research article modeling and optimization of multiple...

Research ArticleModeling and Optimization of Multiple Unmanned AerialVehicles System Architecture Alternatives

Dongliang Qin Zhifei Li Feng Yang Weiping Wang and Lei He

College of Information System and Management National University of Defense Technology Changsha Hunan 410073 China

Correspondence should be addressed to Dongliang Qin qindongliangnudthotmailcom

Received 17 April 2014 Accepted 24 June 2014 Published 20 July 2014

Academic Editor Manoj Jha

Copyright copy 2014 Dongliang Qin et alThis 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

Unmanned aerial vehicle (UAV) systems have already been used in civilian activities although very limitedly Confronted differenttypes of tasksmulti UAVs usually need to be coordinatedThis can be extracted as amulti UAVs system architecture problem Basedon the general system architecture problem a specific description of themulti UAVs system architecture problem is presentedThenthe corresponding optimization problem and an efficient genetic algorithm with a refined crossover operator (GA-RX) is proposedto accomplish the architecting process iteratively in the rest of this paper The availability and effectiveness of overall method isvalidated using 2 simulations based on 2 different scenarios

1 Introduction

Unmanned aerial vehicle (UAV) systems which were devel-oped for military purpose originally are currently in limiteduse for public servicemissionsworldwideUAVsystems comein all sizes and although most are for military applicationsthey have already been used in civilian activities They canoperate in areas where it would be irresponsible to expectpilots to fly for example low level night flights over theArctic Ocean flights over regions where there is low levelstrife Here the disaster management supported by UAVsis taken for demonstrating UAV systems have potentialto augment the effectiveness of disaster response dramat-ically based on their excellent performance in dull dirtyor dangerous environment Disaster relief and emergencyresponse missions could be a fifth category in the civil uses ofUAVs systems [1] they are expected to be ldquoforce multipliersrdquoin disaster response just as in achieving military missionsDisaster response consists of various types of tasks that iswarningevacuation search and rescue providing immediateassistance assessing damage continuing assistance and theimmediate restoration of infrastructure Huge differenceexists between different tasks in the degree of urgency anddifficulty The effectiveness of disaster response depends onthe coordination of these tasks

Studies on UAVs for disaster monitoring have beenconducted by several researchers [2 3] Also some problemsrelated to multiplatforms (UAVs included) collaborative dis-asters monitoring have conducted by BAI GuoQing [4 5]

In this paper we focus on the modeling and optimizationof multiple UAVs system architecture to maximize missionperformance Driven by the tasks to be conducted in givenmission the UAVs system architecture model can be treatedas a solution of corresponding task assignment problem

2 Architecture and Architecting

The first researcher to formalize the concept of ldquosystemsarchitectingrdquo is Rechtin and his book with Maier is the bestintroduction to this field [6] More formally Crawley definesarchitecture as ldquoan abstract description of the entities of asystem and the relationships between those entitiesrdquo How-ever a more precise definition is given by Crawley in MITEngineering SystemsDivision as follows ldquothe embodiment ofa concept the allocation of physicalinformational functionto elements of form and the definition of interfaces amongthe elements and with the surrounding context [7]rdquo Thisprecise definition can be expressed briefly as function-to-form mapping where the function executed by the different

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 189679 8 pageshttpdxdoiorg1011552014189679

2 The Scientific World Journal

13

2

4 5

6 7

1

3

2

4

5

7

6

A

B

C

D

E

F

G

Figure 1 System architecture process

subsystems and the form is the relationship among themThe allocation of physical or informational elements offunction into elements of form is one of the earliest andmost important architectural decisions that have to be madeThe concept of system architecture can be illustrated as inFigure 1There are 7 different subsystems for architecting andevery subsystem can execute certain function It is supposedthat there are two alternatives to be selected The function-to-form mapping of left alternative is A 1 2 and 3 B 4 5C 6 7 Function 1 function 2 and function 3 are mappingto form A function 4 and function 5 are mapping to formB function 6 and function 7 are mapping to form C Themission can be accomplished by the combination of form Aform B and formCThe right alternative is another function-to-form mapping which can also accomplish the missionThen the problem is which alternative to be selected as theultimate architecture The selecting process is usually basedon the mission performanceThis is the essence of the systemarchitecting

The system architecture can be comprehended in twoaspects Firstly it should tell us ldquowhat the system isrdquo or the setof tangible elements that the system is composed of Secondlyit should tell us ldquowhat the system doesrdquo in order to providevalue to the stakeholders System architecting is the processof creating system architecture

The system architecting process can essentially be seenas a decision making process where the decisions to makeconcern the description of the entities of the system as wellas the relationships between them [8] This decision makingprocess can be supported by efficient optimization methodproposed later in this paper

3 Multiple UAVs System Architecture

Based on the basic definition of system architecture thedescription of multiple UAVs system architecture can begivenThe process model for multiple UAVs system architec-ture is presented in Figure 2

It can be extracted from the basic system architecturetheory that the first step is identifying the stakeholder needsThe architecture of multiple UAVs system is designed toaccomplish the value delivery loop based on the stakeholderneeds which is maximizing the mission performance given

Stakeholder needs

General objectives

Specific objectives

Tasks needed Tasks and UAVsdata products

The assignment plan

The executive details

The ultimate architecture

Satisfy

Satisfy

Satisfy

Figure 2 Architecture model for multi-UAVs system

Then the second step is identifying how the multi-UAVsmaximize the mission performance This is the issue in themission level The embodiment of this is maximizing theprobability of accomplishing all the tasks necessary effec-tively In order to reach this goal the suitable UAVs shouldbe chosen firstly This answers ldquowhat the system isrdquoThen theUAVs and the tasks are modelled as an asymmetric bipartitegraph which represents the assignment relationship betweenUAVs and tasks The selecting and assignment process isthe embodiment of system architecting in the context ofmaximizing the mission performance

What is the architect trying to achieve What makes anarchitecture ldquogoodrdquo To answer this question a process isneeded for selecting architectures that are not only capableof accomplishing the demand tasks but are also effectivein terms of their overall value acquired The quality of theproposed architecture is evaluated according to some criteriawhich is the overall value acquired by the UAVs throughconducting the tasks in this paper It is inevitable for architectthat the selecting and assigning should be done iterativelyThe system architecting problem of multi-UAVs can beformulated as a constrained combinatorial optimizationproblem For example these problems can be formulatedas generalized assignment problems quadratic assignmentproblems or their expansions As excellent population-basedsearch algorithms evolutionary algorithms (eg geneticalgorithms particle swarm optimization) can be chosen tosolve these multi-UAVs system architecting problems Thegeneral process of solving multi-UAVs system architectingproblems employing evolutionary algorithms is presented inFigure 3 An optimization problem and an efficient geneticalgorithm with a refined crossover operator (GA-RX) areproposed to accomplish the architecting process iteratively inthe rest of this paper

The Scientific World Journal 3

Start

Create initial population

Termination criteria

Evaluate architectures in

population

Select architectures for new population

Generate new population

Select preferred architectures fromthe last population

End

Figure 3 The general evolutionary process

4 Problem Formulation

41 Notations

119872 Number of available UAVs

119881 = 1198801 1198802 119880

119872 Set of all available UAVs

119873 Number of tasks needed in mission

119879 = 1198791 1198792 119879

119873 Set of all tasks

119870 Number of assets needed to be protected

119866119896 The set of tasks aimed for asset 119896 119896 = 1 2 119870

119899119896 Number of tasks aimed for asset 119896 (ie |119866

119896|) 119896 =

1 2 119870

119882 = [11988211198822 119882

119870] Value vector of assets where

119882119896is the value of asset 119896

119875 = [119901119894119895]119873times119872

The probability that UAV 119895 accomplishtask 119894

120587119894 The damage probability of the asset if the required

tasks are not accomplished

The decision variables will be denoted by 119883 = [119909119894119895]119873times119872

119909119894119895

=

1 if UAV 119895 assigned to task 119894

0 otherwise(1)

42 Objective Function and Constraints

Objective Function The probability of that task 119894 is accom-plished is given as follows

1 minus

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895

(2)

Therefore the probability that asset 119896 is protected success-fully that is without being attacked by all targets is given by

prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(3)

Hence the objective function is given by

119869 =

119870

sum

119896=1

119882119896prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(4)

Constraints The constraint in this problem is due to the factthat each UAV can be assigned to only one target becauseof the emergent property of the mission The constraint isrepresented as follows

119873

sum

119894=1

119909119894119895

= 1 119895 = 1 2 119872 (5)

43 Overall Problem Representation Themultiple UAVs sys-tem architecting problem can be stated as

Max119909119894119895isin01

119869 =

119870

sum

119896=1

119882119896prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(6)

subject to sum119873

119894=1119909119894119895

= 1 119895 = 1 2 119872

5 Optimization Algorithm Design

51 General GA Evolutionary algorithms (EAs) inspired byDarwinian principles of evolution are global stochastic searchmethods simulating the evolution process in nature Amongthe EAs GAs are most popular GAs were introduced byHolland [9] and were applied to many practical problemsby Goldberg [10] GAs are of high availability becausethe properties such as differentiability and continuity arenot necessary On the other hand GAs are population-based optimization methods which guarantee GAs effectiveapproaches in searching for the global optimumThe generalGA is shown in Pseudocode 1 where119875(119905) and119862(119905) are parentsand offspring in generation 119905

52 Population Representation (Encoding) and InitializationGenetic algorithmsworkwith a number of potential solutionsthat are defined by a genotype representation accordingto the real solutions for certain problem Encoding is theprocess of transformation fromphenotype (in solution space)


Procedure GAbegin

119905 = 0initialize 119875(119905)evaluate 119875(119905)while not finished do

begin119905 = 119905 + 1select 119875(119905) from 119875(119905 minus 1)reproduce pairs in 119875(119905)evaluate 119875(119905)

endend

Pseudocode 1 Pseudocode for GA

to genotype (in search space handled by GAs) decodingvice versa The notion of real-valued genetic algorithms hasbeen offered but is really a misnomer because it does notreally represent the building block theory that was proposedby John Henry Holland in the 1970s So we chose binaryrepresentation in this paper

From the formulation given in problem formulation wecan extract the original formulation of the solution as follows

Solution = (

11990911

sdot sdot sdot 1199091119872

d

1199091198731

sdot sdot sdot 119909119873119872

)

119909119894119895

= 1 if UAV 119895 assigned to task 119894

0 otherwise

(7)

In any column (1199091119895

1199092119895

119909119873119895

)119879 the sole task assigned

to the UAV 119895 can be identified The index of task assigned toUAV 119895 is the 119895th bit of the interim integer string Then everybit of the interim integer string is transformed to its binaryform An example is given as follows

Assume there are 5 UAVs and 3 tasks and the originalmatrix 119883 is

(

1 0 1 0 0

0 1 0 0 1

0 0 0 1 0

) (8)

Its interim integer string is (1 2 1 3 2) Then the binaryform which is called genotype is (01 10 01 11 10)

The merit of this representation is embodied as follows(1) The constraint is eliminated so it need not be handledadditionally (2) According to schema theory binary repre-sentation is more beneficial to the growth of useful schematawhich in turn enhances convergence rates

Having decided on the representation the first step inthe GA-RX is to create an initial population We will adoptthe method which is most usually achieved by generatingthe required number of individuals using a random numbergenerator that uniformly distributes numbers in the desiredrange

53 Genetic Operators Setup In Pseudocode 1 it can be seenthat the genetic operators included in GAs are SelectionOperator Crossover Operator and Mutation Operator Inthis paper a refined crossover operator is proposed while forthe other genetic operators the setup is as follows

The desire for efficient selection methods is motivated bythe need to maintain GAs overall time complexity In thispaper the classical roulette wheel selection method basedoperator is selected because it provides zero bias and thespread is lower bounded

In natural evolution mutation is a random process whereone allele of a gene is replaced by another to produce a newgenetic structure Binarymutation operator is selected for thereason that binary representation is selected

A refined crossover operator will be introduced in thenext section

6 A Refined Crossover Operator

61 Origination Crossover is the basic operator for pro-ducing new individuals in the GAs and it is the mostsignificant factor as for the effectiveness of certain GA Intraditional GAs the crossover operator is executed betweentwo individuals randomly extracted from 119875(119905) who areselected from 119875(119905 minus 1) using the selection operator (roulettewheel selection method based operator in this paper) Moreresearch is focused on the pattern of crossover while littleconcerns the rules guiding the selecting of target individualto be operated

Like its counterpart (marriage) in nature in the process ofcrossover an individual in the current 119875(119905) always tends to bepaired with another individual which is good enough ldquoGoodenoughrdquo means the fitness of the partner selected is largeenough It would be best if its partnerrsquos fitness is the largestThis trend in the crossover can be easily comprehended usingthe mate selection of human

62 Modeling and the Result Rule Suppose that an individualin the current119875(119905) observes a sequence of 119899 individuals whosefitness values are known This individual who observes is theso-called administrator The administrator has two choicesfor each randomly selected individual accept or reject forcrossover (like marriage) Once an individual is selected thecrossover will be executed between these two individualsand the next individual as the individual that will be selectedarrives randomly the administrator can rank the applicantamong all the individuals that arrived so far However pleasenote that the administrator cannot select an individual thathas not arrived yet even this individual has a high fitnessThequestion for the administrator individual is to discover therule which can maximize the probability of selecting the bestindividual to execute crossover This optimal policy problemhas a strikingly elegant solution given by Vanderbei [11] Theoptimal policy for the problem is a stopping rule Under itthe administrator individual rejects the first 119903 minus 1 applicants(let applicant 119872 be the best applicant among these 119903 minus 1

applicants) and then selects the first subsequent applicant thatis better than applicant 119872 It can be shown that the optimal


0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

4000

Results distribution indexed by fitness ranking

Tim

es

The results under 1e-law

Figure 4 Simulation results

strategy lies in this class of strategies For an arbitrary cutoff119903 the probability that the best applicant is selected is

119875 (119896) =

119873

sum

119894=119896+1

1

119873times

119896

119894 minus 1=

119896

119873

119873

sum

119894=119896+1

1

119894 minus 1 (9)

Letting 119899 tend to infinity the limit of 119903119899 is denotedby 119909 and using 119905 for 119894119899 and 119889119905 for 1119899 the sum can beapproximated by the integral

119875 (119896) = 119909int

1

119909

1

119905119889119905 = minus119909 ln119909 (10)

Taking the differential coefficient of 119875(119909) with respect to119909 setting it to 0 By solving this equation we can find thatthe optimal 119909 is equal to 1119890 Thus the optimal cutoff tendsto 119899119890 (119890 asymp 2718) as 119899 increases and the best applicant isselected with probability 1119890 (37)

63 Monte Carlo Simulation of the 1119890-Law Monte Carloexperiment can be used to verify the effectiveness of the 1119890-law The parameter settings of the Monte Carlo experimentare as follows

(1) The size of the applicant pool for selection 119899 is set to20

(2) Computational times required are set to 10000

The result is shown in Figure 4 the horizontal axis is thefitness ranking of individuals (as applicants in 1119890-lawmodel)and the vertical axis is the statistical times (the total is 10000)

It can be seen that the best individual is selected withnearly 4000 times out of 10000 times far more than otherindividuals This shows the effectiveness of the 1119890-law inselection of best individual

64 Refined Crossover Operator Based on 1119890-Law Crossoveroperators used by the traditional genetic algorithm are com-mon in selecting strategy The parents are selected randomly

Procedure of RX operatorInput 119875(119905)

Output 119862(119905)

Parameters(1) NINDmdashNumber of individuals(2) 119899mdashthe number of individuals expected arrivingBegin

Rank 119875(119905) based on fitnessfor 119901 isin 119875(119905)if not finished

for 119902 isin 119875 (119905) and 119902 = 119901generate a rand number in1simNINDif the rand number less than 119899119890

mark the largest fitness as 119872else

if fitness of 119902 is larger than 119872Crossover generates childrenSet the child owning largerfitness as 119901

1015840break

Add 1199011015840to 119862(119905)

End

Pseudocode 2 Pseudocode for RX Operator

while in our novel algorithm an effective selecting strategybased on the 1119890-law is employed by the refined crossoveroperator Firstly the individuals produced by the selectionprocess are ranked depending on their fitness values Thenletting the first individual from the ranked population be theadministrator a sequence of up to 119899 individuals is chosenrandomly The administrator rejects the first 37 individuals(let individual 119883 be the best individual among these 37individuals whose fitness value is the largest in the first 37individuals) and then selects the first subsequent individualthat is better than individual 119883

The two mating chromosomes owned by the admin-istrator individual and selected individual are cut once atcorresponding points and the sections after the cuts wereexchanged Here a cross-site or crossover point is selectedrandomly along the length of the mated strings and bitsnext to the cross-sites are exchanged A better solutioncan be obtained by combining good parents A randomrecombination usually produce low quality solutions

The pseudocode of RX operator is listed in Pseudocode 2and the overall process of GA-RX is presented in Figure 5

7 Simulations Results and Analysis

Two groups of simulations are executed and two scenariosare considered

71 Case Description Two different scenarios are consideredThe first scenario considers a simple situation which contains20 UAVs 16 tasks and 10 assets (which are to be protected)The second scenario consists of data for 100 UAVs 80tasks and 60 assets to be protected which is considered as


Overall GA-RX

Generate an initial population randomly

Calculate the fitness value of each individual in the population

The convergencecondition is met

Perform selection operator on current population

Refined crossover operator

Rank population(t) based on fitness

Let p be the first individual of population

Mark the largest fitness as M

The rand number less than ne

Yes

Fitness of q is larger than M

No

p is the last individual

Let q be the next individual of population

p and q are the same

No

No

Yes

Crossover generates childrenLet p be next individual

Yes

Perform mutation operator on the new population generated by RX operator

No

Yes

set t = 0

Set t = t + 1 and let P(t + 1) = C(t)

Add p998400 to C(t)

Generate a rand number within the range of (1 NIND)

Let p998400 be the first child owning a larger fitness than M

Figure 5 The overall process of GA-RX

UAVs

UAV-1 UAV-2 UAV-20

Assets

Asset 1 Asset 2 Asset 10

Task 1 Task 2 Task 16

Map

ping

middot middot middot



[W1W2 middot middot middotW10]

[pij]20lowast 16

Figure 6 Scenario 1

a complicated case formost of the state-of-the-art algorithmsFor both scenarios the following parameters are randomlygenerated which are the value vector of assets (119882) theprobability matrix (119875 = [119901

119894119895]119873times119872

) and the damage proba-bility (120587

119894) Both scenarios can be illustrated by Figure 6 For

Scenario 1 the search space is 24times20 A general evolutionary

algorithm (eg GA PSO ACO and DE) is sufficient to copewith such problems However for Scenario 2 the searchspace is significantly increased that is 27times100 Intuitively an

advanced genetic operator is required such that the algorithmeffectiveness and search efficiency can be improved whensolving this system architecting problem

The main reason for generating these data randomly isas follows to the best of the authorsrsquo knowledge there is nobenchmark problem in the domain of system architectureoptimization Different studies employ different scenariosobjectives and function formulations In order to avoid biason selected datasets and verify the effectiveness and efficiency


0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue

Scenario 1 20 UAVs 16 tasks and 10 assets

GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue


Figure 7 Typical results of simulation 2

Table 1 The 119905-test result of Simulation 2

ScenarioAlgorithm

GA CLPSO DE ACO GA-RXMeanSTD MeanSTD MeanSTD MeanSTD MeanSTD

Scenario 1 15211 17912 15109 16912 18908Scenario 2 35287 39051 33647 35968 47735

of our proposed algorithm that is GA-RX it is better togenerate data randomly rather than choose a fixed scenario

The performance of GA-RX is evaluated in two differentwaysThe first simulation is based on Scenario 1 For this casea performance threshold is set and the GA-RX is executedonly for 50 generations (as previously mentioned this is asimple example 50 generations are sufficient for obtaininggood results) This simulation is conducted using 100 groupsof random data An indicator expressed as a percentagevalue measures the number of times when the thresholdperformance is achieved over the total number of executionsObviously the larger the indicator is the better the algorithmperformance is The second simulation is based on bothscenarios The GA-RX algorithm is compared with classicalGA and three other state-of-the-art intelligent optimizationalgorithms including CLPSO [12] DE [13] and ACO [14]The relationship among these tasks is randomly identified inboth scenarios However the employed data is identical forall simulations under the same scenario (which is to make afair comparison) All simulations are performed 30 timesTheperformance of different algorithms is statistically comparedusing the 119905-test with a significance level of 95

72 Results

Simulation 1 For the 100 groups of data randomly generatedthe times of the threshold performance met are 93 and thepercentage is 93 (The threshold is 18)

Simulation 2 For simulation 2 the 119905-test results are inTable 1

In the 30 times of each scenario two typical simulationresults are presented in Figure 7

73 Analysis Firstly it can be observed that GA-RX impliesa faster convergence rate than the other for algorithms inboth scenariosThis is because the refined crossover operatorderived from the 1119890-law can preserve the beneficial aspectsof candidate solution while it does not destroy the diversityin each generation

Secondly Out of the five algorithms used for comparisonGA-RX is statistically better than all of the other algorithmsIt can be observed that GA-RX can perform better than otheralgorithms in both scenarios It results from the accumulationof refined crossover operator


8 Conclusion

In this paper the modeling and optimization of multi-UAVs system architecture alternatives have been studiedThe multi-UAVs system architecture problem was presentedas a constrained combinatorial optimization problem inSection 4 An enhanced genetic algorithm which employs arefined crossover operator (GA-RX) is proposed and appliedto accomplish the architecting process of multiple UAVssystem in Sections 5 and 6The simulation results in Section 7suggest that the GA-RX algorithm is available and effectivein solving the multiple UAVs system architecture problem asit can preserve the beneficial aspects of candidate solutionwithout degrading the diversity in each generation

With respect to the future study it is valuable to considermultiple objectives on the system architecture optimization[15] Correspondingly effective algorithms for solving thesemulti-objective optimization problems are expected to bedesigned [16 17]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the National NaturalScience Foundation of China under Grant nos 61273198and 71031007 The authors are grateful to the anonymousreviewers for their valuable comments and suggestions toimprove their work

References

[1] W M DeBusk ldquoUnmanned aerial vehicle systems for disasterrelief Tornado alleyrdquo in Proceedings of the AIAA Infotechat Aerospace Conference AIAA-2010-3506 Atlanta Ga USAApril 2010

[2] C Chen Y J Tan and L N Xing ldquoStudy on applicationof unmanned aerial vehicle for disaster monitoringrdquo ResearchJournal of Chemistry and Environment vol 16 pp 51ndash55 2012

[3] L Yun X Wei and W Wei ldquoApplication research on aviationremote sensing UAV for disaster monitoringrdquo Journal of Catas-trophology vol 26 no 1 pp 138ndash143 2011

[4] G Q Bai L N Xing and Y W Chen ldquoScheduling multi-platforms collaborative disasters monitoring based on coevo-lution algorithmrdquo Research Journal of Chemistry and Environ-ment vol 16 pp 43ndash50 2012

[5] G Q Bai L N Xing and Y W Chen ldquoThe knowledge-basedgenetic algorithm to the disasters monitoring task allocationproblemrdquo Research Journal of Chemistry and Environment vol16 pp 27ndash34 2012

[6] MWMaier and E RechtinTheArt of Systems Architecting vol2 CRC Press Boca Raton Fla USA 2000

[7] E F Crawley ESD34 Systems ArchitectingmdashLecture Notes MITEngineering Systems Division IAP 2007

[8] W L Simmons A Framework for Decision Support in SystemsArchitecting Massachusetts Institute of Technology 2008

[9] J H Holland Adaptation in Natural and Artificial Systems AnIntroductory Analysis with Applications to Biology Control andArtificial Intelligence University of Michigan Press Ann ArborMich USA 1975

[10] D E GoldbergGenetic Algorithms in Search Optimization andMachine Learning vol 412 Addison-Wesley Reading MassUSA 1989

[11] R J Vanderbei ldquoThe optimal choice of a subset of a populationrdquoMathematics of Operations Research vol 5 no 4 pp 481ndash4861980

[12] J J Liang A K Qin P N Suganthan and S BaskarldquoComprehensive learning particle swarm optimizer for globaloptimization of multimodal functionsrdquo IEEE Transactions onEvolutionary Computation vol 10 no 3 pp 281ndash295 2006

[13] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997

[14] Y-C Liang and A E Smith ldquoAn ant colony optimization algo-rithm for the redundancy allocation problem (RAP)rdquo IEEETransactions on Reliability vol 53 no 3 pp 417ndash423 2004

[15] R Wang P J Fleming and R C Purshouse ldquoGeneral frame-work for localised multi-objective evolutionary algorithmsrdquoInformation Sciences vol 258 pp 29ndash53 2014

[16] R Wang R C Purshouse and P J Fleming ldquoPreference-inspired coevolutionary algorithms for many-objective opti-mizationrdquo IEEE Transactions on Evolutionary Computation vol17 no 4 pp 474ndash494 2013

[17] R Wang R C Purshouse and P J Fleming ldquoPreference-inspired co-evolutionary algorithms using weight vectorsrdquoEuropean Journal of Operational Research 2014

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13

2

4 5

6 7

1

3

2

4

5

7

6

A

B

C

D

E

F

G

Figure 1 System architecture process

subsystems and the form is the relationship among themThe allocation of physical or informational elements offunction into elements of form is one of the earliest andmost important architectural decisions that have to be madeThe concept of system architecture can be illustrated as inFigure 1There are 7 different subsystems for architecting andevery subsystem can execute certain function It is supposedthat there are two alternatives to be selected The function-to-form mapping of left alternative is A 1 2 and 3 B 4 5C 6 7 Function 1 function 2 and function 3 are mappingto form A function 4 and function 5 are mapping to formB function 6 and function 7 are mapping to form C Themission can be accomplished by the combination of form Aform B and formCThe right alternative is another function-to-form mapping which can also accomplish the missionThen the problem is which alternative to be selected as theultimate architecture The selecting process is usually basedon the mission performanceThis is the essence of the systemarchitecting

The system architecture can be comprehended in twoaspects Firstly it should tell us ldquowhat the system isrdquo or the setof tangible elements that the system is composed of Secondlyit should tell us ldquowhat the system doesrdquo in order to providevalue to the stakeholders System architecting is the processof creating system architecture

The system architecting process can essentially be seenas a decision making process where the decisions to makeconcern the description of the entities of the system as wellas the relationships between them [8] This decision makingprocess can be supported by efficient optimization methodproposed later in this paper

3 Multiple UAVs System Architecture

Based on the basic definition of system architecture thedescription of multiple UAVs system architecture can begivenThe process model for multiple UAVs system architec-ture is presented in Figure 2

It can be extracted from the basic system architecturetheory that the first step is identifying the stakeholder needsThe architecture of multiple UAVs system is designed toaccomplish the value delivery loop based on the stakeholderneeds which is maximizing the mission performance given

Stakeholder needs

General objectives

Specific objectives

Tasks needed Tasks and UAVsdata products

The assignment plan

The executive details

The ultimate architecture

Satisfy

Satisfy

Satisfy

Figure 2 Architecture model for multi-UAVs system

Then the second step is identifying how the multi-UAVsmaximize the mission performance This is the issue in themission level The embodiment of this is maximizing theprobability of accomplishing all the tasks necessary effec-tively In order to reach this goal the suitable UAVs shouldbe chosen firstly This answers ldquowhat the system isrdquoThen theUAVs and the tasks are modelled as an asymmetric bipartitegraph which represents the assignment relationship betweenUAVs and tasks The selecting and assignment process isthe embodiment of system architecting in the context ofmaximizing the mission performance

What is the architect trying to achieve What makes anarchitecture ldquogoodrdquo To answer this question a process isneeded for selecting architectures that are not only capableof accomplishing the demand tasks but are also effectivein terms of their overall value acquired The quality of theproposed architecture is evaluated according to some criteriawhich is the overall value acquired by the UAVs throughconducting the tasks in this paper It is inevitable for architectthat the selecting and assigning should be done iterativelyThe system architecting problem of multi-UAVs can beformulated as a constrained combinatorial optimizationproblem For example these problems can be formulatedas generalized assignment problems quadratic assignmentproblems or their expansions As excellent population-basedsearch algorithms evolutionary algorithms (eg geneticalgorithms particle swarm optimization) can be chosen tosolve these multi-UAVs system architecting problems Thegeneral process of solving multi-UAVs system architectingproblems employing evolutionary algorithms is presented inFigure 3 An optimization problem and an efficient geneticalgorithm with a refined crossover operator (GA-RX) areproposed to accomplish the architecting process iteratively inthe rest of this paper


Start




population




End



41 Notations


119881 = 1198801 1198802 119880



119879 = 1198791 1198792 119879





119896|) 119896 =

1 2 119870

119882 = [11988211198822 119882



119875 = [119901119894119895]119873times119872





119909119894119895

=


0 otherwise(1)



1 minus

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895

(2)


prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(3)


119869 =

119870

sum

119896=1

119882119896prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(4)


119873

sum

119894=1

119909119894119895

= 1 119895 = 1 2 119872 (5)


Max119909119894119895isin01

119869 =

119870

sum

119896=1

119882119896prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(6)


119894=1119909119894119895

= 1 119895 = 1 2 119872





Procedure GAbegin



endend




Solution = (

11990911


d

1199091198731

sdot sdot sdot 119909119873119872

)

119909119894119895


0 otherwise

(7)

In any column (1199091119895

1199092119895

119909119873119895




(

1 0 1 0 0

0 1 0 0 1

0 0 0 1 0

) (8)














0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

4000


Tim

es




119875 (119896) =

119873

sum

119894=119896+1

1

119873times

119896

119894 minus 1=

119896

119873

119873

sum

119894=119896+1

1

119894 minus 1 (9)


119875 (119896) = 119909int

1

119909

1

119905119889119905 = minus119909 ln119909 (10)









Output 119862(119905)






1015840break

Add 1199011015840to 119862(119905)

End









Overall GA-RX










Yes


No




No

No

Yes


Yes


No

Yes

set t = 0


Add p998400 to C(t)




UAVs

UAV-1 UAV-2 UAV-20

Assets



Map

ping





[pij]20lowast 16

Figure 6 Scenario 1


119894119895]119873times119872








0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue


GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue




ScenarioAlgorithm





72 Results







8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start




population




End



41 Notations


119881 = 1198801 1198802 119880



119879 = 1198791 1198792 119879





119896|) 119896 =

1 2 119870

119882 = [11988211198822 119882



119875 = [119901119894119895]119873times119872





119909119894119895

=


0 otherwise(1)



1 minus

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895

(2)


prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(3)


119869 =

119870

sum

119896=1

119882119896prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(4)


119873

sum

119894=1

119909119894119895

= 1 119895 = 1 2 119872 (5)


Max119909119894119895isin01

119869 =

119870

sum

119896=1

119882119896prod

119894isin119866119896

[

[

1 minus 120587119894

119872

prod

119895=1

(1 minus 119901119894119895)119909119894119895]

]

(6)


119894=1119909119894119895

= 1 119895 = 1 2 119872





Procedure GAbegin



endend




Solution = (

11990911


d

1199091198731

sdot sdot sdot 119909119873119872

)

119909119894119895


0 otherwise

(7)

In any column (1199091119895

1199092119895

119909119873119895




(

1 0 1 0 0

0 1 0 0 1

0 0 0 1 0

) (8)














0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

4000


Tim

es




119875 (119896) =

119873

sum

119894=119896+1

1

119873times

119896

119894 minus 1=

119896

119873

119873

sum

119894=119896+1

1

119894 minus 1 (9)


119875 (119896) = 119909int

1

119909

1

119905119889119905 = minus119909 ln119909 (10)









Output 119862(119905)






1015840break

Add 1199011015840to 119862(119905)

End









Overall GA-RX










Yes


No




No

No

Yes


Yes


No

Yes

set t = 0


Add p998400 to C(t)




UAVs

UAV-1 UAV-2 UAV-20

Assets



Map

ping





[pij]20lowast 16

Figure 6 Scenario 1


119894119895]119873times119872








0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue


GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue




ScenarioAlgorithm





72 Results







8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Procedure GAbegin



endend




Solution = (

11990911


d

1199091198731

sdot sdot sdot 119909119873119872

)

119909119894119895


0 otherwise

(7)

In any column (1199091119895

1199092119895

119909119873119895




(

1 0 1 0 0

0 1 0 0 1

0 0 0 1 0

) (8)














0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

4000


Tim

es




119875 (119896) =

119873

sum

119894=119896+1

1

119873times

119896

119894 minus 1=

119896

119873

119873

sum

119894=119896+1

1

119894 minus 1 (9)


119875 (119896) = 119909int

1

119909

1

119905119889119905 = minus119909 ln119909 (10)









Output 119862(119905)






1015840break

Add 1199011015840to 119862(119905)

End









Overall GA-RX










Yes


No




No

No

Yes


Yes


No

Yes

set t = 0


Add p998400 to C(t)




UAVs

UAV-1 UAV-2 UAV-20

Assets



Map

ping





[pij]20lowast 16

Figure 6 Scenario 1


119894119895]119873times119872








0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue


GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue




ScenarioAlgorithm





72 Results







8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

4000


Tim

es




119875 (119896) =

119873

sum

119894=119896+1

1

119873times

119896

119894 minus 1=

119896

119873

119873

sum

119894=119896+1

1

119894 minus 1 (9)


119875 (119896) = 119909int

1

119909

1

119905119889119905 = minus119909 ln119909 (10)









Output 119862(119905)






1015840break

Add 1199011015840to 119862(119905)

End









Overall GA-RX










Yes


No




No

No

Yes


Yes


No

Yes

set t = 0


Add p998400 to C(t)




UAVs

UAV-1 UAV-2 UAV-20

Assets



Map

ping





[pij]20lowast 16

Figure 6 Scenario 1


119894119895]119873times119872








0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue


GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue




ScenarioAlgorithm





72 Results







8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Overall GA-RX










Yes


No




No

No

Yes


Yes


No

Yes

set t = 0


Add p998400 to C(t)




UAVs

UAV-1 UAV-2 UAV-20

Assets



Map

ping





[pij]20lowast 16

Figure 6 Scenario 1


119894119895]119873times119872








0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue


GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue




ScenarioAlgorithm





72 Results







8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

Generation

Best

fitne

ss v

alue


GA-RXGACLPSO

DEACO

GA-RXGACLPSO

DEACO

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

50

GenerationBe

st fit

ness

val

ue




ScenarioAlgorithm





72 Results







8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










8 Conclusion





Acknowledgments


References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article modeling and optimization of multiple...

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