconsequences when a hazmat incident occurs [10 11] All ofthese produce an effect on link risk

Hamouda et al [32] developed a risk assessment modelwhich considers emergency responseThey assumed that riskis reduced if a demand nodelink can be responded to by anemergency team Moreover the reduced risk also dependson the type of material transported and the travel distancefrom the accident site to the response team location It isreasonable to assume that the response teams always drive tothe accident sites along a shortest path and let the midpointbe the concentrated point of a road link Then the traveldistance from a response node 119902 to a demand link (119894 119895) canbe described using the shortest distance from the midpoint

of link (119894 119895) to node 119902 that is 119863119902

119894119895 Meanwhile this distance

cannot exceed the maximum service distance 119863max of theemergency response teams Therefore if link (119894 119895) is coveredby node 119902 that is ℎ119902

119894119895= 1 then the reduced risk can be

described as a function of the distance 119863119902

119894119895and 119863max For

convenience it is assumed that the reduced risk and the traveldistance meet a linear relation such as 120572(119863max minus 119863

119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902

119894119895describes the percentage of

reduced risk when link (119894 119895) is covered by emergencyresponse team located in node 119902 120572 is a coefficient related tothe category of undesirable accident consequences and thepower of the emergency response teams 120572119863max reflects themaximum power of the emergency response teams to servicea hazardous accident that is how much the accident conse-quences can be reduced when an accident is serviced by avery timely emergency team The maximum service distance119863max can be obtained from the experience of the emergencyresponse teams The parameter 120572 can be estimated by ananalysis of the category of undesirable accident consequencesand the power of the emergency response teams as outlinedin Figure 6 First the service ability of the emergency teamsshould be evaluated Then the undesirable consequences areclassified and their weights are determined based on theanalysis of past accidents Next for each category of accidentconsequences estimate a possible range of the decrease ifan accident is serviced by a very timely emergency responseteam The median values of these ranges are taken as themost possible values Finally the weight sum of these valuesis determined as the final value of parameter 120572 In fact it isvery difficult to get an accurate value of 120572 because it is alsodependent on the managersrsquo attitude However a sensitivityanalysis on 120572 can assist in the managersrsquo decision makingThus the total uncertain transportation risk can be describedas

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)

In the risk described previously 119903119894119895119896

is a Fu-Fu variable so thetotal risk is also a Fu-Fu variable However it is difficult tomake a decision when it involves uncertain information soit is necessary to transform the Fu-Fu risk to a determinateone In this case the authorities tend to design a networkwith minimal expected risk That is the Fu-Fu risk canbe transformed to a determinate one by an expected valueoperation the expected total transportation risk can bedescribed as follows

Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896

times (1 minus 120572 (119863max minus 119863119902

119894119895) ℎ

119902

119894119895)]

]

(19)


Evaluation of the ability of emergency response teams

Consequences Can be mitigated by an emergency response

How much can bereduced

Weight of theconsequence

Injuries and fatalities

Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899

1199081 + 1199082 + middot middot middot + 119908119899 = 1

120572 = 11990811205721 + 11990821205722 + middot middot middot + 119908119899120572119899

Figure 6 Estimation of the value of 120572

In the expected total risk only 119903119894119895119896

is a Fu-Fu variableBased on Definition 4 andTheorem 5 the expected total riskcan be transformed into following equation

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)

For this objective the variables 119909119894119895119896

and ℎ119894119895are solved in

the lower level model Hence the network design model canbe modelled as follows

min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896

and ℎ119894119895are solved in the

lower-level model

(21)

33 A Network Flow Model The main concern of a govern-ment authority is to minimize the total transportation risk bydesigning a new transportation networkHowever risk is alsoaffected by the carriersrsquo transportation routes and the locationof the emergency response teamsThe hazmat carriers choosetheir routes from the upper-level designednetworkThus thisis a multicommodity network flow assignment problem Tothese carriers the minimization of their total transportationcost is a primary objective which conflicts with that of thegovernment authority as cost is not their primary concernHence the flow model should be considered as a separate

model rather than being merged into the network designmodel Therefore the authority faces a bilevel decisionproblemThat is while designing transportation network theauthority must also consider the actual use of the hazmatnetwork by the carriers and emergency response teams Erkutand Gzara [8] also carried out a comparison analysis toexplainwhy it is better to consider the hazmat network designproblem as a bilevel model

In the model the total cost can be described assum

119870

119896=1sum

(119894119895)isin119860119889119896119888119894119895119896119897119894119895119909119894119895119896 For the flow problem two con-

straints must be met One is the flow equilibrium constraintwhich ensures the flow of commodity 119896 from its origin to itsdestination

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)

The others are the road capacity constraint which ensuresthat only the routes selected by the government can be usedby the carriers and the logic constraint which ensures thatthe variables only take a binary value

119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)


The objective and constraints constitute the routes choicemodel of the carriers as follows

min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)

34 A Maximal Arc-Covering Location Model Usually atransportation network is designed by a local traffic andtransportation department However the location of emer-gency response teams is often chosen by the emergencyresponse departments such as the fire department the first-aid department the police office or their unionThe locationof these emergency response teams plays an important role inmitigating transportation risk so the location is consideredto be a decision on the lower level when designing thetransportation network The emergency response depart-ments decide the teams location based on the road networkdesign and the carriersrsquo chosen routes They hope to coverall the road links so maximizing the total weighted arclength covered is the objective This is a maximal coveringlocation problem for hazardousmaterials transportationThemaximal covering location model was originally developedby Church and ReVelle [33] and was used to locate hazmatresponse teams in [10 32]

Here the weight of link (119894 119895) describes the gain whenlink (119894 119895) is covered by emergency response teams that isthe reduced risk sum

119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The

expected value operation is used to deal with the Fu-Fu risk119903119894119895119896 where ℎ119902

119894119895takes value 1 if (119894 119895) is covered by emergency

response team located at note 119902 and 0 otherwise Then theobjective can be modelled as follows

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)

At the same time two constraints must also be consid-ered First all located teams must be equal to its sum Let119911119902describe whether a team is located in node 119902 and 119891max

describes the total number of located emergency responseteams then the constraint can be stated as follows

sum119902isin119867

119911119902= 119891max (26)

Moreover a link (119894 119895) is covered by node 119902 only if a team islocated at node 119902 then this constraint can be stated as follows

ℎ119902

119894119895le 119911

119902 (27)

Meanwhile in most cases when an accident occurs onlyone nearest emergency response team is arranged to serviceTherefore it is assumed that each link is only serviced by asingle response team

sum119902isin119867

ℎ119902

119894119895le 1 (28)

Finally the maximum travel distance of an emergencyresponse team to any link traversed by hazardous materialswithin its jurisdiction should not exceed the threshold119863maxIt can be described as the following constraint

sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)

From the aforementioned the maximal arc-coveringlocation problem can be modelled as

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max forall (119894 119895) isin 119860

119911119902 ℎ

119902

119894119895isin 0 1

(30)

35 Bilevel Programming Model As outlined in Section 2the considered problem should be modelled as a bilevelprogramming model The decision maker on the upperlevel is the authority who hopes to mitigate the hazmatstransportation risk by designing a new road network Theyknow that the risk is dependent on the carriersrsquo selectedroutes and the designed emergency response network whichthey do not have the right to determine Fortunately they alsoknow that the carriers and the emergency response depart-ment will make decisions based on the designed networkTherefore the authority can consider their decision makingand influence the lower-level model On the lower level thecarriers first choose their routes so that total transportationcost isminimizedThen the emergency response departmentlocates their emergency service teams with the objective ofmaximizing the total weighted arc length covered Hencethe complete bilevel programming model can be establishedbased on the previous discussion as follows

min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)

In this model the Fu-Fu risks have been dealt withusing expected value operation defined in (7) For someespecial types of Fu-Fu variables the expected risk can becalculated directly As for others they can be calculated bysome simulationmethods as introduced in [22] In this paperthe risk [119903

119894119895119896] is modelled as a discrete triangular Fu-Fu

variable (see (9)) and its expected value can be calculated by(10)

4 An Improved ABC Algorithm withPriority-Based Encoding

The proposed model is a bilevel programming model whichis considered an NP-hard [34] problem and is a strong NP-hard problem [35] It is often difficult to obtain an analyticaloptimal solution for such problems and the most commonlyusedmethods are to obtain a numerically optimal solution ora numerically efficient solution using an approximation algo-rithm In addition transportation networks contain numer-ous nodes and links which greatly increase the computingcomplexity In such conditions many heuristic algorithmshave been developed to solve the bilevel programming

problems In this paper an improved artificial bee colonyalgorithm with priority-based encoding is proposed

41 Introduction to ABC Algorithm The artificial bee colony(ABC) algorithm proposed by Karaboga in 2005 for real-parameter optimization is a recently introduced optimiza-tion algorithm which simulates the foraging behaviour of abee colony [36] In the ABC algorithm the position of afood source represents a possible solution to the optimizationproblem and the nectar amount of a food source correspondsto the quality (fitness) of the associated solution The colonyof artificial bees is made up of three groups of bees employedbees onlookers and scouts Half of the colony consists ofemployed artificial bees and the others are composed of theonlookers Each food source has one employed bee After aninitial population (food source positions) each employed beestarts to exploit the discovered source and then returns to thehive with the nectar to onlooker bees Onlooker bees wait inthe hive and decide on a food source to exploit based on theinformation shared by the employed beesThe exploitation ofemployed bees and onlooker bees represents themodificationof solutions In order to find better solution if a source isexhausted (ie the position of the food source has not beenmodified through a predetermined number of cycles) theemployed bee will become a scout to search for a new sourceLike this the population is subjected to a repeat of the cyclesof the search processes of the employed onlooker and scoutbees respectively until the termination criteria are met

The ABC algorithm has been successfully applied tosuch areas as scheduling clustering and engineering designResults have showed that the performance of the ABCalgorithm is better than or similar to other optimizationalgorithms although it uses less control parameters and itcan be efficiently used for solving multivariable and mul-tidimensional optimization problems [37ndash39] The problemconsidered in this paper is a multivariable problem so theABC algorithm was chosen To express the problem moreeffectively and solve themodel more quickly a priority-basedencoding method is also proposed

42 Overall Procedure of the Proposed Algorithm For theproposed algorithm the ABC algorithm is primarily usedto solve the upper-level programming First food sourcepositions are randomly generated and then encoded intothe upper-level road networks Next after solving the lower-level programming using existing methods these sourcesare evaluated Then the neighbourhood is searched and thesources are updated by employed bees onlookers and scoutsrespectively The flow chart of the proposed algorithm isillustrated in Figure 7 and the main procedure is presentedas follows

Main procedure for the proposed ABC algorithm is asfollows

Step 1 Initialize the number of food sources SN the max-imum cycle number MCN and the control parameter forthe abandoned food source limit Let iteration 119905 = 1 For


Begin

Step 1 initialize the food source and parameters

Step 2 encode the positions of food sources into solutions

Step 3 calculate the fitness values and memorize the position of the best food source

The stopping criterion is met

End

Step 41 search the neighborhood by employed bees and conduct a position modification

Step 43 produce new food sources randomly by scouts

Yes

Find abandoned food sources

No

No

Yes

Step 4 update the food sources

Step 42 select food source sites by onlookers with a probability119901119894

Figure 7 The flow chart of the proposed algorithm

119894 = 1 SN generate the position of food source 119865119894and let

the holding trials counter cou119894= 0

Step 2 Encode each food source position 119865119894into the solution

using priority-based encoding method the set of upper-leveldecision variables 119910

119894119895 that is the designed transportation

Step 3 Evaluate each food source site 119865119894by solving the lower-

level flow programming and teams location problemwith theencoded initialization result and calculating the fitness valueof each food source Memorize the position of the best foodsource

Step 4 Update the food sources using employed beesonlookers and scouts respectively

(41) An employed bee produces a modification on thefood source position 119865

119894depending on local informa-

tion and finds a neighbouring food source and thenevaluates its quality using the procedures in Step 2and Step 3 If it represents better than119865

119894 the employed

bee memorizes it as the new position 119865119894

(42) An onlooker bee evaluates the fitness value informa-tion fit

119894of food source 119894 taken from all employed bees

and modifies the food source site with a probability

119901119894related to its fitness value If the position of the

modified food source is better than 119865119894 replace it

(43) Determine an abandoned solution for the scout Ifthe position of food source 119894 is not modified afterthe employed bees and onlooker bees phases its trialscounter cou

119894is increased by 1 otherwise the counter

is reset to 0 Check the counter cou119894 if cou

119894gt limits

replace 119865119894with a new randomly produced position

and reset cou119894to 0

Step 5 If the stopping criterion ismet that is 119905 gt MCN stopOtherwise let 119905 = 119905 + 1 and go to Step 2

43 Food Source Representation and Encoding Method Theproblem here is composed of three nested decision problemsThe outer decision problem is the decision of the government(leader)The leader decides a feasible transportation networkso that each commodity can be transported to the destinationnode from its source node Therefore the feasible solutioncan be given by the set of feasible paths and each pathis associated with a transportation commodity In theseheuristic algorithms for the pathnetwork problem encodingmethods are the focus Priority-based encoding method isone of the most popular methods which has been used with


Begin put in food source 119865119894

for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0

while (119899 lt 119873) doif (120578 = 119905(119896))break

else119869 = 119895 | 119895 isin 119881 and (120578 119895) isin 119860 120574 = argmax

119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while

end forEnd put out the complete path 119875

119896

Algorithm 1 Procedure priority-based encoding

8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority

middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot

Food source 119865119894 = [11986511989411 11986511989412 middot middot middot 1198651198941119873 11986511989421 11986511989422 middot middot middot 1198651198942119873 middot middot middot 1198651198941198701 1198651198941198702 middot middot middot 119865119894119870119873]

Figure 8 An example of food source representation in a network with 10 nodes

PSO [40] and GA [41] Here it is proposed to encode thepaths into a food source

431 Matrix Representation of Food Source In the problema feasible network is made up of several transportation pathsEach path can be first stated as a priority sequence of 1 to119873Hence the position of each food source 119865

119894can be represented

as a matrix with 119870 rows and 119873 columns That is 119865119894= [119865

11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865

119894119896119873] is a priority sequence of 1

to119873 At the beginning of the algorithm all food sources aregenerated randomly Figure 8 illustrates an example of foodsource representation in a network with 10 nodes

432 Encoding Food Source into Transportation NetworkThefood sources can be encoded into a feasible network usinga priority-based encoding method For the path constructionof each commodity the source node 119904(119896) is taken as thefirst node Then there are usually several nodes available(connected with the given node) at each step the one withpriority is chosen into the path and the priority of thechosen node is reset to 0 This process is iterated until thedestination node 119905(119896) is found Take the network in Figure 8as an example and assume that there are three consideredcommodities 1ndash10 2ndash9 and 3ndash8 Then according to thefood source codes (119896 = 1 2 3) three paths can be easilydetermined using the given encoding method 1 rarr 4 rarr

5 rarr 6 rarr 9 rarr 7 rarr 10 2 rarr 4 rarr 7 rarr 9 3 rarr

5 rarr 7 rarr 6 rarr 8 Further the feasible solution can befound 119910

14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)

be the original node and destination node of commodity 119896let 119875

119896record the encoded path of commodity 119896 let 120578 record

the chosen node and let 119883119896(119895) record the priority of node 119895

for commodity 119896 then the detailed encoding procedure is asfollows in Algorithm 1

44 Evaluation of Food Sources In this study the objectivefunction of the upper programming is directly used as thefitness function of each food source At the first step eachfood source is encoded into the solution variables 119910

119894119895 Then

the following equation is used to calculate the fitness value

fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896

and ℎ119894119895are dependent on the lower-

level flow programming and emergency response teamslocationmodel In fact the upper-level solution has defined adesigned network The Dijkstra algorithm is used to find theshortest path for each transportation commodity that is 119909

119894119895119896

is determined After this the ldquobintprogrdquo function inMatlab isused to solve the emergency response teams location model


1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7

Step 1 choose food source119895 randomly

Step 2 choose modified position 119899 randomly 119899 = 4

Step 3 update the priority of chosen position

119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966

Figure 9 An example of neighbourhood search of employed bees

45 Modification of Food Source Position In ABC algorithmthe modification of food source position (ie search fornew solution) consists of three steps First an employed beeproduces a modification of the position of the food source(solution) in her memory depending on local informationNext an onlooker bee evaluates the nectar information takenfrom all employed bees and chooses a food source with aprobability related to its nectar amount Finally the foodsourcewhose nectar is abandoned by the bees is replacedwitha new food source by the scout

451 Employed Bees Phase In the ABC algorithm eachemployed bee is associated with only one food source siteAfter being sent to a food source site each employed beewill produce a modification of the position of the food sourcedepending on local information and find a neighboring foodsource Generally the production of a new food sourceposition is based on a comparison of food source positionsFor each food source a position is randomly chosen andmodified according to a comparison with another foodsource [37]

In the original ABC algorithm each food source was a119863-dimensional vector and the modification is only executedin one dimension of the vector The considered problem isa discrete optimization problem Different from the originalABC algorithm the food sources in the proposed algorithmare represented by a matrix with 119870 rows and 119873 columns(ie 119870 random sequences from 1 to 119873) and each row isa representation of a commodity path In order to producea search with a bigger range each path (ie each row ofthe matrix) should execute a modification otherwise it isvery difficult to find a better food source because of the tinysearch space Moreover since each row is a sequence from1 to 119873 then each position alteration will lead to anothercorresponding position modification Therefore the methoddescribed in previous research cannot be applied to thisproblem In this study in order to produce a modification tofood source position 119865

119894 a food source position 119865

119895(119895 = 119894) is

first randomly chosen Then for every row 119896 a position 119899 isalso randomly determined In succession when the priorityof the chosen position is replaced by one of the same positionsof the food source 119895 that is 119865

119894119896119899= 119865

119895119896119899 the position whose

value is equal to 119865119894119896119899

must be found and its value replaced by119865119894119896119899 Finally the new source position is memorized and the

old one forgotten if its fitness value is smaller An examplewith 10 nodes is illustrated in Figure 9

452 Onlooker Bees Phase After all employed bees completethe search process they share the food source nectar informa-tion (solutions) and their position with the onlooker bees onthe dance area Each onlooker bee evaluates the fitness valuestaken from all employed bees and modifies the food sourcewith a probability119901

119894related to its fitness valueTheprobability

value is calculated using the following expression produces aposition modification

119901119894=

fit119894

sumSN119899=1

fit119899

(33)

where fit119894is the fitness value of the solution 119894 evaluated by the

employed beeAfter that a parameter value is randomly generated

between 0 and 1 If it is smaller than 119901119894 then the onlooker

bee produces a position modification to the food sourceotherwise it chooses the food source from the employed beeIn the employed bees phase the positionmodification is onlyexecuted to a node of one path This is a tiny modificationand leads to a slow convergence speed Hence a greatermodification that is a path modification is proposed in thisphaseThe onlooker first chooses a path 119865

119894119896and another food

source 119895 randomly Then it will replace the path with thesimilar path from another food source that is 119865

119894119896= 119865

119895119896 An

example is given in Figure 10

453 Scout Bees Phase In each cycle after all employed beesand onlooker bees complete their searches the algorithmchecks to see if there is any exhausted food source to beabandoned In order to decide if a source is to be abandoned atrial counter cou

119894is used If the position of food source 119894 is not

modified after the employed bees and onlooker bees phasesits trials counter cou



119894gt limits replace

119865119894with a new randomly produced position and reset cou

119894to 0

Here limits are a predetermined control parameter Since thescouts can accidentally discover rich entirely unknown foodsources they plays the role of fast discovery of the group offeasible solutions

5 Case Study HTND for Shuibuya Project

In this section computational experiments that were carriedout on a real application are presentedThrough an illustrativeexample on the data set adopted from a case study the pro-posed method is validated and the efficiency of the algorithmis tested The data for material requisition transportationcost transportation risk road network and others involvedin the case are from the Shuibuya Hydropower Stationlarge-scale construction project The case is introduced todemonstrate the potential real world applications of theproposed methods


1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

Step 2 update priority sequence of path 119896119865119894

119865119895

Step 1 choose 119896 randomly 119896 = 2

119865119895119896 rArr 119865119894119896

Figure 10 An example of the neighbourhood search for onlooker bees

Gongshanbao borrow area

Heimagou orphan bank

Changtanghe stockpile area

Actual transportsituation

Right bank of the dam

Left bank of the dam

Explosive warehousein the left bank

Explosive warehousein the right bank

The spillway

Sandstone concrete system

Sandstone concrete systemN

Figure 11 The floor plan of the Shuibuya project

51 Presentation of Case Problem The Shuibuya hydropowerproject is located in Badong County in the middle reachesof the Qingjiang River It is the first cascaded project onthe Qingjiang mainstream At 233m tall and containing15640000m3 ofmaterial it is the tallest concrete face rockfilldam in the world This is a large scale project which has acomplex transportation network for construction materialswithin the construction yard In the network large quantitiesof hazardous materials such as explosives are also shippedevery day However there is no specified network for hazmattransportation As a result the project managers and publicin the yard are concerned about the potential risk Thereforeit is necessary to design a hazmat transportation network inthe construction yard In this case the project manager is thedecision maker on the upper level who hopes to mitigate thehazmat transportation risk by designing a new road network

Meanwhile he also considers the decision making of thecarriers and the emergency response department Here theemergency response department is a union of the fire-fightingdepartment the first-aid department and the police station

The transportation network in the project includes aninternal road network and an external road network Inthis case only the internal road network is considered Theinternal road network has 17 preexisting trunk roads and 9temporary roads located on the left and right banks forminga solid network of cycle traffic There is a Cross River bridgeconnecting the left and right banks The actual constructionfloor plan is as in Figure 11 In order to apply the proposedmethods more conveniently adjacent roads of the sametype have been combined and the road shapes have beenignored An abstracted transportation network illustration isin Figure 12The illustration has 37 nodes and 53 links in total


Table 2 Detailed data on the eight transportation commodities

Commodity 119896 1 2 3 4 5 6 7 8Source 119904(119896) No 2 No 2 No 2 No 2 No 2 No 23 No 23 No 23Destination 119905(119896) No 1 No 7 No 9 No 16 No 18 No 25 No 32 No 36119889119896(kg) 600 420 1500 2000 800 420 2000 480

22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River

Figure 12 An abstracted network of the Shuibuya project

and the application of the proposed methodologies does notaffect the result of the case problem

In the network there are two hazardous materials ware-houses (node no 2 and no 23) eight main demand nodes(node no 1 no 7 no 9 no 16 no 18 no 25 no 32 and no36) and eight transportation commodities Detailed data onthe transportation commodities is shown in Table 2

52 Data Collection and Computing Results In this caseall data on the transportation network hazardous material(explosive) and emergency response were obtained from theHubei Qingjiang Shuibuya Project Construction CompanyThe transportation data is shown in Table 3 However therewas no ready-made data on transportation risk In this papertransportation risk is described as a Fu-Fu variable composedof two fuzzy factors fuzzy accident possibility and fuzzyaccident consequences In a construction project an accidentmay lead to various losses such as fatalities damage to roadnetworks and construction facilities project duration delayand social impacts In this paper fatalities project durationdelay and damage to road network and construction facilitiesare considered accident consequences The data fuzzificationmethod outlined in Section 2 is used to obtain the accidentprobability and consequences of fuzzy data Based on thismethod and considering the convenience of use and inter-pretation the probabilities are modelled as discrete fuzzynumbers and the consequences are transformed into costsand modelled as triangle fuzzy numbers Hence the unittransportation risk for each road section is modelled as a

22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River

The roads used to transport hazardous explosivesThe sites selected to locate emergency response teams

Figure 13 The optimal network for the explosives transportation

discrete triangular Fu-Fu number and the detailed data isshown in Table 4

In addition the emergency response department plans tolocate two emergency response teams for potential hazmattransportation accidents while six nodes are optional for thislocation (ie no 7 no 9 no 13 no 23 no 25 and no32) The service range of the emergency response teams is2 kilometers Based on this coverage distance all coveredlinks by each optional location are predetermined Hence theset 119873

119894119895is also determined In order to achieve the maximal

coverage if a link is covered partially then it is divided intotwo links (one is entirely covered and another is not covered)by adding a new node

Using this data after running the computer programfor the improved ABC algorithm using MATLAB 2007 thesolutions for the case problem and the efficiency of theproposed algorithm were obtained

The algorithm and model parameters for the case prob-lem were set as follows the number of the food sourcesSN = 40 the value of limit = 20 the maximum cyclenumber MCN = 200 and the mitigated risk coefficientfor emergency response 120572 = 03 The computer runningenvironment was an Intel Core 2Duo 226GHz clock pulsewith 2048MB memory After 1046 minutes on averagethe optimal solutions for the bilevel programming weredeterminedThe optimal transportation network is shown inFigure 13


Table 3 Data on the road network of Shuibuya hydropower project

Links Nodes Distant(miles)

Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58

The road network without considering emergency responseThe road network considering emergency response

22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River

Figure 14 Difference between the two proposed networks

53 Model Analysis

531 Two Different Networks As discussed the authorityneeds to consider the emergency response network whenthe hazardous materials transportation network is designedbecause an emergency response network has an impact on thetransportation network

In this study a comparison is given for a networkconsidering emergency response and one without regard toemergency response Figure 14 illustrates the two differentnetworks From this it can be seen that there are somedistinct differences between the two networks Links No7 No 8 No 15 No 16 and No 17 would be selected ifemergency response were considered though their unit risksare higher than other links while they would not be includedin the network without considering the emergency responseIn addition there is also a lower risk (80644 thousand CNYand 104906 thousand CNY in the two networks resp) ifthe emergency response is considered when designing thetransportation network Therefore the total transportationrisk is reduced by 2313 due to the existence of emergencyresponse teams

532 Sensitivity Analysis to 120572 In Section 3 it is assumed thatthe risk of link (119894 119895) can be reduced by 120572(119863max minus 119863

119902

119894119895)ℎ

119902

119894119895119903119894119895119896


Table 4 Transportation risk on each road section

Links Transportation risk (CNYkg) Links Transportation risk (CNYkg) Links Transportation risk(6 12 18) 02 (6 9 12) 03 (12 15 18) 03

(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04

Table 5 Sensitivity analysis of parameter 120572

Value of 120572 Total risk Location Road links for hazmat transportation120572 = 000 104906 mdash 1 2 3 5 6 9 10 13 14 18 20 21 23 31 34 35 44 45 48 49120572 = 005 101637 7 32 1 2 3 5 6 9 10 13 14 18 20 21 23 31 34 35 44 45 48 49120572 = 010 98367 7 32 1 2 3 5 6 9 10 13 14 18 20 21 23 31 34 35 44 45 48 49120572 = 015 94917 7 32 1 2 3 5 6 9 10 13 14 18 20 21 23 31 34 35 44 45 48 49120572 = 020 90159 9 32 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 44 45 48 49120572 = 025 85402 9 32 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 44 45 48 49120572 = 030 80644 9 32 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 44 45 48 49120572 = 035 75887 9 32 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 44 45 48 49120572 = 040 71129 9 32 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 44 45 48 49120572 = 045 66319 9 25 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 37 38 42 43 48 49120572 = 050 61234 9 25 1 2 3 5 6 7 8 15 16 17 18 20 21 23 31 34 35 37 38 42 43 48 49

Table 6 Comparisons among the three model types based on therisk-minimizing objective

Type Complex fuzzy type Fuzzy type Determined typeBest result 73668 72022 69836Worst result 85435 90284 93207Average result 80604 83452 84236

if it is covered by an emergency response team located atnode 119902 It is known that the value of parameter 120572 is a keyfactor impacting the results In fact the decision maker isable to adjust the parameter to obtain different solutions Asensitivity analysis is represented in Table 5 From Table 5it can be seen that total risk decreases as the value of 120572increases The designed networks are also related to 120572 Withan adjustment in 120572 three different optimal networks werefound Each optimal network is related to a value range of120572 It shows that the optimal network is not sensitive to 120572 anda range of 120572 is enough for the proposed network designingproblem Hence the authority only needs to determine therange of 120572 when designing the transportation network

533 Uncertainty Analysis In addition uncertainty is alsoan important consideration in this study Fu-Fu variables are

used to model the transportation risk because of the lackof precise data such as the accident probabilities and theaccident consequences on specific roads so the proposedmodel contains a complex fuzzy factor Besides the modelconsidering a Fu-Fu factor there are two other kinds con-sidered one without uncertainty and one that includes onefuzzy factor Truly determinate data does not exist in projectpractice so the managers make decisions from historicalstatistical data and their own experience This factor makesit very difficult to select decision-making data with most ofit obtained by ignoring the uncertainty and using an averagevalue or data chosen at random If only one fuzzy factor isconsidered such as the fuzzy accident consequences thenother uncertain information needs to be ignored such as theaccident probabilitiesThen the accident probabilities have tobe randomly chosen from the given interval All these willlead to an imprecise solution Table 6 shows a comparisonresult of the three model types In the comparison themodel considering a complex fuzzy factor finds differentsolutions by adjusting the optimistic and pessimistic index 120582when the others find different solutions by choosing differenttransportation risk randomly It is clear that the proposedmodel considering the Fu-Fu factors has a much betterperformance than the others not only in the average valueof the results but also in their stability


Table 7 Parameter values used in the experiments

MCN Pop size Limit Weight 119888119901best gt119888119892best 119903crossover 119903mutation

ABC 200 40 20 mdash mdash mdash mdash mdashPSO 200 40 mdash 1 05 08 mdash mdashGA 200 40 mdash mdash mdash mdash 08 005

Table 8 Performance of the proposed ABC PSO GA and ES basedon 50 experiments

Performance ABCalgorithm

PSOalgorithm

GAalgorithm

Enumerationsearch

Accuracy 9547 8799 9645 100FBS 14 5 16 100CPU usage 523 415 684 8362Memory 424 424 424 53FBS Frequency to find best solution Memory required memory space torepresent a solution

54 Algorithm Evaluation In this paper an improved arti-ficial bee colony algorithm with priority-based encoding hasbeen proposed In order to test the efficiency of the algorithma comparison with other solution methods was conducted

The proposed problem is modeled as a linear bilevel pro-gramming model in this paper The most common solutionstrategy for linear bilevel problems is to transform the bilevelmodel into a single one by the use of its Karush-Kuhn-Tucker(KKT) conditions However it is difficult when there arebinary variables in the inner models This also results inthat it cannot be solved by common commercial solvers Intheory it is possible to solve this problem by conducting anenumeration search (ES) over the design variables 119910

119894119895on the

upper level and solving a series of linear programs on thelower level for each selection of design variables Howeverthis search would be conducted 253 times because of the 57binary design variables This is impractical for large-scaleproblems Hence it is not appropriate to solve the problemby KKT conditions and enumeration search in most casesFortunately it is found that the transportation network inthis case can be divided into two subnetworks along theriver because all these hazmats transportation would notgo through the river Moreover some road links such as(1 4) (2 3) (17 20) (18 20) and (36 37) can be determinedby observing the network Therefore the network can bedivided into two networks with 25 and 23 links respectivelyThe problem in the case study can be solved by conducting223+ 2

25 searches In experiments it spends 186 minutesin running the search program Although the solution isoptimal the too long time is not acceptable

In order to show the efficiency of the proposed ABCalgorithm a comparative experiment among the proposedABC algorithm a particle swarm optimization (PSO) agenetic algorithm (GA) and the enumeration search methodwas also conducted In the experiment the same encodingmethod (ie priority-based encoding) was used for the threealgorithms For the GA the partially mapped crossover andlocal search-based mutation method are used For the PSO

820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA

Figure 15 The average convergence curves of the proposed ABCPSO and GA

a hybrid particle-updating mechanism is used in the PSOThe other parameters for the algorithms are shown in Table 7The experiments for the algorithms were carried out over50 times Figure 15 shows the convergence histories for thethree heuristic algorithms The detailed performance of thefour algorithms is stated in Table 8 The results indicate thatthe ABC needs less time than the GA and has a more stabletendency than the PSO Moreover the accuracy of both theABC and the GA is very high even the optimal solutioncan be found with a percentage more than 14 Thereforethe performance of the ABC is on par with that of both thePSO and the GA The proposed algorithm is also useful andefficient for solving the proposed case

6 Conclusion

In this paper a bilevel optimization model for an integratedhazardous materials transportation and emergency responsenetwork design was proposed In the model three decisionswere considered On the upper level the authority (theleader) designs the transportation network with the criterionof minimizing total transportation risk On the lower levelthe carriers and the emergency response department (thefollowers) make their decision based on the leaderrsquos decisionThe carriers first choose their routes so that total trans-portation cost is minimized Then the emergency responsedepartment locates their emergency service teams so as tomaximize the total weighted arc length covered In contrast toprior studies the uncertainties associatedwith transportationrisk were explicitly considered in the objective function ofthe mathematical model Specifically this research uses a Fu-Fu variable to model the transportation risk and an expectedvalue operation is proposed to transform the uncertain riskto a determinate oneThen an improved artificial bee colonyalgorithm was applied to search for the optimal solutionof the bilevel model Finally the efficiency of the proposedmodel and algorithm was evaluated using a practical caseand various computing attributes Two comparisons for themodelwere conducted one looking at three uncertainty types


and the other between the networks taking into considerationthe emergency response and the other without this consid-eration The results show that it is significant to considera network design problem with emergency response in acomplex fuzzy environment The efficiency of the proposedalgorithm was also evaluated by comparing it with the GAthe PSO and the enumeration search method

The area for future research has four aspects Firstlyinvestigate the methods to deal with other types of uncertainrisks for hazmat transportation such as the uncertainty riskincluding fuzzy factor and random factor at the same timeSecondly apply the proposed model and algorithm to morecomplex road network such as an urban traffic networkThirdly develop more efficient heuristic methods to solvesuch bilevel problems Fourthly consider other cases forcontrolling hazmat transportation risk for example only toclose the roads in some time range Each of these areas is veryimportant and equally worthy of attention

Appendices

A Notations for Modelling

A1 Indices

119894119895 The index of node 119894 isin 119881(119894 119895) The index of links (119894 119895) isin 119860119902 The index of located notes 119902 isin 119867119896 The index of transportation commodity

A2 Parameters

119860 The set of all the links119881 The set of all nodes119867 The set of nodes that can locate emergency response

teams119867 sub 119873119889119896 The number of shipments of commodity 119896

119904(119896) The original node of commodity 119896119905(119896) The destination node of commodity 119896119897119894119895 The length of link (119894 119895)

V119894119895 The weight of link (119894 119895)

119901119894119895 The fuzzy accident probability

119862119894119895 The fuzzy undesirable accident consequence119903119894119895119896 The unit distance transportation risk associated witha unit flow of commodity 119896 on link (119894 119895)

119888119894119895119896 The unit distance transportation cost associated witha unit flow of commodity 119896 on link (119894 119895)

120572 The coefficient of risk decrease when link (119894 119895) iscovered by an emergency response team

119863119902

119894119895 The shortest distance from the midpoint of link (119894 119895)to node 119902

Risk The total transportation risk

Cost The total transportation costCover The total weighted arc length covered119891max The total number of located emergency teams119863max The maximum service distance for emergency

response teams

A3 Variables

119910119894119895= 1 if arc (119894 119895) is in the network0 otherwise

119909119894119895119896=

1 if arc (119894 119895) is used by commodity 119896in the optimal network

0 otherwise

119911119894=

1 if a emergency response team islocated at node 119894

0 otherwise

ℎ119902

119894119895=

1 if link (119894 119895) is covered by emergencyresponse team located at node 119902

0 otherwise

(A1)

B Notations for ABC Algorithm

119905 Iteration index 119905 = 1 MCN119894 Food source index 119894 = 1 SN119896 Transportation commodity index 119896 = 1 119870119899 Network node index 119899 = 1 119873

SN Number of food sourcesMCN Maximum cycle numberlimit Control parameter of abandoned food source119865119894 Position of food source 119894

fit119894 Fitness value of food source 119894119901119894 Probability value of food source 119894

cou119894 Trials counter of food source 119894

Acknowledgments

This research was supported by the National Science Founda-tion for the Key Program of NSFC (Grant no 70831005) andldquo985rdquo Program of Sichuan University ldquoInnovative ResearchBase for Economic Development and Managementrdquo

References

[1] E Erkut and V Verter ldquoModeling of transport risk for haz-ardous materialsrdquo Operations Research vol 46 no 5 pp 625ndash642 1998


[2] K G Zografos and K N Androutsopoulos ldquoA heuristic algo-rithm for solving hazardous materials distribution problemsrdquoEuropean Journal of Operational Research vol 152 no 2 pp507ndash519 2004

[3] C Ren and Z Wu ldquoOn route-choice analysis of hazardousmaterials transportationrdquo Journal of Safety and Environmentvol 6 no 2 2006

[4] K N Androutsopoulos and K G Zografos ldquoSolving the bicri-terion routing and scheduling problem for hazardous materialsdistributionrdquo Transportation Research C vol 18 no 5 pp 713ndash726 2010

[5] A Lozano A Munoz L Macıas and J P Antun ldquoHazardousmaterials transportation in Mexico City chlorine and gasolinecasesrdquo Transportation Research C vol 19 no 5 pp 779ndash7892011

[6] M Verma ldquoRailroad transportation of dangerous goods aconditional exposure approach to minimize transport riskrdquoTransportation Research C vol 19 no 5 pp 790ndash802 2011

[7] B Y Kara and V Verter ldquoDesigning a road network forhazardous materials transportationrdquo Transportation Sciencevol 38 no 2 pp 188ndash196 2004

[8] E Erkut and F Gzara ldquoSolving the hazmat transport networkdesign problemrdquo Computers and Operations Research vol 35no 7 pp 2234ndash2247 2008

[9] L Bianco M Caramia and S Giordani ldquoA bilevel flow modelfor hazmat transportation network designrdquo TransportationResearch C vol 17 no 2 pp 175ndash196 2009

[10] O Berman V Verterb and B Karac ldquoDesigning emergencyresponse networks for hazardous materials transportationrdquoComputers and Operations Research vol 34 pp 1374ndash13882007

[11] K G Zografos and K N Androutsopoulos ldquoA decision supportsystem for integrated hazardous materials routing and emer-gency response decisionsrdquo Transportation Research C vol 16no 6 pp 684ndash703 2008

[12] E Erkut S Tjandra and V Verter ldquoHazardousMaterials Trans-portationrdquo inHandbooks of Operation Reserch andManagementScience C Barnhart and G Laporte Eds vol 14 2007

[13] MAbkowitz A Eiger and S Srinivasan ldquoEstimating the releaserates and costs of transporting hazardous wasterdquoTransportationResearch Record pp 22ndash30 1984

[14] R F Boykin R A Freeman and R R Levary ldquoRisk assessmentin a chemical storage facilityrdquoManagement Science vol 30 no4 pp 512ndash517 1984

[15] B Y Kara E Erkut and V Verter ldquoAccurate calculationof hazardous materials transport risksrdquo Operations ResearchLetters vol 31 no 4 pp 285ndash292 2003

[16] S Bonvicini P Leonelli and G Spadoni ldquoRisk analysis ofhazardous materials transportation evaluating uncertainty bymeans of fuzzy logicrdquo Journal of Hazardous Materials vol 62no 1 pp 59ndash74 1998

[17] A Boulmakoul ldquoFuzzy graphs modelling for HazMat telege-omonitoringrdquo European Journal of Operational Research vol175 no 3 pp 1514ndash1525 2006

[18] Y Qiao N Keren and M S Mannan ldquoUtilization of accidentdatabases and fuzzy sets to estimate frequency of HazMattransport accidentsrdquo Journal of Hazardous Materials vol 167no 1ndash3 pp 374ndash382 2009

[19] L A Zadeh ldquoThe concept of a linguistic variable and itsapplication to approximate reasoning Irdquo Information Sciencevol 8 pp 199ndash249 1975

[20] L A Zadeh ldquoQuantitative fuzzy semanticsrdquo Information Sci-ence vol 3 pp 177ndash200 1971

[21] B Liu ldquoToward fuzzy optimization without mathematicalambiguityrdquo Fuzzy Optimization and Decision Making vol 1 no1 pp 43ndash63 2002

[22] J Xu and X Zhou Fuzzy-Like Multiple Objective DecisionMaking Springer 2011

[23] E Erkut and O Alp ldquoDesigning a road network for hazardousmaterials shipmentsrdquoComputersampOperations Research vol 34no 5 pp 1389ndash1405 2007

[24] V T Covello and M W Merkhofer Risk Assessment MethodsApproaches For Assessing Health and Environmental RisksPlenum Press New York NY USA 1993

[25] G de Tre and R de Caluwe ldquoLevel-2 fuzzy sets and theirusefulness in object-oriented database modellingrdquo Fuzzy Setsand Systems vol 140 no 1 pp 29ndash49 2003

[26] Y Liu and J Xu ldquoA class of bifuzzy model and its application tosingle-period inventory problemrdquo World Journal of Modellingand Simulation vol 2 no 2 pp 109ndash118 2006

[27] J Xu and Y Liu ldquoA class of multi-objective inventory modelwith bifuzzy coefficients and its applicationrdquo Dynamics ofContinuous Discrete amp Impulsive Systems B vol 18 no 1 pp77ndash97 2011

[28] J Xu and F Yan ldquoA multi-objective decision making model forthe vendor selection problem in a bifuzzy environmentrdquo ExpertSystems with Applications vol 38 no 8 pp 9684ndash9695 2011

[29] J C Bezdek ldquoFuzzy models what are they and whyrdquo IEEETransactions on Fuzzy Systems vol 1 no 1 pp 1ndash6 1993

[30] S G Chen and Y K Lin ldquoOn performance evaluation ofERP systems with fuzzy mathematicsrdquo Expert Systems withApplications vol 36 no 3 pp 6362ndash6367 2009

[31] R Biswas ldquoAn application of fuzzy sets in studentsrsquo evaluationrdquoFuzzy Sets and Systems vol 74 no 2 pp 187ndash194 1995

[32] G Hamouda F Saccomanno and L Fu ldquoQuantitative riskassessment decision-support model for locating hazardousmaterials teamsrdquo Transportation Research Record no 1873 pp1ndash8 2004

[33] R Church and C ReVelle ldquoThe maximal covering locationproblemrdquo Papers of the Regional Science Association vol 32 no1 pp 101ndash118 1974

[34] O Ben-Ayed and C E Blair ldquoComputational difficulties ofbilevel linear programmingrdquo Operations Research vol 38 no3 pp 556ndash560 1990

[35] P Hansen B Jaumard and G Savard ldquoNew branch-and-boundrules for linear bilevel programmingrdquo Society for Industrial andApplied Mathematics vol 13 no 5 pp 1194ndash1217 1992

[36] D Karaboga ldquoAn idea based on honey bee swarm for numericaloptimizationrdquo Technical Report TR06 ErciyesUniversity Engi-neering Faculty Computer Engineering Department 2005

[37] D Karaboga and B Basturk ldquoA powerful and efficient algo-rithm for numerical function optimization artificial bee colony(ABC) algorithmrdquo Journal of Global Optimization vol 39 no 3pp 459ndash471 2007

[38] D Karaboga and B Basturk ldquoOn the performance of artificialbee colony (ABC) algorithmrdquo Applied Soft Computing Journalvol 8 no 1 pp 687ndash697 2008

[39] D Karaboga and B Akay ldquoA comparative study of artificial Beecolony algorithmrdquo Applied Mathematics and Computation vol214 no 1 pp 108ndash132 2009


[40] A W Mohemmed N C Sahoo and T K Geok ldquoSolvingshortest path problem using particle swarm optimizationrdquoApplied Soft Computing Journal vol 8 no 4 pp 1643ndash16532008

[41] N Selvanathan and W J Tee ldquoA genetic algorithm solution tosolve the shortest path problem in OSPF andMPLSrdquoMalaysianJournal of Computer Science vol 16 no 1 pp 58ndash67 2003

Submit your manuscripts athttpwwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society



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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Table 1 Comparison among these network design models for transportation of hazardous materials

Author and year Model Decision maker Objective Main contribution

Kara and Verter 2004 [7]Bi-level integernetwork designmodel

Leader localauthorityFollower carriers

Minimum of total riskMinimum of totalcost

The transportation network design isfirst considered as a bi-level modelThe bi-level model is generalized to theundirected caseErkut and Gzara 2008 [8]

Bi-level undirectednetwork designmodel

Bianco et al 2009 [9] Bi-level networkflow model

Leader metalocalauthorityFollower regionalauthority

Risk equityMinimum of total risk

Multiple layers of authorities and riskequity are first considered

Our paperBi-level uncertainnetwork designmodel

Leader localauthorityFollower 1emergency deptFollower 2 carriers

Minimum of total riskMaximum of coverageMinimum of totalcost

Emergency response and uncertaintyof risk are first considered in networkdesign model

Statement

How to model the network design problem withemergency response and complex fuzzy risk

Section 2

Section 3

Section 6

Section 5

Section 4

Conclusion

Case study

Algorithm

Modelling

How to solve the proposed bilevel model

How to apply the model and algorithm in practiceWhat is the performance of the model and algorithm

Conclusion to the paper and future direction

Why is the problem considered as a bilevel modelHow to model the complex fuzzy transportation risk

Figure 1 The structure of the remainder of this paper

of methods for risk assessment One is called quantitative riskanalysis method [12] such as frequency analysis [13] logicaldiagram-based techniques [14] andmodelling of impact area[1 15]They canworkwell when data is sufficient tomodel therisk However in many cases there are no enough availablehistorical data As a result fuzzy approaches [16ndash18] havebeen used to model the risk In these fuzzy approaches fuzzytheory was often used to model only a single parametersuch as accident probability or accident consequence whichtended to lead to a lack of a comprehensive and uniformdescription for risk uncertainty However transportation riskis a complex uncertain parameter which has much imperfectinformation For example both of the accident consequenceand the accident probability may be fuzzy as a result the risksometimes could be stated as ldquoit is about in the interval [119886 119887]dollarsmilerdquoThis is a complex fuzzy problemwhich containstwo fuzzy factors To deal with such complex fuzzy problema number of complex fuzzy theories have been proposedsuch as type-2 fuzzy sets [19] level-2 fuzzy sets [20] bifuzzyvariable [21] and Fu-Fu variable [22] In this paper a Fu-Fuvariable is used to model the risk

By comparison to previous researches (see Table 1) theeffect of the emergency response service is first considered inthis paperThus here a newmodel for hazmat transportation

network design is presented which considers an emergencyresponse teams location problem In this problem there arethree considered actors the authority the carriers and theemergency response department The government authorityhopes to reduce the hazmats transportation risk by designingan effective transportation network However it must alsoconsider the decisions of the carriers and the emergencyresponse department which are closely involved with thetransportation risk Hence this is considered as a bilevelproblem On the upper level the authority designs thetransportation network On the lower level the carriers andemergency response department select the routes and locatesthe emergency service teams respectively In contrast to priorstudies the uncertainty of transportation risk is also explicitlyconsidered in the mathematical modelThe remainder of thispaper is organized as in Figure 1

2 Problem Statement

Every day around the world large quantities of hazmatsare carried by truck Potential dangers from the hazmatstransportation always concern the general public Thereforegovernmental authorities always seek to take measures to



Leaderauthority




Minimize total cost

Emergencyservice

department



119909119894119895119896

119910119894119895

119909119894119895119896

ℎ119894119895








119903119894119895= 119901

119894119895119862119894119895 (1)


119894119895is






119880119901and 119901

119894119895= (119909 120583

119901119894119895(119909)) | 119909 isin 119880


can be given as 119903119894119895 120583

119903119894119895(119901

119894119895119862119894119895) = 120583

119901119894j(119901

119894119895) 119901 isin 119880

119901 where

120583119901119894119895



119894119895119896 respectively




119894119895


119894119895isin 119880


119903119894119895=

119873

sum119899=1

119862119899

119894119895119901119894119895 119901

119894119895isin 119880

119901(2)


120583119903119894119895(

119873

sum119899=1

119862119899

119894119895119901119894119895) = 120583

119901119894119895(119901

119894119895) 119901

119894119895isin 119880

119901 (3)








2 119906

119898 Define



1 119908

2 119908

119898]


egre

e of m

embe

rshi

p



119901min 119901max



120595119894119895=

119899119894119895119899

119894 where 119899






1 ℎ119901

2 ℎ119901







119894119895= [119862

119899

119897 119862

119899

119898 119862

119899


be described as119903 = 119901 [119862

119897 119862

119898 119862

119903]

=

[1198621198971199011 119862

1198981199011 119862


grade of 120583119901(119901

1)

[1198621198971199012 119862

1198981199012 119862


grade of 120583119901(119901

2)

[119862119897119901119899 119862

119898119901119899 119862


grade of 120583119901(119901

119899)

(4)

3 Modelling




and 119888119894119895119896




Example 2 Let 1205851 120585

2 120585


let 1205831 120583

2 120583


1or 120583

2or


120585 =


1


2


119899

(5)

is a Fu-Fu variable

Example 3 120585 = (119871 120574 119877) with 120574 sim (120574119871 120574

119872 120574



120583120585(119909) =

(119909 minus 119871)

120574 minus 119871 if 119871 le 119909 le 120574

(119877 minus 119909)

119877 minus 120574 if 120574 le 119909 le 119877

0 otherwise

120583120574(119909

1015840) =

(119909 minus 120574119871)

120574119872minus 120574

119871

if 120574119871le 119909 le 120574

119872

(120574119877minus 119909)

120574119877minus 120574

119872

if 120574119872le 119909 le 120574

119877

0 otherwise

(6)


119871 120574

119872 and 120574




120583

120583120585

120574119871 120574119872 120574119877

119871

119877

00

1

1



119864 [120585] = int+infin

0

Cr 120579 isin Θ | 119864 [120585 (120579)] ge 119903 119889119903

minus int0

minusinfin

Cr 120579 isin Θ | 119864 [120585 (120579)] le 119903 119889119903(7)



119864 [119886120585 + 119887120578] = 119886119864 [120585] + 119887119864 [120578] (8)



119903119894119895119896=

[1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] with membership

grade of 1205831198941198951198961

[1199031

1198941198951198962 119903

2

1198941198951198962 119903

3

1198941198951198962] with membership

grade of 1205831198941198951198962

[1199031

119894119895119896119899 119903

2

119894119895119896119899 119903

3

119894119895119896119899] with membership

grade of 120583119894119895119896119899

(9)

where [1199031119894119895119896119898 119903

2

119894119895119896119898 119903

3


1198941198951198961



1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] and 1199031

1198941198951198961 1199032

1198941198951198961 and 1199033



119894119895119896is

119864 [119903119894119895119896] =1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905 (10)

120583119903(119903)

1

0 6 12 18 24 30 119903

119901

120583(119901 = 5) = 02

120583(119901 = 4) = 06

120583(119901 = 3) = 1120583(119901 = 2) = 06

120583(119901 = 1) = 02



1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(11)

Proof For any 119898 = 1 2 119899 119903119894119895119896(119909

119898) = [119903

1

119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898]


119864 [119903119894119895119896(119909

119898)] =

1

4(119903

1

119894119895119896119898+ 2119903

2

119894119895119896119898+ 119903

3

119894119895119896119898) (12)


119864 [119903119894119895119896] = 119864 [119864 [119903

119894119895119896 (119909)]]

= 119864 [1

4(119903

1

119894119895119896(119909) + 2119903

2

119894119895119896(119909) + 119903

3

119894119895119896(119909))]

=1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

(13)



120583119903119904

119894119895119896(119909) (120579) =

1205831198941198951198961 if 120579 = 119903119904

1198941198951198961

1205831198941198951198962 if 120579 = 119903119904

1198941198951198962

120583119894119895119896119899 if 120579 = 119903119904

119894119895119896119899

(14)


119864 [119903119904

119894119895119896] =

119899

sum119905=1

(119903119904

119894119895119896119905119908119894119895119896119905) 119904 = 1 2 3 (15)


where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)



119894119895








119894119895and 119863max For


119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902



119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)



Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)]

]

(19)







Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Leaderauthority




Minimize total cost

Emergencyservice

department



119909119894119895119896

119910119894119895

119909119894119895119896

ℎ119894119895








119903119894119895= 119901

119894119895119862119894119895 (1)


119894119895is






119880119901and 119901

119894119895= (119909 120583

119901119894119895(119909)) | 119909 isin 119880


can be given as 119903119894119895 120583

119903119894119895(119901

119894119895119862119894119895) = 120583

119901119894j(119901

119894119895) 119901 isin 119880

119901 where

120583119901119894119895



119894119895119896 respectively




119894119895


119894119895isin 119880


119903119894119895=

119873

sum119899=1

119862119899

119894119895119901119894119895 119901

119894119895isin 119880

119901(2)


120583119903119894119895(

119873

sum119899=1

119862119899

119894119895119901119894119895) = 120583

119901119894119895(119901

119894119895) 119901

119894119895isin 119880

119901 (3)








2 119906

119898 Define



1 119908

2 119908

119898]


egre

e of m

embe

rshi

p



119901min 119901max



120595119894119895=

119899119894119895119899

119894 where 119899






1 ℎ119901

2 ℎ119901







119894119895= [119862

119899

119897 119862

119899

119898 119862

119899


be described as119903 = 119901 [119862

119897 119862

119898 119862

119903]

=

[1198621198971199011 119862

1198981199011 119862


grade of 120583119901(119901

1)

[1198621198971199012 119862

1198981199012 119862


grade of 120583119901(119901

2)

[119862119897119901119899 119862

119898119901119899 119862


grade of 120583119901(119901

119899)

(4)

3 Modelling




and 119888119894119895119896




Example 2 Let 1205851 120585

2 120585


let 1205831 120583

2 120583


1or 120583

2or


120585 =


1


2


119899

(5)

is a Fu-Fu variable

Example 3 120585 = (119871 120574 119877) with 120574 sim (120574119871 120574

119872 120574



120583120585(119909) =

(119909 minus 119871)

120574 minus 119871 if 119871 le 119909 le 120574

(119877 minus 119909)

119877 minus 120574 if 120574 le 119909 le 119877

0 otherwise

120583120574(119909

1015840) =

(119909 minus 120574119871)

120574119872minus 120574

119871

if 120574119871le 119909 le 120574

119872

(120574119877minus 119909)

120574119877minus 120574

119872

if 120574119872le 119909 le 120574

119877

0 otherwise

(6)


119871 120574

119872 and 120574




120583

120583120585

120574119871 120574119872 120574119877

119871

119877

00

1

1



119864 [120585] = int+infin

0

Cr 120579 isin Θ | 119864 [120585 (120579)] ge 119903 119889119903

minus int0

minusinfin

Cr 120579 isin Θ | 119864 [120585 (120579)] le 119903 119889119903(7)



119864 [119886120585 + 119887120578] = 119886119864 [120585] + 119887119864 [120578] (8)



119903119894119895119896=

[1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] with membership

grade of 1205831198941198951198961

[1199031

1198941198951198962 119903

2

1198941198951198962 119903

3

1198941198951198962] with membership

grade of 1205831198941198951198962

[1199031

119894119895119896119899 119903

2

119894119895119896119899 119903

3

119894119895119896119899] with membership

grade of 120583119894119895119896119899

(9)

where [1199031119894119895119896119898 119903

2

119894119895119896119898 119903

3


1198941198951198961



1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] and 1199031

1198941198951198961 1199032

1198941198951198961 and 1199033



119894119895119896is

119864 [119903119894119895119896] =1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905 (10)

120583119903(119903)

1

0 6 12 18 24 30 119903

119901

120583(119901 = 5) = 02

120583(119901 = 4) = 06

120583(119901 = 3) = 1120583(119901 = 2) = 06

120583(119901 = 1) = 02



1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(11)

Proof For any 119898 = 1 2 119899 119903119894119895119896(119909

119898) = [119903

1

119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898]


119864 [119903119894119895119896(119909

119898)] =

1

4(119903

1

119894119895119896119898+ 2119903

2

119894119895119896119898+ 119903

3

119894119895119896119898) (12)


119864 [119903119894119895119896] = 119864 [119864 [119903

119894119895119896 (119909)]]

= 119864 [1

4(119903

1

119894119895119896(119909) + 2119903

2

119894119895119896(119909) + 119903

3

119894119895119896(119909))]

=1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

(13)



120583119903119904

119894119895119896(119909) (120579) =

1205831198941198951198961 if 120579 = 119903119904

1198941198951198961

1205831198941198951198962 if 120579 = 119903119904

1198941198951198962

120583119894119895119896119899 if 120579 = 119903119904

119894119895119896119899

(14)


119864 [119903119904

119894119895119896] =

119899

sum119905=1

(119903119904

119894119895119896119905119908119894119895119896119905) 119904 = 1 2 3 (15)


where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)



119894119895








119894119895and 119863max For


119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902



119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)



Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)]

]

(19)







Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119880119901and 119901

119894119895= (119909 120583

119901119894119895(119909)) | 119909 isin 119880


can be given as 119903119894119895 120583

119903119894119895(119901

119894119895119862119894119895) = 120583

119901119894j(119901

119894119895) 119901 isin 119880

119901 where

120583119901119894119895



119894119895119896 respectively




119894119895


119894119895isin 119880


119903119894119895=

119873

sum119899=1

119862119899

119894119895119901119894119895 119901

119894119895isin 119880

119901(2)


120583119903119894119895(

119873

sum119899=1

119862119899

119894119895119901119894119895) = 120583

119901119894119895(119901

119894119895) 119901

119894119895isin 119880

119901 (3)








2 119906

119898 Define



1 119908

2 119908

119898]


egre

e of m

embe

rshi

p



119901min 119901max



120595119894119895=

119899119894119895119899

119894 where 119899






1 ℎ119901

2 ℎ119901







119894119895= [119862

119899

119897 119862

119899

119898 119862

119899


be described as119903 = 119901 [119862

119897 119862

119898 119862

119903]

=

[1198621198971199011 119862

1198981199011 119862


grade of 120583119901(119901

1)

[1198621198971199012 119862

1198981199012 119862


grade of 120583119901(119901

2)

[119862119897119901119899 119862

119898119901119899 119862


grade of 120583119901(119901

119899)

(4)

3 Modelling




and 119888119894119895119896




Example 2 Let 1205851 120585

2 120585


let 1205831 120583

2 120583


1or 120583

2or


120585 =


1


2


119899

(5)

is a Fu-Fu variable

Example 3 120585 = (119871 120574 119877) with 120574 sim (120574119871 120574

119872 120574



120583120585(119909) =

(119909 minus 119871)

120574 minus 119871 if 119871 le 119909 le 120574

(119877 minus 119909)

119877 minus 120574 if 120574 le 119909 le 119877

0 otherwise

120583120574(119909

1015840) =

(119909 minus 120574119871)

120574119872minus 120574

119871

if 120574119871le 119909 le 120574

119872

(120574119877minus 119909)

120574119877minus 120574

119872

if 120574119872le 119909 le 120574

119877

0 otherwise

(6)


119871 120574

119872 and 120574




120583

120583120585

120574119871 120574119872 120574119877

119871

119877

00

1

1



119864 [120585] = int+infin

0

Cr 120579 isin Θ | 119864 [120585 (120579)] ge 119903 119889119903

minus int0

minusinfin

Cr 120579 isin Θ | 119864 [120585 (120579)] le 119903 119889119903(7)



119864 [119886120585 + 119887120578] = 119886119864 [120585] + 119887119864 [120578] (8)



119903119894119895119896=

[1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] with membership

grade of 1205831198941198951198961

[1199031

1198941198951198962 119903

2

1198941198951198962 119903

3

1198941198951198962] with membership

grade of 1205831198941198951198962

[1199031

119894119895119896119899 119903

2

119894119895119896119899 119903

3

119894119895119896119899] with membership

grade of 120583119894119895119896119899

(9)

where [1199031119894119895119896119898 119903

2

119894119895119896119898 119903

3


1198941198951198961



1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] and 1199031

1198941198951198961 1199032

1198941198951198961 and 1199033



119894119895119896is

119864 [119903119894119895119896] =1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905 (10)

120583119903(119903)

1

0 6 12 18 24 30 119903

119901

120583(119901 = 5) = 02

120583(119901 = 4) = 06

120583(119901 = 3) = 1120583(119901 = 2) = 06

120583(119901 = 1) = 02



1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(11)

Proof For any 119898 = 1 2 119899 119903119894119895119896(119909

119898) = [119903

1

119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898]


119864 [119903119894119895119896(119909

119898)] =

1

4(119903

1

119894119895119896119898+ 2119903

2

119894119895119896119898+ 119903

3

119894119895119896119898) (12)


119864 [119903119894119895119896] = 119864 [119864 [119903

119894119895119896 (119909)]]

= 119864 [1

4(119903

1

119894119895119896(119909) + 2119903

2

119894119895119896(119909) + 119903

3

119894119895119896(119909))]

=1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

(13)



120583119903119904

119894119895119896(119909) (120579) =

1205831198941198951198961 if 120579 = 119903119904

1198941198951198961

1205831198941198951198962 if 120579 = 119903119904

1198941198951198962

120583119894119895119896119899 if 120579 = 119903119904

119894119895119896119899

(14)


119864 [119903119904

119894119895119896] =

119899

sum119905=1

(119903119904

119894119895119896119905119908119894119895119896119905) 119904 = 1 2 3 (15)


where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)



119894119895








119894119895and 119863max For


119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902



119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)



Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)]

]

(19)







Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










egre

e of m

embe

rshi

p



119901min 119901max



120595119894119895=

119899119894119895119899

119894 where 119899






1 ℎ119901

2 ℎ119901







119894119895= [119862

119899

119897 119862

119899

119898 119862

119899


be described as119903 = 119901 [119862

119897 119862

119898 119862

119903]

=

[1198621198971199011 119862

1198981199011 119862


grade of 120583119901(119901

1)

[1198621198971199012 119862

1198981199012 119862


grade of 120583119901(119901

2)

[119862119897119901119899 119862

119898119901119899 119862


grade of 120583119901(119901

119899)

(4)

3 Modelling




and 119888119894119895119896




Example 2 Let 1205851 120585

2 120585


let 1205831 120583

2 120583


1or 120583

2or


120585 =


1


2


119899

(5)

is a Fu-Fu variable

Example 3 120585 = (119871 120574 119877) with 120574 sim (120574119871 120574

119872 120574



120583120585(119909) =

(119909 minus 119871)

120574 minus 119871 if 119871 le 119909 le 120574

(119877 minus 119909)

119877 minus 120574 if 120574 le 119909 le 119877

0 otherwise

120583120574(119909

1015840) =

(119909 minus 120574119871)

120574119872minus 120574

119871

if 120574119871le 119909 le 120574

119872

(120574119877minus 119909)

120574119877minus 120574

119872

if 120574119872le 119909 le 120574

119877

0 otherwise

(6)


119871 120574

119872 and 120574




120583

120583120585

120574119871 120574119872 120574119877

119871

119877

00

1

1



119864 [120585] = int+infin

0

Cr 120579 isin Θ | 119864 [120585 (120579)] ge 119903 119889119903

minus int0

minusinfin

Cr 120579 isin Θ | 119864 [120585 (120579)] le 119903 119889119903(7)



119864 [119886120585 + 119887120578] = 119886119864 [120585] + 119887119864 [120578] (8)



119903119894119895119896=

[1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] with membership

grade of 1205831198941198951198961

[1199031

1198941198951198962 119903

2

1198941198951198962 119903

3

1198941198951198962] with membership

grade of 1205831198941198951198962

[1199031

119894119895119896119899 119903

2

119894119895119896119899 119903

3

119894119895119896119899] with membership

grade of 120583119894119895119896119899

(9)

where [1199031119894119895119896119898 119903

2

119894119895119896119898 119903

3


1198941198951198961



1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] and 1199031

1198941198951198961 1199032

1198941198951198961 and 1199033



119894119895119896is

119864 [119903119894119895119896] =1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905 (10)

120583119903(119903)

1

0 6 12 18 24 30 119903

119901

120583(119901 = 5) = 02

120583(119901 = 4) = 06

120583(119901 = 3) = 1120583(119901 = 2) = 06

120583(119901 = 1) = 02



1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(11)

Proof For any 119898 = 1 2 119899 119903119894119895119896(119909

119898) = [119903

1

119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898]


119864 [119903119894119895119896(119909

119898)] =

1

4(119903

1

119894119895119896119898+ 2119903

2

119894119895119896119898+ 119903

3

119894119895119896119898) (12)


119864 [119903119894119895119896] = 119864 [119864 [119903

119894119895119896 (119909)]]

= 119864 [1

4(119903

1

119894119895119896(119909) + 2119903

2

119894119895119896(119909) + 119903

3

119894119895119896(119909))]

=1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

(13)



120583119903119904

119894119895119896(119909) (120579) =

1205831198941198951198961 if 120579 = 119903119904

1198941198951198961

1205831198941198951198962 if 120579 = 119903119904

1198941198951198962

120583119894119895119896119899 if 120579 = 119903119904

119894119895119896119899

(14)


119864 [119903119904

119894119895119896] =

119899

sum119905=1

(119903119904

119894119895119896119905119908119894119895119896119905) 119904 = 1 2 3 (15)


where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)



119894119895








119894119895and 119863max For


119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902



119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)



Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)]

]

(19)







Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










120583

120583120585

120574119871 120574119872 120574119877

119871

119877

00

1

1



119864 [120585] = int+infin

0

Cr 120579 isin Θ | 119864 [120585 (120579)] ge 119903 119889119903

minus int0

minusinfin

Cr 120579 isin Θ | 119864 [120585 (120579)] le 119903 119889119903(7)



119864 [119886120585 + 119887120578] = 119886119864 [120585] + 119887119864 [120578] (8)



119903119894119895119896=

[1199031

1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] with membership

grade of 1205831198941198951198961

[1199031

1198941198951198962 119903

2

1198941198951198962 119903

3

1198941198951198962] with membership

grade of 1205831198941198951198962

[1199031

119894119895119896119899 119903

2

119894119895119896119899 119903

3

119894119895119896119899] with membership

grade of 120583119894119895119896119899

(9)

where [1199031119894119895119896119898 119903

2

119894119895119896119898 119903

3


1198941198951198961



1198941198951198961 119903

2

1198941198951198961 119903

3

1198941198951198961] and 1199031

1198941198951198961 1199032

1198941198951198961 and 1199033



119894119895119896is

119864 [119903119894119895119896] =1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905 (10)

120583119903(119903)

1

0 6 12 18 24 30 119903

119901

120583(119901 = 5) = 02

120583(119901 = 4) = 06

120583(119901 = 3) = 1120583(119901 = 2) = 06

120583(119901 = 1) = 02



1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(11)

Proof For any 119898 = 1 2 119899 119903119894119895119896(119909

119898) = [119903

1

119894119895119896119898 119903

2

119894119895119896119898 119903

3

119894119895119896119898]


119864 [119903119894119895119896(119909

119898)] =

1

4(119903

1

119894119895119896119898+ 2119903

2

119894119895119896119898+ 119903

3

119894119895119896119898) (12)


119864 [119903119894119895119896] = 119864 [119864 [119903

119894119895119896 (119909)]]

= 119864 [1

4(119903

1

119894119895119896(119909) + 2119903

2

119894119895119896(119909) + 119903

3

119894119895119896(119909))]

=1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

(13)



120583119903119904

119894119895119896(119909) (120579) =

1205831198941198951198961 if 120579 = 119903119904

1198941198951198961

1205831198941198951198962 if 120579 = 119903119904

1198941198951198962

120583119894119895119896119899 if 120579 = 119903119904

119894119895119896119899

(14)


119864 [119903119904

119894119895119896] =

119899

sum119905=1

(119903119904

119894119895119896119905119908119894119895119896119905) 119904 = 1 2 3 (15)


where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)



119894119895








119894119895and 119863max For


119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902



119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)



Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)]

]

(19)







Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










where

1199081198941198951198961=1

2(120583

1198941198951198961+ max

1le119898le119899

120583119894119895119896119898minus max

1lt119898le119899

120583119894119895119896119898)

119908119894119895119896119897=1

2(max1le119898le119897

120583119894119895119896119898minus max

1le119898lt119897

120583119894119895119896119898+ max

119897le119898le119899

120583119894119895119896119898


120583119894119895119896119898) 2 le 119897 lt 119899

119908119894119895119896119899=1

2(max1le119898le119899

120583119894119895119896119898minus max

1le119898lt119899

120583119894119895119896119898+ 120583

119894119895119896119899)

(16)

And then

119864 [119903119894119895119896] =1

4(119864 [119903

1

119894119895119896(119909)] + 2119864 [119903

2

119894119895119896(119909)] + 119864 [119903

3

119894119895119896(119909)])

=1

4

119899

sum119905=1

(1199031

119894119895119896119905+ 2119903

2

119894119895119896119905+ 119903

3

119894119895119896119905)119908

119894119895119896119905

(17)



119894119895








119894119895and 119863max For


119902

119894119895)ℎ

119902

119894119895119903119894119895119896

Here 120572(119863max minus 119863119902

119894119895)ℎ

119902



119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896(1 minus 120572 (119863max minus 119863

119902

119894119895) ℎ

119902

119894119895) (18)



Risk = 119864[

[

119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119903119894119895119896119897119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)]

]

(19)







Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















Property damage

Traffic delay

Environment damage

And so on

Y

Y

Y

Y

YN

1205721

1205722

1205723

1205724

120572119899

1199081

1199082

1199083

1199084

119908119899






Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

(20)




min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)

st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

where 119909119894119895119896


lower-level model

(21)




119870

119896=1sum



sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise(22)


119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870 (23)



min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











min119909119894119895119896

Cost =119870

sum119896=1

sum

(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896

=

minus1 119895 = 119904 (119896)

1 119895 = 119905 (119896) forall119895 isin 119881 119896 = 1 2 119870

0 otherwise119909119894119895119896le 119910

119894119895 119909

119894119895119896isin 0 1 forall (119894 119895) isin 119860 119896 = 1 2 119870

(24)



119902isin119867sum

119870

119896=1119889119896119897119894119895120572(119863max minus 119863

119902

119894119895)119903

119894119895119896119909119894119895119896 The




Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572 (119863max minus 119863

119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

(25)



sum119902isin119867

119911119902= 119891max (26)


ℎ119902

119894119895le 119911

119902 (27)


sum119902isin119867

ℎ119902

119894119895le 1 (28)


sum119902isin119867

119863119902

119894119895ℎ119902

119894119895le 119863max (29)


max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896] 119909

119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

(30)


min119910119894119895

Risk =119870

sum119896=1

sum

(119894119895)isin119860

sum119902isin119867

119889119896119864 [119903

119894119895119896] 119897

119894119895119909119894119895119896


119894119895) ℎ

119902

119894119895)


st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










st

119910119894119895= 119910

119895119894 119910

119894119895isin 0 1

max119911119902 ℎ119902

119894119895

Cover = sum

(119894119895)isin119860

sum119902isin119867

119870

sum119896=1

119889119896119897119894119895120572

times (119863max minus 119863119902

119894119895) 119864 [119903

119894119895119896]

times 119909119894119895119896ℎ119902

119894119895

st

sum119902isin119867

119911119902= 119891max

ℎ119902

119894119895le 119911

119902 forall (119894 119895) isin 119860 119902 isin 119867

sum119902isin119867

ℎ119902

119894119895le 1 forall (119894 119895) isin 119860

sum119902isin119867

119863119902

119894119895ℎ119902


119911119902 ℎ

119902

119894119895isin 0 1

min119909119894119895119896

Cost =119870

sum119896=1

sum(119894119895)isin119860

119889119896119888119894119895119896119897119894119895119909119894119895119896

st

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= minus1

119895 = 119904 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 1

119895 = 119905 (119896)

sum

(119894119895)isin119860

119909119894119895119896minus sum

(119894119895)isin119860

119909119895119894119896= 0

119895 = 119904 (119896) 119905 (119896)

119909119894119895119896le 119910

119894119895

119909119894119895119896isin 0 1

(31)













Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Begin





End



Yes


No

No

Yes















119894 the employed










119894gt limits







for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











for 119896 = 1 to 119870let119883

119896= 119865

119894119896 119899 = 0 119875

119896larr 119904(119896) 120578 = 119904(119896)119883

119896(120578) = 0



119895isin119869119883

119894119895 119875

119896larr 119875

119896 120574

119899 = 119899 + 1119883119896(119895) = 0 120578 = 120574

end ifend while


119896


8

64

10

9

1

3

2

75

1 2 3 4 5 6 7 8 9 103 5 1 8 10 9 2 4 6 72 9 3 10 4 1 7 5 8 61 2 5 4 8 10 9 3 6 7

Node119896 = 1

119896 = 2

119896 = 3

119896 = 119870 1199091198941198701 1199091198941198702 1199091198941198703 1199091198941198704 1199091198941198705 1199091198941198706 1199091198941198707 1199091198941198708 1199091198941198709 11990911989411987010

Node priority








11989411

11986511989412 119865

1198941119873 119865

11989421 119865

11989422 119865

1198942119873 119865

1198941198701 119865

1198941198702 119865

119894119870119873] where

each row 119865119894119896= [119865

1198941198961 119865

1198941198962 119865






14= 119910

45= 119910

56= 119910

69= 119910

97= 119910

710= 119910

24=

11991047= 119910

79= 119910

35= 119910

57= 119910

76= 119910

68= 1 Let 119904(119896) 119905(119896)






119894119895 Then


fit =119870

sum119896=1

sum

(119894119895) isin119860

119889119896119864Me(SF (119903

119894119895119896)) 119909

119894119895119896(1 minus 120572ℎ

119894119895) (32)

In the equation 119909119894119895119896



119894119895119896



1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1 6 8 9 5 2 4 10 3 7

1 3 2 8 6 9 4 5 10 7

1 3 2 9 6 8 4 5 10 7




119865119895119896

119865119894119896

119865119894119896

1198651198951198964 rArr 1198651198941198964 1198651198941198964 rArr 1198651198941198966






119895(119895 = 119894) is


119894119896119899= 119865


value is equal to 119865119894119896119899






119901119894=

fit119894

sumSN119899=1

fit119899

(33)







119894119896= 119865

119895119896 An









119894to 0





1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1 3 2 8 6 9 4 5 10 76 2 3 7 10 1 5 4 8 53 6 8 9 5 2 4 7 1 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10

2 3 10 1 5 7 4 8 9 74 2 7 3 10 6 9 1 5 81 5 8 9 4 2 6 7 3 10


119865119895


119865119895119896 rArr 119865119894119896










The spillway










22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River





22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Cost(CNY)

1 1 4 095 522 2 3 076 383 2 4 086 484 3 6 198 955 4 5 098 506 4 7 075 307 5 6 027 128 6 9 087 409 7 8 102 5010 8 9 095 5011 9 10 053 2512 10 16 082 3613 7 11 178 9614 8 13 085 3515 9 13 082 4616 11 12 022 1017 12 13 067 3518 13 14 067 3519 10 14 087 4620 14 15 133 6221 15 16 033 2122 11 17 022 2023 17 18 190 10824 12 18 033 2125 14 19 292 10326 18 19 158 6827 17 20 524 29728 18 20 411 26229 19 33 086 2530 21 22 090 4031 22 23 088 2532 21 24 169 7533 21 26 055 2534 22 26 060 3035 25 26 055 2936 24 25 046 3637 25 29 027 1938 29 30 068 3239 24 28 022 1940 28 29 053 3841 28 30 068 3242 30 31 105 5443 31 32 027 0944 23 27 070 3945 27 32 200 12946 25 27 076 3847 32 33 132 76

Table 3 Continued


Cost(CNY)

48 32 34 200 14849 34 36 156 8650 33 35 036 2151 35 36 222 14652 34 35 081 5753 36 37 086 58


22 23

2

37

16

41

32

30

2524

21

36

19

33

7

188

9

13

1120

14

5

27

34

35

26

3

6

17

10

12

15

31

2928

Qingjiang River


53 Model Analysis




119902

119894119895)ℎ

119902

119894119895119903119894119895119896




(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












(8 16 24) 07 (8 12 16) 07 (16 20 24) 07

1 (10 20 30) 10 2 3 (10 15 20) 10 4 (20 25 30) 10

(12 24 36) 06 (12 18 24) 06 (24 30 36) 06

(14 28 42)03 (14 21 28) 04 (28 35 42) 04

(24 32 40) 02 (48 60 72) 03 (8 12 16) 03

(30 40 50) 07 (56 70 84) 07 (10 15 20) 07

5 6 (36 48 60) 10 7 8 (64 80 96) 10 9 (12 18 24) 10

(42 56 70) 06 (72 90 108) 06 (14 21 28) 06

(48 64 80) 03 (80 100 120) 04 (16 24 32) 04

(8 12 16) 03 (80 90 100) 03 (8 10 12) 03

(10 15 20) 07 (96 108 120) 07 (12 15 18) 07

10 (12 18 24) 10 11 12 (112 126 140) 10 13 (16 20 24) 10

(14 21 28) 06 (128 144 160) 06 (20 25 30) 06

(16 24 32) 04 (144 162 180) 04 (24 30 36) 04

(8 10 12) 03 (8 10 12) 03 (12 15 18) 03

(12 15 18) 07 (12 15 18) 07 (16 20 24) 07

14 (16 20 24) 10 15 (16 20 24) 10 16 17 (20 25 30) 10

(20 25 30) 06 (20 25 30) 06 (24 30 36) 06

(24 30 36) 04 (24 30 36) 04 (28 35 42) 04

(12 15 18) 03 (24 32 40) 02 (12 15 18) 03

(16 20 24) 07 (30 40 50) 07 (16 20 24) 07

18 19 (20 25 30) 10 20 21 (36 48 60) 10 22 23 (20 25 30) 10

(24 30 36) 06 (42 56 70) 06 (24 30 36) 06

(28 35 42) 04 (48 64 80) 03 (28 35 42) 04

(12 15 18) 03 (18 21 24) 03 (12 15 18) 03

(16 20 24) 07 (24 28 32) 07 (16 20 24) 07

24 25 (20 25 30) 10 26 (30 35 40) 10 27 28 (20 25 30) 10

(24 30 36) 06 (36 42 48) 06 (24 30 36) 06

(28 35 42) 04 (42 49 56) 04 (28 35 42) 04

(6 12 18) 02 (12 15 18) 03 (6 9 12) 03

(8 16 24) 07 (16 20 24) 07 (8 12 16) 07

29 (10 20 30) 10 30 33 (20 25 30) 10 31 (10 15 20) 10

(12 24 36) 06 (24 30 36) 06 (12 18 24) 06

(14 28 42) 03 (28 35 42) 04 (14 21 28) 04

(6 9 12) 03 (6 12 18) 02 (6 12 18) 02

(8 12 16) 07 (8 16 24) 07 (8 16 24) 07

32 (10 15 20) 10 34 35 (10 20 30) 10 36 40 (10 20 30) 10

(12 18 24) 06 (12 24 36) 06 (12 24 36) 06

(14 21 28) 04 (14 28 42) 03 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03 (6 12 18) 02

(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

37 38 (20 25 30) 10 39 41 (10 15 20) 10 42 43 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03


Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table 4 Continued


(16 20 24) 07 (8 12 16) 07 (8 16 24) 07

44ndash46 (20 25 30) 10 47 (10 15 20) 10 48 49 (10 20 30) 10

(24 30 36) 06 (12 18 24) 06 (12 24 36) 06

(28 35 42) 04 (14 21 28) 04 (14 28 42) 03

(12 15 18) 03 (6 9 12) 03

(16 20 24) 07 (8 12 16) 07

50 51 (20 25 30) 10 52 53 (10 15 20) 10

(24 30 36) 06 (12 18 24) 06

(28 35 42) 04 (14 21 28) 04














PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















PSOalgorithm

GAalgorithm

Enumerationsearch




119894119895on the




820

870

920

970

1020

1070

1120

1170

1 14 27 40 53 66 79 92 105

118

131

144

157

170

183

196

ABCPSO

GA



6 Conclusion





Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Appendices


A1 Indices


A2 Parameters









119863119902




response teams

A3 Variables


119909119894119895119896=


0 otherwise

119911119894=


0 otherwise

ℎ119902

119894119895=


0 otherwise

(A1)






Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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