Journal of Hydrology 531 (2015) 964–976

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Journal of Hydrology

journal homepage: www.elsevier .com/locate / jhydrol

Integrated optimal allocation model for complex adaptive systemof water resources management (I): Methodologies

http://dx.doi.org/10.1016/j.jhydrol.2015.10.0070022-1694/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: State Key Laboratory of Water Resources andHydropower Engineering Science, Wuhan University, Wuhan 430072, China.Tel./fax: +86 27 68773568.

E-mail address: zyl23bulls@whu.edu.cn (Y. Zhou).

Yanlai Zhou a,b,⇑, Shenglian Guo a, Chong-Yu Xu a,c, Dedi Liu a, Lu Chen d, Yushi Ye b

a State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, ChinabChangjiang River Scientific Research Institute, Wuhan 430010, ChinacDepartment of Geo-sciences, University of Oslo, NorwaydCollege of Hydropower & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, China

a r t i c l e i n f o

Article history:Available online 9 October 2015This manuscript was handled by GeoffSyme, Editor-in-Chief

Keywords:Water resources managementComplex adaptive systemOptimal allocationMulti-objectiveAgent-based

s u m m a r y

Due to the adaption, dynamic and multi-objective characteristics of complex water resources system, it isa considerable challenge to manage water resources in an efficient, equitable and sustainable way. Anintegrated optimal allocation model is proposed for complex adaptive system of water resources man-agement. The model consists of three modules: (1) an agent-based module for revealing evolution mech-anism of complex adaptive system using agent-based, system dynamic and non-dominated sortinggenetic algorithm II methods, (2) an optimal module for deriving decision set of water resources alloca-tion using multi-objective genetic algorithm, and (3) a multi-objective evaluation module for evaluatingthe efficiency of the optimal module and selecting the optimal water resources allocation scheme usingproject pursuit method. This study has provided a theoretical framework for adaptive allocation, dynamicallocation and multi-objective optimization for a complex adaptive system of water resourcesmanagement.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

Water resources play an important role in the development ofsocioeconomic and environmental system. Because waterresources are dynamic interactions and adaptations with relatedsocioeconomic and environmental factors, water resources alloca-tion is a complex adaptive problem involving population, economy,environment, ecology and policy, etc. (Singh, 2014). The optimalwater resources allocation literature mainly treated one or moreof the following three elements: (1) complex adaptive allocationof water resources, (2) dynamic allocation of water resources and(3) multi-objective optimization of water resources allocation.

The agent-based on genetic algorithm, i.e., intelligent agent oradaptive agent is one approach that can help decision makers builda complex adaptive model for water resources allocation (Galánet al., 2009; Ng et al., 2011). Zhao et al. (2004) proposed a complexadaptive model for water resources allocation based on geneticalgorithm and agent-based. The model was used to analyze the

rational amount of diversion water for the West Line of WaterTransfer Project from South China to North China and its utilizationbenefit. Berger et al. (2007) applied multi-agent simulation to cap-ture the complex adaptation of multiple users and their socio-economic implications within water resources management.Yang et al. (2009) presented a decentralized optimization algo-rithm for water shed management based on multi-agent simula-tion with outer river human agent, inner river human agent andecological agent. Chu et al. (2009) developed an agent-based sim-ulation to capture the complex characteristics of residential waterusage. Rieker and Labadie (2012) explored an intelligent agent foroptimization of complex river-reservoir system management andlong-term operation. Akhbari and Grigg (2013) introduced anagent-based model to resolve and mitigate conflicts of parties par-ticipating in water resources management. Giuliani and Castelletti(2013) used multi-agent simulation to model and analyze differentlevels of cooperation and information exchange among multipledecision makers in order to allow the downstream agents to betteradapt to the upstream behaviors in water resource system. Ni et al.(2014) applied an agent-based model to deal with water resourcesoptimal allocation based on genetic algorithm. Yuan et al. (2014)developed an agent-based model for prediction of urban household

Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976 965

water demand so as to simulate stochastic behavior and feedbackscaused by administrative agent and domestic agent.

System dynamic (SD) is a well-known methodology that sup-plies a theoretical framework and concepts for modelling dynamicallocation of water resources (Forrester, 1958; Ahmad andSimonovic, 2004; Feng et al., 2008; Willuweit and O’Sullivan,2013; Hoekema and Sridhar, 2013). An overview of generaldynamic allocation models for water resources has been summa-rized by Winz et al. (2009). Yang et al. (2008) applied SD to seeka balance between mitigating water shortages and total financialcost in water resources management. Zhang et al. (2008) devel-oped a SD model for making decision on water resources allocationand management. Zhang et al. (2009) developed an integrateddynamic model of water consumption based on SD and waterresources carrying capacity theory. Gastélum et al. (2010) exploreda SD model for water right transfer with regards to the degree ofcomplexity and uncertainty of the water right allocation processto different economic variables. Rehan et al. (2013) developed aSD model for financially sustainable management of urban waterdistribution networks. Akhtar et al. (2013) applied SD simulationto present comprehensive response of the society–biosphere–climate–economy–energy system by considering climate, carboncycle, land use, population, food production, hydrologic cycle,water demand, water quality and energy–economy. Chen andWei (2014) applied SD method to research on water securityincluding flood security, water resources security, carrying capac-ity, water environment security. Wang et al. (2014) used a complexsystem dynamic model to study relationship among populationgrowth, economic development, climate change, managementstrategies and water resources, and identify the best managementstrategy to adapt with the changing environment.

The multi-objective algorithm and multi-objective evaluationare alternative methods in solving multi-objective optimizationof water resources allocation (Nicklow et al., 2009; Singh, 2014).Nayak and Panda (2001) used multi-objective evaluation to solvingwater resources allocation for water manager and decision-makers. Srdjevic et al. (2004) used an integrated simulation oper-ation, system performance indices and multi-objective evaluationmodel to simulate operation of reservoir system. Castelletti et al.(2008) used multi-objective decision to cope with the preferenceand subjective aspects of the water resources allocation.Shourian et al. (2008) used a multi-objective model to allocatewater resources optimally over time and space among competingdemands based on particle swarm optimization algorithm. Changet al. (2009) proposed an integrated multi-objective model forregional water resources allocation and planning problem basedon multi-objective genetic algorithm and operating rules. Kilicand Anac (2010) developed a multi-objective planning model forlarge scale irrigation system in order to increase the benefit fromproduction, increase the size of the total area irrigated and reducethe water losses. Kim and Chung (2013) developed a multi-objective evaluation model for assessing climate change vulnera-bility of water resources management. Hou et al. (2014) used amulti-objective optimization model for maximizing benefit to theeconomy, society and environment in water resources allocation.Nouiri (2014) used multi-objective genetic algorithm and Paretooptimality concept to optimize daily management schedule ofhydraulic system. Roozbahani et al. (2014) proposed a multi-objective optimization model for sharing water among stakehold-ers of a trans boundary river by transforming the multi-objectiveproblem to a three-step single objective problem.

This study is an integrated optimal allocation model of complexadaptive allocation, dynamic allocation and multi-objectiveoptimization, focusing on complex adaptive management of waterresources allocation. The paper is organized as follows: Section 2

describes the method adopted in this study, which comprises threeparts: introduction of a general framework of integrated optimalallocation model by firstly setup an agent-based module(Section 2.1), secondly setup an optimal module (Section 2.2),and finally setup a multi-objective evaluation module (Section 2.3).The conclusions are drawn in Section 3.

2. Development of methodology

The integrated optimal allocation model (IOAM) for complexadaptive system (CAS) of water resources management consistsof following three separately modules: (1) an agent-based module,(2) an optimal module including multi-objective function, con-straints and algorithm, and (3) an evaluation module consistingof multi-objective evaluation indices as well as projection pursuitmethod. The structure of the IOAM is described in Fig. 1. Thedetails of each module are given as follows.

2.1. Agent-based module

Due to the dynamic, multi-objective, multi-reaction and adap-tion characteristics of CAS of water resources management, SD,agent-based and non-dominated sorting genetic algorithm II(NSGA-II) are used to reveal evolution mechanism of CAS.

2.1.1. Evolution mechanism of CASThe procedures of applying SD, agent-based and NSGA-II to

revealing evolution mechanism of CAS are shown in Fig. 2. CASof water resources management consists of administrative agent,water supply agent (including reservoir and hydropower stationagent), water user agent (including industrial production wateragent, agricultural production water agent, domestic water agent,reservoir and hydropower station agent as well as ecological wateragent), sewage treatment agent (Zhao et al., 2004). Because func-tions of reservoir and hydropower station are mainly includedflood control, water supply, power generation as well as naviga-tion, etc., reservoir is both water supplier and water user. Thedetails of evolution mechanism of CAS are described as follows:

(1) The planning strategies of society and economy develop-ment including population, economy, agriculture and ecol-ogy are formulated by administrative agent as well astransmitted to water user agents.

(2) Water demand of water user is predicted by inner stimulus–response of agent and outer feedback relationship betweenagents based on SD, when the planning strategies of eco-nomic and social development are transmitted to water useragents.

(3) Preliminary water supply strategy is formulated by adminis-trative agent and transmitted to reservoir and hydropowerstation agent according to feedback information of waterdemand simulated by SD.

(4) Water supply and storage of reservoir as well as hydropowerstation agent is simulated by inner stimulus–response ofagent and outer feedback relationship between agents basedon SD according to reservoir operating rules and storage, andthen that information is fed back to administrative agent.

(5) The preliminary water supply strategies are simulated byreservoir operation and transmitted to water user agents,at the same time, utilization benefit and sewage dischargeof water user agent simulated by SD is fed back to adminis-trative agent and sewage treatment agent, respectively.

(6) Sewage treatment agent is simulated by SD and fed back toadministrative agent.

Start

Simulation of inner stimulus-response of agent by SD

Simulation of outer feedback relationship between agents by SD

Initialization of parent population of decision variables

Evaluation of fitness of of decision variables based on NSGA-II

Evolution of new population based on NSGA-II

Revelation of evolution mechanism of CAS based on NSGA-II

Selection of multi-objective evaluation indices

Optimization of projection pursuit problem

Selection of optimal scheme of water resources allocation

Classification of agent-based

Generation of optimal decision set

Stop

Agent-based module Multi-objective evaluation moduleOptimal module

Fig. 1. The structure of the integrated optimal allocation model.

Administrative agent

Water user agent

Sewage treatment agent

Reservoir and hydropower station agent

Adaptation of planning strategies and water supply strategies based on

NSGA-II

Formulation of planning strategies

Prediction of water demand based on SD

Formulation of water supply strategies

Simulation of water supply and storage of reservoir and hydropower station agent

based on SD

Simulation of water use based on SD

Out

put o

f ut

iliza

tion

bene

fit

Output of sewage discharge

Simulation result of sewage treatment based on SD

Evaluation of fitness function

Water user agent

Administrative agent

Administrative agent

Fig. 2. The procedures for revealing evolution mechanism of complex adaptive system.

966 Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976

Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976 967

(7) Fitness function composed of multi-objective function isevaluated by administrative agent according to the feedbackof water user agent and sewage treatment agent, and thenthe strategies of economic and social growth rates as wellas water supply are optimized by NSGA-II in order to pursuebetter adaption of CAS.

2.1.2. Inner stimulus–response of agent and outer feedbackrelationship between agents based on SD

The basic building blocks for SD method are stock, flow, con-verter and connector, as shown in Fig. 3. Stock (box shown inFig. 3) represents accumulations both physical and non-physical.Flow represents actions in a stock which transport quantities intoand out of a stock instantaneously or over time. Connector (arrowshown in Fig. 3) establishes relationships between various ele-ments of agent-based and move information as inputs for decisionsor actions. Converter (circle shown in Fig. 3) represents agent andits inner stimulus–response function.

Mathematically the state equation (SE) between stock and flowcan be described using the following integral form (Sterman,2000):

StockðtÞ ¼Z t

t0

½InflowðsÞ � OutflowðsÞ�dsþ Stockðt0Þ ð1Þ

where t0 is the initial time, t is the current time, Stock(t0) is the ini-tial value of the stock, Inflow(s) and Outflow(s) are flow rates intoand out of a stock at any time between the initial time t0 and cur-rent time t.

The SD method for simulating inner stimulus–response of agentand outer feedback relationship between agents in CAS is devel-oped using VensimPLE Version 5.0a development tool (VentanaSystem Inc., Harvard, Massachusetts). The water agents includeindustrial production water agent, agricultural production wateragent, domestic water agent, reservoir and hydropower stationagent, ecological water agent as well as sewage treatment agent.

(1) Industrial production water agent

The inner stimulus–response of industrial production water

agent as well as outer feedback relationship among industrial pro-duction water agent, administrative agent and sewage treatmentagent is shown in Fig. 4. Firstly, water quota per 10,000 yuan ofeconomic value-added by industry (WQVAI), planning economicvalue-added by industry (PVAI) and water demand of industry(WDI) are calculated by Eqs. (2)–(4) according to the values ofplanning growth rate of economic value-added by industry(PGRVA) and growth rate of water consumption per 10,000 yuaneconomic value-added by industry (GRWC) formulated by

Converter

StockFlow

Connector

Fig. 3. The basic building blocks for SD method.

administrative agent, respectively, and then the WDI is fed backto administrative agent, secondly, economic value-added by indus-try (VAI), industrial sewage productivity (ISP) and industrialreturn-flow (IRF) are calculated by Eqs. (5)–(7) according to watersupply for industry (WSI) fed back by administrative agent, respec-tively, lastly, discharge of industrial sewage (DIS) is fed back tosewage treatment agent as well as VAI and IRF are fed back toadministrative agent.

SE : WQVAIi;tþ1 ¼ WQVAIi;t þ GRWCi;t ð2Þ

SE : PVAIi;tþ1 ¼ PVAIi;t � ð1þ PGRVAi;tÞ ð3Þ

Auxiliary equation ðAEÞ : WDIi;t ¼ PVAIi;t �WQVAIi;tCIPNi;t

ð4Þ

SE : VAIi;tþ1 ¼ WSIi;tWQVAIi;t

ð5Þ

AE : DISi;t ¼ WSIi;t � ISPi;t ð6Þ

AE : IRFi;t ¼ WSIi;t � CIRFi;t ð7Þwhere i is the serial number of water-intake, t is the serial numberof time, CIPNi,t is coefficient of industrial pipe network of ith water-intake in time t, CIRFi,t is coefficient of industrial return-flow of ithwater-intake in time t.

(2) Agricultural production water agentThe inner stimulus–response of agricultural production water

agent as well as outer feedback relationship between agriculturalproduction water agent and administrative agent is shown inFig. 5. Firstly, water demand of crop production (WDCP) and waterdemand of forest, animal husbandry and fishery production(WDFAFP) are calculated by Eqs. (8) and (9) according to the valuesof crop area (CA) and development scale of forest, animal hus-bandry and fishery production (DSFAFP) formulated by administra-tive agent, respectively, and then the WDCP and water demand offorest, animal husbandry and fishery production (WDFAFP) are fedback to administrative agent, secondly, economic value-added bycrop production (VACP), economic value-added by forest, animalhusbandry and fishery production (VAFAF) and economicvalue-added by agricultural production (VAAP) are calculated byEqs. (10)–(12) according to the values of water supply for cropproduction (WSCP) and water supply for forest, animal husbandryand fishery production (WSFAFP) fed back by administrative agent,respectively, lastly, agricultural return-flow (ARF) is calculated byEq. (13) and fed back to administrative agent.

AE : WDCPi;t ¼Xmj¼1

CA ji;t � f ðIPCP j

i ; Pi;tÞCCSi;t

ð8Þ

AE : WDFAFPi;t ¼Xnk¼1

DSFAFPki;t � IPCPk

i;t

CCSi;tð9Þ

AE : VACPi;t

¼Xmj¼1

CA ji;t � BPUC j

i;t �WSCP ji;t

WDCP ji;t

þ CA ji;t � BPUC j

i;t

BCPI ji;t

� 1� WSCP ji;t

WDCP ji;t

!ð10Þ

AE : VAFAFi;t ¼Xnk¼1

DSFAFPki;t � BPUFAFki;t �WSFAFPk

i;t

WDFAFP ji;t

ð11Þ

Fig. 4. The inner stimulus–response and outer feedback of industrial production water agent.

Fig. 5. The inner stimulus–response and outer feedback of agricultural production water agent.

968 Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976

SE : VAAPi;t ¼ VACPi;t þ VAFAFi;t ð12Þ

AE : ARFi;t ¼ CARFi;t � ðWSCPi;t þWSFAFPi;tÞ ð13Þ

where m is the number of crop productions, n is the number ofhusbandry and fishery productions, j is the serial number of cropproduction, k is the serial number of husbandry and fishery produc-

tion, Pi,t is the precipitation of ith water-intake in time t, IPCP ji is the

irrigation quota of jth crop production in ith water-intake, f(�) is the

function relationship between IPCP ji and Pi,t, CCSi,t is the coefficient

of canal system of ith water-intake in time t, BPUC ji;t is the benefit

per unit jth crop production of ith water-intake in time t, BCPI ji;t isthe benefit coefficient of jth crop production-added by irrigation

of ith water-intake in time t, BPUFAFki;t is the benefit per unit kthproduction of forest, animal husbandry and fishery of ithwater-intake in time t, CARFi,t is the coefficient of agriculturalreturn-flow of ith water-intake in time t.

ydrology 531 (2015) 964–976 969

(3) Domestic water agent

The inner stimulus–response of domestic water agent as well as

outer feedback relationship among domestic water agent,administrative agent and sewage treatment agent is shown inFig. 6. Firstly, total population (TP), domestic water quota (DWQ)and domestic water demand (DWD) are calculated byEqs. (14)–(16) according to the values of growth rate of population(GRP), domestic water price (DWP) and income per capita (IPC)formulated by administrative agent, respectively, and then the TPand DWD are fed back to administrative agent, secondly, domesticsewage discharge (DSD) and domestic return-flow (DRF) are calcu-lated by Eqs. (17) and (18) according to domestic water withdrawal(DWW) fed back by administrative agent, respectively, lastly, DSDis fed back to sewage treatment agent as well as DRF is fed back toadministrative agent.

SE : TPi;tþ1 ¼ TPi;t � ð1þ GRPi;tÞ ð14Þ

AE : DWQ i;t ¼ gðDWPi;t; IPCi;tÞ ð15Þ

AE : DWDi;t ¼ DWQ i;t � TPi;t

CDPNi;tð16Þ

AE : DSDi;t ¼ DWWi;t � DSPi;t ð17Þ

AE : DRFi;t ¼ CDRFi;t � DWWi;t ð18Þwhere g(�) is the function relationship among DWQi,t, DWPi,t andIPCi,t, CDPNi,t is the coefficient of domestic pipe network of ithwater-intake in time t, DSPi,t is the domestic sewage productivityof ith water-intake in time t, CDRFi,t is the coefficient of domesticreturn-flow of ith water-intake in time t.

Y. Zhou et al. / Journal of H

Fig. 6. The inner stimulus–response and ou

(4) Reservoir and hydropower station agentThe inner stimulus–response of reservoir and hydropower

station agent as well as outer feedback relationship amongreservoir and hydropower station agent, administrative agentand other water user agent is shown in Fig. 7. Firstly, reservoirwater supply (RWS) and reservoir outflow (RO) are calculated byEq. (19) according to the values of reservoir required water supply(RRWS) fed back by administrative agent as well as reservoirinflow (RI), reservoir volume (RV) and reservoir constraints, andthen the RWS and RO are fed back to administrative agent, lastly,RV, hydropower output (HO) and benefit of hydropower station(BHS) are calculated by Eqs. (19)–(21), respectively, as well asthe RV, HO and BHS are fed back to administrative agent.

SE : RVi;tþ1 ¼ RVi;t þ RIi;t � ROi;t� � � Dt � RVLi;t ð19Þ

AE : HOi;t ¼ CHOi;t �WHHSi;t � ROi;t ð20Þ

AE : BHSi;t ¼ HOi;t � EPi;t � Dt ð21Þwhere Dt is the time interval, RVLi,t is the reservoir volume loss ofith reservoir in time t, CHOi,t is the coefficient of hydropower outputof ith hydropower station in time t, WHHSi,t is the water head of ithhydropower station in time t, EPi,t is the electric price in time t.

(5) Ecological water agentThe inner stimulus–response of ecological water agent as well

as outer feedback relationship among ecological water agent,administrative agent and sewage treatment agent is shown inFig. 8. Firstly, outer-river ecological water demand (OEWD) iscalculated by Eq. (22) according to total population (TP) fed backby administrative agent, and then the OEWD and inner-river

ter feedback of domestic water agent.

Fig. 7. The inner stimulus–response and outer feedback of reservoir and hydropower station agent.

Fig. 8. The inner stimulus–response and outer feedback of ecological water agent.

970 Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976

ecological flow (IEF) are fed back to administrative agent, secondly,ecological water shortage (EWS) is calculated by Eqs. (23)–(25)according to outer-river ecological water withdrawal (OEWW)and IEF fed back by administrative agent as well as the EWS isfed back to administrative agent, lastly, outer-river ecologicalsewage discharge (OESD) is calculated by Eq. (26) and fed backto sewage treatment agent as well as ecological return-flow (ERF)is calculated by Eq. (27) and fed back to administrative agent.

AE : OEWDi;t ¼ TPi;t � EAPCi;t � OEWQ i;t

CEPNi;tð22Þ

AE : EWSi;t ¼ OEWSi;t þ IEWSi;t ð23Þ

AE : OEWSi;t ¼ OEWDi;t � OEWWi;t ð24Þ

AE : IEWSi;t ¼IEWDi;t � IEFi;t; IEWDi;t > IEFi;t0; IEWDi;t 6 IEFi;t

�ð25Þ

AE : OESDi;t ¼ OESPi;t � OEWWi;t ð26Þ

AE : ERFi;t ¼ OEWWi;t � CERFi;t ð27Þwhere EAPCi,t is the ecological area per capita of ith water-intake intime t, OEWQi,t is the outer-river ecological water quota of ithwater-intake in time t, OEWSi,t is the outer-river ecological watershortage of ith water-intake in time t, IEWSi,t is the inner-river

Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976 971

ecological water shortage of ith water-intake in time t, IEWDi,t is theinner-river ecological water demand of ith water-intake in time t,OESPi,t is the outer-river ecological sewage productivity of ithwater-intake in time t, CERFi,t is the coefficient of ecologicalreturn-flow of ith water-intake in time t.

(6) Sewage treatment agentThe inner stimulus–response of sewage treatment agent as well

as outer feedback relationship among water user agent, adminis-trative agent and sewage treatment agent is shown in Fig. 9. Firstly,total sewage discharge (TSD) is calculated by Eq. (28) according tothe values of domestic sewage discharge (DSD), secondary industrysewage (SIS), tertiary industry sewage (TIS) and outer-river ecolog-ical sewage discharge (OESD) fed back by administrative agent, andthen the TSD is fed back to administrative agent, secondly, sewagetreatment capacity (STC), sewage treatment fee (STF) and volumeof pollutant index of sewage treatment (VPIST) are calculated byEqs. (29)–(31) according to sewage treatment productivity (STP)and economic value-added by sewage treatment capacity (VASTC)fed back by administrative agent, respectively, lastly, STC, STF andVPIST are fed back to administrative agent.

AE : TSDi;t ¼ DSDi;t þ SISi;t þ TISi;t þ OESDi;t ð28Þ

SE : STCi;tþ1 ¼ STCi;tþ1 þ VASTCi;tþ1 ð29Þ

AE : STFi;t ¼ TSDi;t � STPi;t � TCPSDi;t ð30Þ

AE : VPISTi;t

¼ TSDi;t � STPi;t � VPIPSTi;t þ TSDi;t � ð1� STPi;tÞ � VPIPSDi;t ð31Þwhere TCPSDi,t is the treatment cost per sewage discharge of ithwater-intake in time t, VPIPSTi,t is the volume of pollutant index persewage treatmentof ithwater-intake in time t, VPIPSDi,t is thevolumeof pollutant index per sewage discharge of ith water-intake in time t.

2.2. Optimal module

Water resource is an integral part of the socio-economic–ecological–environmental system, which is a CAS dominated byadministrative agent.Optimalmodule is anextensionof thepreviousmulti-objective optimal applications (Hou et al., 2014;Nouiri, 2014;

Fig. 9. The inner stimulus–response and out

Roozbahani et al., 2014), focusing on the social, economic, ecologicaland environmental objectives optimization of the CAS.

2.2.1. Multi-objective functionMulti-objective functions are described as follows:

(1) Social objective function

Gini coefficient denotes the equity of resources allocation pro-

posed by Gini based on Lorenz curve in 1922. The Lorenz curve isshown in Fig. 10. The letter A denotes area between curve of abso-lute equity allocation and curve of actual income allocation as wellas the letter B denotes area below curve of actual income alloca-tion. Gini coefficient is equal to A/(A + B). The value of Gini coeffi-cient is less, the allocation is tend to be more equity. Three kinds ofGini coefficients are selected as objective function evaluating theequity of resources allocation among society, economy and waterresources in different regions, i.e., Gini coefficient between popula-tion and water consumption (Gini-P), Gini coefficient betweengross domestic product (GDP) and water consumption(Gini-GDP) and Gini coefficient between available water resources(AWR) and water consumption (Gini-AWR).

The annual average of Gini-P is defined as follows:

AGini-P ¼XTyt¼1

Gini-Pt

Ty

¼ 1�XTyt¼1

XNi¼1

ðCPWi;t þ CPWi�1;tÞ � CPPi;t � CPPi�1;t� �

Tyð32Þ

where AGini-P is annual average of Gini-P, Gini-Pt is Gini-P in time t,Ty is the number of years; N is the number of water-intakes, CPWi,t

is the cumulative percentage of water consumption (CPW) of ithwater-intake in time t, CPPi,t is the cumulative percentage of popu-lation (CPP) of ith water-intake in time t, as well as CPWi,0 and CPPi,0are equal to zero in initial time.

The annual average of Gini-GDP is defined as follows:

AGini-GDP¼XTyt¼1

Gini-GDPt

Ty¼1�

XTyt¼1

XNi¼1

ðCPWi;t þCPWi�1;tÞ � CPGi;t �CPGi�1;t� �

Ty

ð33Þ

where AGini-GDP is annual average of Gini-GDP, Gini-GDPt is Gini-GDP in time t, CPGi,t is the cumulative percentage of GDP of ith

er feedback of sewage treatment agent.

100

100

Perc

enta

ge o

f cum

ulat

ive

inco

me

(%)

Percentage of cumulative population (%)

Curve o

f abso

lute e

quali

ty all

ocatio

n

Curve o

f actu

al inc

ome a

llocat

ion

A

B

0

Fig. 10. The Lorenz curve.

972 Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976

water-intake in time t, as well as CPGi,0 is equal to zero in initialtime.

The annual average of Gini-AWR is defined as follows:

AGini-AWR¼XTyt¼1

Gini-AWRt

Ty¼1�

XTyt¼1

XNi¼1

ðCPWi;t þCPWi�1;tÞ � ðCPAi;t �CPAi�1;tÞTy

ð34Þ

where AGini-AWR is annual average of Gini-AWR, Gini-AWRt isGini-AWR in time t, CPAi,t is the cumulative percentage of AWR ofith water-intake in time t, as well as CPAi,0 is equal to zero in initialtime.

In order to consider the effect of water consumption by threekinds of Gini coefficients, weighting method (Fang et al., 2009;Zhou and Guo, 2013) is used to calculate the integrated Gini coef-ficient (IGC). Therefore, the social objective function, i.e., the equityof water consumption is shown in

f 1ðXÞ ¼ min IGC ¼ min ðw1 � AGini-Pþw2 � AGini-GDPþw3 � AGini-AWRÞ ð35Þ

where f 1ðXÞ is the equity objective function of water consumption,X is the vector of decision variables including economic and socialgrowth rates and water supply,w1;w2 andw3 are the weighting fac-tors of AGini-P, AGini-GDP and AGini-AWR, respectively, as well asthe sum of w1;w2 and w3 is equal to one.

(2) Economic objective functionGDP is generally recognized as an important evaluation index of

economic strength and situation for country or region. Thus, GDP isselected as economic objective for evaluating the economic benefitof administrative agent in CAS of water resources. The economicobjective function maximizing annual average GDP is shown in

f 2ðXÞ ¼ maxXTyt¼1

IGDPt

Tyð36Þ

where f 2ðXÞ is economic objective function, IGDPt is the integratedGDP including economic value-added by industrial production,agricultural production, hydropower generation and sewage treat-ment in time t.

(3) Ecological objective functionEcological water shortages are composed of inner-river and

outer-river ecological water shortages. Hence, the ecological objec-tive function minimizing ecological water shortage is shown in

f 3ðXÞ ¼ minXT2t¼1

XNi¼1

ðIEWSi;t þ OEWSi;tÞT2

ð37Þ

where f 3ðXÞ is ecological objective function, IEWSi,t and OEWSi,t areinner-river and outer-river ecological water shortage of ith water-intake in time t, respectively.

(4) Environmental objective functionThe environmental objective function minimizing VPIST is

shown in

f 4ðXÞ ¼ minXTmt¼1

XNi¼1

VPISTi;t

Tmð38Þ

where f 4ðXÞ is the environmental objective function, VPISTi,t is theVPIST of ith water-intake in time t.

Multi-objective functions can be determined as follows:

FðXÞ ¼ ðf 1ðXÞ; f 2ðXÞ; f 3ðXÞ; f 4ðXÞÞ ð39Þwhere F(X) is the vector of multi-objective functions.

2.2.2. ConstraintsThe multi-objective functions subject themselves to seven kinds

of constraints: (1) water conservancy projects including reservoir,hydropower station and water-intake, (2) social developmentincluding population and growth rate of population, (3) economicdevelopment including growth rate of agriculture and industry,proportion between agriculture and industry as well as waterprice, (4) production water demand, (5) domestic water demand,(6) ecological water demand and (7) sewage treatment capacityand water environment capacity.

2.2.3. Optimal algorithmNSGA-II is elitist and characterized by weak parameter numbers

and good distribution of optimal solutions on the Pareto front(Reed et al., 2003; Kapelan et al., 2005). The Pareto optimalityconcept is used to test the multi-objective genetic algorithm tocompare solutions, according to their objective functions, and toselect the non-dominated ones. NSGA-II is applied to solve multi-objective optimization of water resources allocation. The detailsof main procedure are as follows:

(1) Initialization of parent population: parent population ofplanning growth rates of agricultural and industrial pro-duction as well as people population is first randomly gen-erated by pseudo-random sampling. Water demand ofwater user is predicted by inner stimulus–response ofagent and outer feedback relationship between agentsbased on SD, when the planning growth rates are transmit-ted to water user agents. Initial population of water supplystrategy is randomly generated by pseudo-randomsampling after the water demand is fed back fromadministrative agent.

(2) Evaluation of fitness: the multi-objective functions of soci-ety, economy, ecology and environment are calculatedaccording to utilization benefit and sewage discharge ofwater user agent simulated by SD. Then the fitness of deci-sion variables is evaluated for each chromosome by thenon-dominated sorting and calculating crowding distancein NSGA-II (Reed et al., 2003).

(3) Evolution of new population: children population isgenerated by operators of selection, crossover and mutationin NSGA-II as well as evolution of new population is pro-duced by combination children population with parentpopulation.

Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976 973

(4) Stopping iteration: before going on to the next step, makesure the stopping criteria of iteration are satisfied. Other-wise, steps (2) and (3) are repeated. Pareto optimal set basedon non-dominated sorting is confirmed as optimal decisionset for water resources allocation.

2.3. Multi-objective evaluation module

2.3.1. Multi-objective evaluation indicesMulti-objective evaluation module is used to evaluate the effi-

ciency of optimal module and select out the optimal scheme ofwater resources allocation. Therefore, the above four multi-objective functions are selected as multi-objective evaluationindices, i.e., (1) minimizing the integrated Gini coefficient, (2) max-imizing the annual average GDP, (3) minimizing the VPIST and (4)minimizing the ecological water shortage.

2.3.2. Projection pursuit methodIf fy�ijji ¼ 1;2; � � � ;n; j ¼ 1;2; � � � ;mg (n is the number of samples,

m is the number of cluster factors of the samples) is the initialvalue of the jth factor of the ith sample, the procedure of develop-ing the projection pursuit method is described as follows.

(1) Data standardization

In order to eliminate the effect of different ranges of values of

cluster factors, the initial data are standardized before they areused in the projection pursuit method. And the standardizationformulas used for two kinds of cluster factors are

yij ¼y�ij � ymin;j

ymax;j � ymin;jð40Þ

yij ¼ymax;j � y�ij

ymax;j � ymin;jð41Þ

where ymin;j and ymax;j are the minimum and maximum of samples,respectively, and other notations have the same meaning as above.

(2) Linear projectionEssentially, projection is used to observe data characteristic from

all angles. The main purpose of projection pursuit is to find the hid-den structure fromhigh dimensional data sets by searching throughall their low dimensional projections. If~a ¼ ða1; a2; � � � ; aj; � � � ; amÞT isa m dimensional unit vector and zi is the projected characteristicvalue of yij, linear projection can be described as

zi ¼Xmj¼1

ajyij ð42Þ

(3) Projection indexCluster analysis is a tool for exploratory data analysis that tries

to find the intrinsic structure of data by organizing patterns intogroups or clusters. In the projection pursuit method, a new projec-tion index is generated on the basis of dynamic cluster principle.

Define s(zi, zk) (k = 1,2, . . .,n) as the absolute value of distancebetween the projected characteristic value zi and zk, namelys(zi, zk) = |zi � zk|.

Let X ¼ fz1; z2; � � � ; zng, and define

ssðaÞ ¼Xzizk2X

sðzi; zkÞ ð43Þ

Then, it is assumed that the all samples are classified as p (2 6 p < n)clusters. Rh (h = 1,2, . . .,p) is the projected characteristic value spaceof cluster h, which contains all the projected characteristic value ofcluster h, and thus Rh = {zi|d(Ah � zi) 6 d(Ai � zi) 8t = 1,2, . . .,p, t– h}.

Where d(Ah � zi) = |zi � Ah| and d(Ai � zi) = |zi � Ai|, Ah and Ai arethe initial cluster cores of both cluster h and cluster i, respectively.In practice, the average projected characteristic value of clusters isused as new cluster core to conduct the iteration. We also define

dðaÞ ¼X

zizk2Rhsðzi; zkÞ ð44Þ

ddðaÞ ¼Xph¼1

dhðaÞ ð45Þ

Finally, the new projection index QQ(a) in the projection pursuitmethod is calculated as follows

QQðaÞ ¼ ssðaÞ � ddðaÞ ð46ÞThe projection index QQ(a) measures the degree to which the datapoints in the projection are both concentrated locally (ss(a) small)and, at the same time, expanded globally (dd(a) large).

(4) Projection pursuit optimizationAccording to the above analysis, it can be found that the projec-

tion pursuit optimization can be expressed by

max QQðaÞkak ¼ 1

�ð47Þ

Eq. (25) shows that the projection pursuit method reflects an opti-mum problem. As Friedman and Turkey (1974) pointed out, projec-tion pursuit method strongly depends on the ability of theoptimization algorithm to find substantive optima of the projectionindex among a forest of dummy optima caused by sampling fluctu-ations. Therefore, an efficient algorithm is one of the key issues ofthe projection pursuit method.

2.3.3. Accelerating Genetic AlgorithmAccelerating Genetic Algorithm (AGA) (Wang et al., 2006; Chen

and Yang, 2007; Fang et al., 2009) is used to optimize the projec-tion pursuit problem. The steps of AGA are briefly described asfollows:

Step 1: Encoding. Transform the intervals of the variables into[0, 1].Step 2: Initialization of parent population. Generate n individu-als (also called population size) using uniform random num-bers. Calculate the objection function and sort them.Step 3: Fitness evaluation. Calculate the fitness function andretain the first ns individuals which are smart individuals.Step 4: Reproduction. The smart individuals are directly copiedto offspring in AGA, while the other (n � ns) individuals areselected by the selection probability ps from the parent popula-tion. This will generate the first offspring population.Step 5: Crossover. Crossover of the parent individuals occurs togenerate the second offspring population according to thecrossover probability.Step 6: Mutation. Mutate the poor individuals using a mutationprobability pm to generate the third offspring population.Step 7: Evolution and iteration. Sort the three offspring popula-tions by their fitness, and then select the first n individuals asthe new generation. Go back to step 3 and repeat the steps3–7 twice.Step 8: Accelerating cycle. Through every other iteration, com-press the intervals of the variables until the terminated rulessatisfied. As a result, the optimal solution of AGA is obtained.

Generally, the operations of reproduction, crossover and muta-tion of genetic algorithm (GA) are executed in series. However,these operations are performed in parallel for AGA, which will fur-

974 Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976

ther protect the genetic information of each individual. Thus, AGAmay have much more opportunities to reach the global optimalsolution to GA. The interval accelerating mechanism in Step 8accelerates the convergence of the optimization process.

3. Conclusions

IOAM for CAS of water resources management is done in threeparts, (1) an agent-based module, (2) an optimal module and (3) amulti-objective evaluation module, employing different methods.Firstly, SD, agent-based and NSGA-II are used to reveal evolutionmechanism of CAS. Secondly, NSGA-II is employed to solve theoptimal module made up of multi-objective function and con-straints. Lastly, projection pursuit method and AGA are appliedto evaluating the efficiency of optimal module and selecting outthe optimal scheme of IOAM. Part 2 of this paper is presented asa case study paper dealing with the execution of these integratedmethods for CAS of water resources management.

Acknowledgements

This study is financially supported by the InternationalCooperation in Science and Technology Special Project of China(2014DFA71910), National Natural Science Foundation of China(51509008 and 41501319), Natural Science Foundation of HubeiProvince (2015CFB217 and 2015CFA157) and Open Foundation ofState Key Laboratory of Water Resources and HydropowerEngineering Science in Wuhan University (2014SWG02).

Appendix A

Abbreviations for variables and parameters in the IOAM.

No.

Abbreviation Description Unit

1

ARF Agricultural return-flow (104 m3) 2 BCPI Benefit coefficient of

production-added byirrigation

(%)

3

BHS Benefit of hydropowerstation

(104 yuan)

4

BPUC Benefit per unit cropproduction

(108 yuan/mu)

5

BPUFAF Benefit per unitproduction of forest,animal husbandry andfishery

(108 yuan/mu)

6

CA Crop area (mu) 7 CARF Coefficient of

agricultural return-flow

(–)

8

CCS Coefficient of canalsystem

(–)

9

CDRF Coefficient of domesticreturn-flow

(–)

10

CDPN Coefficient of domesticpipe network

(–)

11

CEPN Coefficient of ecologicalpipe network

(–)

12

CERF Coefficient of ecologicalreturn-flow

(–)

13

CHO Coefficient ofhydropower output

(–)

14

CIPN Coefficient of industrialpipe network

(–)

No.

Abbreviation Description Unit

15

CIRF Coefficient of industrialreturn-flow

(–)

16

DIS Discharge of industrialsewage

(104 ton)

17

DRF Domestic return-flow (104 m3) 18 DSD Domestic sewage

discharge

(104 ton)

19

DSP Domestic sewageproductivity

(%)

20

DSFAFP Development scale offorest, animalhusbandry and fisheryproduction

(mu)

21

DWD Domestic waterdemand

(104 m3)

22

DWP Domestic water price (yuan) 23 DWQ Domestic water quota (liter/

(people�day))

24 DWWD Difference between

water withdrawal anddemand

(104 m3)

25

DIS Discharge of industrialsewage

(104 ton)

26

EAPC Ecological area percapita

(mu/people)

27

EP Electric price (yuan) 28 ERF Ecological return-flow (104 m3) 29 EWS Ecological water

shortage

(104 m3)

30

GRCA Growth rate of croparea

(%)

31

GRP Growth rate ofpopulation

(%)

32

GRWC Growth rate of waterconsumption per10,000 yuan economicvalue-added byindustry

(%)

33

HO Hydropower output (kW) 34 IEF Inner-river ecological

flow

(m3/s)

35

IEWD Inner-river ecologicalwater demand

(104 m3)

36

IEWS Inner-river ecologicalwater shortage

(104 m3)

37

IPCP Irrigation quota of cropproduction

(104 m3/mu)

38

IPC Income per capita (104 yuan/people)

39

IRF Industrial return-flow (104 m3) 40 ISP Industrial sewage

productivity

(%)

41

OESD Outer-river ecologicalsewage discharge

(104 m3)

42

OESP Outer-river ecologicalsewage productivity

(%)

43

OEWS Outer-river ecologicalwater shortage

(104 m3)

44

OEWD Outer-river ecologicalwater demand

(104 m3)

45

OEWQ Outer-river ecologicalwater quota

(104 m3/mu)

Y. Zhou et al. / Journal of Hydrology 531 (2015) 964–976 975

Appendix A (continued)

No.

Abbreviation Description Unit

46

OEWW Outer-river ecologicalwater withdrawal

(104 m3)

47

P Precipitation (mm) 48 PGRVA Planning growth rate of

economic value-addedby industry

(%)

49

PVAI Planning economicvalue-added byindustry

(108 yuan)

50

RI Reservoir inflow (m3/s) 51 RO Reservoir outflow (m3/s) 52 ROR Reservoir operating

rules

(–)

53

RRWS Reservoir requiredwater supply

(104 m3)

54

RTWL Reservoir tail waterlevel

(m)

55

RWL Reservoir water level (m) 56 RWS Reservoir water supply (104 m3) 57 RV Reservoir volume (104 m3) 58 RVL Reservoir volume loss (104 m3) 59 SIS Secondary industry

sewage

(104 ton)

60

STC Sewage treatmentcapacity

(ton/d)

61

STF Sewage treatment fee (104 yuan) 62 STP Sewage treatment

productivity

(%)

63

TCPSD Treatment cost persewage discharge

(yuan/ton)

64

TIS Tertiary industrysewage

(104 ton)

65

TP Total population (104 people) 66 TSD Total sewage discharge (104 ton) 67 VAAP Economic value-added

by agriculturalproduction

(108 yuan)

68

VACP Economic value-addedby crop production

(108 yuan)

69

VAFAF Economic value-addedby forest, animalhusbandry and fisheryproduction

(108 yuan)

70

VAI Economic value-addedby industry

(108 yuan)

71

VASTC Economic value-addedby sewage treatmentcapacity

(ton/d)

72

VPIPSD Volume of pollutantindex per sewagedischarge

(m3/ton)

73

VPIPST Volume of pollutantindex per sewagetreatment

(m3/ton)

74

VPIST Volume of pollutantindex of sewagetreatment

(m3)

75

WDCP Water demand of cropproduction

(104 m3)

No.

Abbreviation Description Unit

76

WDFAFP Water demand of forest,animal husbandry andfishery production

(104 m3)

77

WDI Water demand ofindustry

(104 m3)

78

WHHS Water head ofhydropower station

(m)

79

WQFAFP Water quota of forest,animal husbandry andfishery production

(104 m3/mu)

80

WQVAI Water quota per10,000 yuan ofeconomic value-addedby industry

(m3/104 yuan)

81

WSCP Water supply for cropproduction

(104 m3)

82

WSFAFP Water supply for forest,animal husbandry andfishery production

(104 m3)

83

WSI Water supply forindustry

(104 m3)

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