J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640

DOI: 10.1007/s12204-013-1442-x

Application of Particle Swarm Algorithm in the Optimal Allocation ofRegional Water Resources Based on Immune Evolutionary Algorithm

QU Guo-dong∗ (���), LOU Zhang-hua (���)(Institute of Hydrology and Water Resource Engineering, Zhejiang University, Hangzhou 310058, China)

© Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg 2013

Abstract: The optimal allocation model of regional water resources is built with the purpose of maximizing thecomprehensive economic, social and environmental benefits of regional water consumption. In order to solve theproblems that easily appear during the model solution of regional water resource optimal allocation with multiplewater sources, multiple users and multiple objectives like “curse of dimensionality” or sinking into local optimum,this paper proposes a particle swarm optimization (PSO) algorithm based on immune evolutionary algorithm(IEA). This algorithm introduces immunology principle into particle swarm algorithm. Its immune memorizingand self-adjusting mechanism is utilized to keep the particles in the fitness level at a certain concentration andguarantee the diversity of population. Also, the global search characteristics of IEA and the local search capacityof particle swarm algorithm have been fully utilized to overcome the dependence of PSO on initial swarm andthe deficiency of vulnerability to local optimum. After applying this model to the allocation of water resources inZhoukou, we obtain the scheme for optimization allocation of water resources in the planning level years, i.e. 2015and 2025 under the guarantee rate of 50%. The calculation results indicate that the application of this algorithmto solve the issue of optimal allocation of regional water resources is reliable and reasonable. Thus it offers a newidea for solving the issue of optimal allocation of water resources.Key words: immune evolutionary algorithm (IEA), particle swarm optimization (PSO), water resources, optimalallocationCLC number: TV 212.2 Document code: A

0 Introduction

With the quick regional economic and social develop-ment, growth of population, increasingly intense waterresources, etc., water problems like shortage of waterresources and deterioration of water environment be-come very obvious. The optimal allocation of waterresources is the main approach to solve the shortage ofregional water resources. Allocation of water resourcesis a main regulation approach for human beings to de-velop and utilize water resources sustainably. It is thecore work of management of water resources. Withthe continuous deepening of management of water re-sources, the concept of allocation of water resources be-comes increasingly clarified[1]. The optimal allocationof water resources refers to transfer and allocation ofspace and time of limited water resources through en-gineering or non-engineer measures within river basinor a specific region by following natural sustainabledevelopment principles. Under the precondition that

Received date: 2012-09-07Foundation item: the National Natural Science Founda-

tion of China (No. 40839902)∗E-mail: quguodong@163.com

the ecological environment is not influenced, it aimsat satisfying the water consumption demands of eachregion, promoting the sustainable and stable develop-ment of river basin and regional economy, and assuringa healthy, stable and ecological environment[2].

The main train of thought for the study of optimalallocation of water resources is to build an optimiza-tion model with multiple objectives, multiple water re-sources and multiple users. The scheme for optimalallocation of water resources is obtained through themodel solution in order to realize the reasonable allo-cation of water resources. However, the optimal allo-cation model of water resources usually features highdimension, high nonlinearity and other uncertainties.These all make the model optimization relatively com-plicated. As a result, the intelligent optimization algo-rithms are widely used in the model solution. Such asHuang et al.[3] proposed the multi-objective chaotic op-timization algorithm for deployment of water resources.The multi-objective property is coupled with the er-godicity of chaos and magnifies the chaos series engen-dered by logistic mapping to the feasible range, andseeks the best result by comparison and iterative cal-culation. Hou et al.[4] established the multi-objective

J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640 635

fish-ant colony algorithm in accordance with the in-tegration of pheromone positive feedback of the antcolony optimization and fast track change and jump-ing out of local extremum of the artificial fish-swarmalgorithm. Sun et al.[5] proposed the multi-objectivewater resources optimization model based on the the-ory of large scale system general optimization, and ap-plied the mixed genetic simulated annealing algorithmto solve the model.

As an efficient and parallel optimization method,particle swarm algorithm is capable of realizing thesearch and analysis of the optimal solution in a com-plicated space. It is suitable for solving nonlinear,non-differential and multi-objective complicated opti-mal problems. However, the degree of optimizationcannot be assured and it is vulnerable to sink into lo-cal optimum. Besides, it has relatively significant de-pendence on initial population. Based on the studiesof the formers, this paper builds an optimal allocationmodel of regional water resources, combines the charac-teristics of particle swarm algorithm and immune evo-lutionary algorithm (IEA), and utilizes particle swarmalgorithm solution module based on IEA so as to fi-nally obtain the scheme for optimal allocation of waterresources.

1 Optimal Allocation Model of RegionalWater Resources

1.1 Objective Function

Currently, China is in a quick economic developmentstage. The promotion of better and quicker growth ofregional economy is still a short-term objective for re-gional development. During economic development, thesocial problems and ecological environmental problemsbrought by shortage of water resources and increasinglydeterioration of water environment have drawn growingattention from people. Therefore, it has become an ob-jective of optimal allocation of regional water resourcesso as to realize scientific development and coordinateddevelopment of regional economy, society and environ-ment as well as give equal consideration to social andenvironmental benefits, maximize the overall benefitsgenerated by water consumption and keep the coordi-nated and sustainable development of the system whileconsidering the economic development.

Three objective functions are selected in this paper.

(1) Economic objective. Maximize the economic ben-efits generated by regional water consumption.

Since Zhoukou is still in a relatively backward re-gion, the development of economy and the improve-ment of people’s living standards are still local priori-ties. Therefore, the allocation of water resources shallaim at maximizing the economic benefits generated by

the water consumption:

max f1(x) =110

Ks∑

k=1

J∑

j=1

Ir∑

i=1

b(k)ij x

(k)ij , (1)

where, Ir, J and Ks refer to the total numbers of re-gional water resources, regional water users and subar-eas, respectively; x

(k)ij in unit km3/a refers to the output

of supplying water provided by water resource i to userj in subarea k; b

(k)ij in unit Yuan/m3 refers to benefit

coefficient of unit output of supplying water providedby water source i to user j in subarea k.

(2) Social objective. Minimize the total regional wa-ter deficiency. And the regional water resources shallbe balanced as much as possible.

Social benefit is an objective difficult to measure. Ifconsidered from the influence of water resources on soci-ety, it can be regarded the dimension or degree of waterdeficiency which directly influences the social develop-ment and stability. It is a reflection of social benefit.Therefore, the minimum regional total water deficiencycan be used to reflect the social benefit objective in anindirect way:

min f2(x) =110

Ks∑

k=1

J∑

j=1

[D

(k)j −

Ir∑

i=1

x(k)ij

], (2)

where D(k)j in unit km3/a refers to total water demand

of user j in subarea k.(3) Ecological environmental objective. Minimize the

discharge of important pollutants in the region:

min f3(x) =Ks∑

k=1

J∑

j=1

d(k)j p

(k)j

(Ir∑

i=1

x(k)ij

)(3)

where d(k)j in unit µg/L refers to the content of impor-

tant polluting factors in the unit wastewater dischargeof user j in subarea k, and p

(k)j refers to the sewage

discharge coefficient of user j in subarea k.1.2 Constraint Conditions

Water volume restraints can be classified into wa-ter supply restraint and water demand restraint. Theformer guarantees that the water volume distributedby different water supply resources to different users ineach subarea does not exceed water volume that canbe provided by such water resources. The water de-mand restraint guarantees the water demands of differ-ent users.

(1) Formulate the restraint of water volume thatcan be supplied by public water source or independent

636 J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640

water resource:Ks∑

k=1

J∑

j=1

x(k)cj � Wc

Ks∑

k=1

J∑

j=1

x(k)ij � W

(k)i

⎫⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎭

, (4)

where, x(k)cj in unit km3/a refers to the water volume

provided by public water resource c to user j in subareak; Wc in unit km3/a refers to the water volume thatcan be supplied by public water source c; W

(k)i in unit

km3/a refers to the water volume that can be suppliedby independent water source i in subarea k.

(2) Formulate the restraint of user water demandcapacity:

G(k)j,min �

I∑

i=1

x(k)ij +

C∑

c=1

x(k)cj � G

(k)j,max, (5)

where, I refers to the total number of independent wa-ter resource; C refers to the total number of publicwater resource; G

(k)j,min in unit km3/a refers to the min-

imum water demand of user j in subarea k; G(k)j,max in

unit km3/a refers to the maximum water demand ofuser j in subarea k.

(3) Formulate the restraint of water volume that canbe supplied by independent water source. Since theconsumption of groundwater in Zhoukou is relativelysignificant, the restraint of groundwater volume thatcan be supplied is formulated as follows.

The total groundwater volume used by different usersin different subareas shall not exceed the groundwatervolume that can be supplied in each level year:

Ks∑

k=1

J∑

j=1

x(k)j � W (k), (6)

where, x(k)j refers to the groundwater volume of super-

ficial layer supplied to user j in subarea k; W (k) refersto the total water supply of groundwater in superficiallayer of subarea k.

(4) Formulate the restraint of discharge of importantpollutants in the region:

Pn =Ks∑

k=1

J∑

j=1

d(k)j p

(k)j

(Ir∑

i=1

x(k)ij

)� Pn0, (7)

where, Pn in unit kg/a refers to annual discharge of thenth important pollutant factor in regional sewage dis-charge of planning level year; Pn0 in unit kg/a refers tothe maximum allowable load (capacity of water envi-ronment) of the nth important pollutant factor in theregional sewage discharge in planning level year.

(5) Variable non-negative restraint is also a factor.

2 Particle Swarm Optimization (PSO)

2.1 Basic Principles of PSOPSO is a new global optimization algorithm proposed

by Eberhart and Kennedy[6-7] when studying the grouphunting of birds in 1995. Population is a basic unit as it-eration evolution. Each particle corresponds to a poten-tial solution of optimization problem with certain posi-tion and speed. The particle keeps changing position inthe solution space to continuously increase the functionfitness valve until the optimal position is found[8]. Theparticle flies at a certain speed in the space and grad-ually moves to the optimal position. The movementposition and speed are determined by two extreme val-ues, i.e. individual extreme value and global extremevalue.

Set the position of particle as x, and speed as v.Then, the evolution equation of PSO algorithm can bedescribed as

vi(k + 1) = wvi(k) + c1r1[xPBi (k) − xi(k)]+

c2r2[xGBi (k) − xi(k)], (8)

xi(k + 1) = xi(k) + vi(k + 1), (9)

where, subscript i refers to particle index; superscriptPB and GB refer to individual extreme value and globalextreme value, respectively; w refers to inertia weightcoefficient with the value range of 0.4—0.9; k refers tothe iterative algebra; c1 and c2 refer to acceleration con-stants; r1 and r2 are evenly distributed random num-bers between 0 and 1.2.2 Problems and Solutions of PSO Algorithm

During the operation of PSO algorithm, if a parti-cle finds a currently optimal position, other particleswill quickly get close to this particle. If this position isthe local optimum, the particle swarm will be unableto search in the solution space again. Therefore, thealgorithm can easily sink into local optimum. Besides,the convergence rate of the algorithm will become slowsince the particle can easily lose diversity in the laterstage[9]. Currently, the genetic algorithm is also appliedor inertia weight is selected to solve the insufficiency ofPSO algorithm. However, since the variation methodand parameter selection are determined by experience,genetic algorithm is vulnerable to the phenomena ofprematurity and convergence[10]. Zhang et al.[8] pro-posed methods like self-adaption index inertia weightcoefficient, thus obviously improving the performanceof PSO algorithm. However, such methods cannot trulyreflect the complicated and nonlinear changing charac-teristics during operation process. The IEA convergesto global optimal solution with the probability of 100%and it seldom relies on people’s experience. Combiningthe characteristics of PSO and IEA, this paper proposesPSO algorithm based on IEA to fully utilize the global

J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640 637

search capacity of IEA for global search and contin-uously optimizes the best individuals obtained as theinitial solution of particle swarm algorithm so as to ob-tain the optimal solution.

3 Basic Principle of IEA

IEA is an optimization method developed based onthe principles of immunity system thanks to the bio-logical immunity mechanism. The core of IEA lies inthe full utilization of information of the best individu-als and the replacement of the evolution of groups withthe evolution of the best individuals. The local searchand global search are combined in an organic way dur-ing evolution through the adjustment of standard de-viation. The realization approach of this algorithm isintensively reflected in the preservation and reproduc-tion of the best individuals and the dynamic adjustmentof standard deviation. Compared with other existingevolutionary algorithms, IEA features high search effi-ciency, invulnerability to local optimum, etc.

4 Implementation of PSO Algorithmin Optimal Allocation of Water Re-sources Based on IEA

4.1 Establishment of Fitness FunctionAll individuals in the colony are adopted to sort the

superiority of different objective functions so as to cal-culate the total fitness according to the characteristicsof multi-objective optimal allocation of water resources.One particle in IEA-PSO algorithm refers to a waterdistribution scheme, and each scheme reflects multipleobjective function values. Use Z(i) (i = 1, 2, · · · , n) torepresent objective function (n refers to total number ofobjectives), and N to represent the total number of par-ticle individuals. As for each objective i, all individualswill generate a feasible collating sequence according tothe superiority of function value of this objective. Af-ter each objective is sorted, the general performance ofindividuals for all objective functions can be obtained.The fitness can be calculated according to the individ-ual sorting:

Fi(Xj) =

{[N − Yi(Xj)]2, Yi(Xj) > 1

aN2, Yi(Xj) = 1, (10)

F (Xj) =n∑

i=1

Fi(Xj), (11)

where, Xj refers to the jth individual in the colony; Yi

is the serial number obtained after superiority sortingof all individuals in the colony for object i; Fi(Xj) rep-resents the fitness of Xj for objective i, while F (Xj)refers to the comprehensive fitness obtained by Xj forall objectives; a is a constant between the interval of

(1, 2) and is used to increase the function value of in-dividual and reflect the fitness upon optimization.4.2 Particle Coding

According to the characteristics of the optimizationmodel established in this paper, set the particle H asthe water supply x

(k)ij from the ith water source to sector

j (= 1, 2, · · · , J) of subarea k. One particle adopts atwo-dimensional array for coding, i.e.

H =

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

x(1)11 · · · x

(1)1J

......

x(1)i1 · · · x

(1)iJ

x(2)(i+1)1 · · · x

(2)(i+1)J

......

x(K)I1 · · · x

(K)IJ

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, (12)

where H refers to the calculated particle.The particle codes with this form adopted have di-

rectly reflected the allocation of each water sourceamong sectors. The actual utilization condition of acertain water source can be obtained by adding valuesin a certain row, and the actual water distribution ofrelevant sectors in a certain column in a certain sub-area can be obtained by adding the values in a certaincolumn within the range of this subarea.4.3 Combination of IEA-PSO Algorithm

The best individual (antibody) in IEA is the feasi-ble solution with the highest fitness in each generation.When antigen intrudes, the matched antibody will beexcited (immune response) to make sure the usable an-tibody to be preserved once generated. The elite reten-tion strategy has been implemented in the algorithm,and the information of the best individual in each gen-eration is fully utilized.

The best individual in IEA is taken as the neighbor-hood extreme value in the particle swarm colony, andthe initial speed of each particle is determined accord-ing to the difference of each particle and neighborhoodextreme value in the particle swarm. Then, the parti-cle swarm algorithm is utilized again to conduct localsearch so as to accelerate the convergence speed in thelate stage of algorithm.4.4 Implementation Steps

Step 1 Take Eqs. (1)—(3) as objective functionsof optimal allocation of regional water resources. Theconstraint conditions are shown in Eqs. (4)—(7).

Step 2 Initialize the colony in IEA, set parametersin the algorithm�and randomly generate initial waterresource distribution population x(0).

Step 3 Take Eq. (11) as fitness function to conductfitness evaluation on each individual in the populationand also make the individual in x(0) with the highestfitness as xdbest(0).

638 J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640

Step 4 Conduct evolutionary operation for each in-dividual xi(k) in x(k). Generate filial-generation colonyin the solution space.

Step 5 Calculate the fitness of each filial gen-eration, determine the best individual xdbest(k + 1),and determine whether the parent generation or filialgeneration shall be selected according to its size. IfE[xdbest(k + 1)] > E[xdbest(k)], select the best indi-vidual as xdbest(k + 1). Otherwise, xdbest(k) will beselected as the best individual.

Step 6 If k+1 has already reached the preset evolu-tionary algebra, stop and record the individuals xk(m)generated in each generation. Otherwise, put k = k +1and go to Step 3.

Step 7 The best value xk(m) of M individuals gen-erated in IEA is taken as the initial particle of particleswarm algorithm. Besides, the speed of each particlewill be initialized, and the fitness of particles will becalculated to pick up the best particles.

Step 8 Update the speed and position of the parti-cle. As the first updating of initial particle, the individ-ual optimization is the particle itself. Later, the finalpoint that this particle has gone through during themovement in solution space will be adopted. Duringthe updating process, if the speed calculated exceedsthe maximum speed, revise it to the maximum speed;if the position of a certain dimension of particle exceedsthe generation space of initial particle, the position ofthis dimension of the particle is set as the relevant ex-treme value of generation space of this dimension.

Step 9 Judge if the updated particles satisfyEqs. (4)—(7). If they fail to satisfy these formulas, se-lect a group of particles again.

Step 10 Calculate the fitness of particles updatedcompare, select and record the individual optimal po-sition and global optimal position of the particle.

Step 11 Judge if the maximum iteration times aresatisfied. Exit from cycle and output optimal solutionif yes. Otherwise, return to Step 8.

5 Case Analysis

5.1 Overview of Study AreaLocated in southeast of Henan province, Zhoukou

covers an area of 1.19 × 1010 m2 (farmland: 8.26 ×109 m2) with a population of 10.90 million. It ad-ministers eight counties, one city, one district and oneprovincial economic development zone. Zhoukou fea-tures flat terrain and fertile land. It is an importantgrain, cotton, edible oil, meat, egg, and milk produc-tion base of China and is thus known as “Granary ofCentral Plains”; the grain output of Zhoukou reached7.235× 108 kg in 2010, ranking the first place in Henanprovince. The average total water resources of Zhoukouover the years are 2.610× 108 m3. The water resourcesper capita in Zhoukou reaches 244m3, which is 48.8%

of the average water resources per capita of Henanprovince, i.e. 500m3; the water resources per squaremeter is only 0.31m3 which is 51.6% of the average wa-ter resources per square meter of Henan province, i.e.0.59m3. Therefore, Zhoukou is a region seriously lackof water resources.

In recent years, due to the acceleration of construc-tion of Central Plains Economic Region and the con-tinuous promotion of urbanization, the shortage of wa-ter resources in Zhoukou has become increasingly obvi-ous, especially the water quality-induced water short-age which comes to front together with the aggrega-tion of water pollution and water environmental prob-lems. Various problems triggered by water resourceshave restrained the economic development in a veryeye-catching way. The quantity and quality of wa-ter resources are no longer capable of undertaking thesustainable development of local economy and society.Therefore, it is very urgent to allocate the limited wa-ter resources in this region in a more scientific and rea-sonable way so as to maximize the overall benefits ofutilization of water resources.5.2 Solution of Optimal Allocation of Regional

Water Resources Based on IEA-PSOTen counties and cities of Zhoukou are divided into

ten subareas in this paper according to administrativeareas. With 2010 as the benchmark year, a multi-objective water resource optimal allocation model is es-tablished. The optimal allocation of water resources of2 categories of water sources (surface water and ground-water) and 4 water consumption sectors (industrial wa-ter consumption, agricultural water consumption, liv-ing water consumption and ecological water consump-tion) has been analyzed under the guarantee rate of50% in two planning level years, i.e. 2015 and 2025.Table 1 shows the optimal allocation results in 2015and 2025.

(1) It is discovered through the comparison of solu-tion of PSO algorithm that IEA-PSO algorithm con-sumes more time than PSO algorithm, for it takes arelatively long time for IEA-PSO algorithm to calculatethe initial feasible solution. However, after generationof initial feasible solution, the evolutionary efficiencywill be greatly improved. The water resource alloca-tion scheme solved by using IEA-PSO algorithm cangive more consideration to ecological benefits since theintroduction to the principles of immunity comparedwith PSO. For example, the ecological water consump-tion of 2015 is 9.850×106 m3, which is higher than thatof PSO scheme (7.540×106 m3). Therefore, bigger eco-logical benefit can be obtained. Under the conditionthat the water volume that can be supplied remainsunchanged, the regional water shortage in the alloca-tion scheme obtained by using IEA-PSO algorithm isless than that obtained by using PSO algorithm. Forexample, the water shortage in the scheme obtained by

J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640 639

Table 1 Results of optimal allocation of water resources of Zhoukou with 50% of guarantee rate in 2015and 2025 (108 m3/a)

SubareaCategory of

water source

Industry Agriculture Living Ecology

2015 2025 2015 2025 2015 2025 2015 2025

Downtown Surface water 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.051 6 0.096 7

Groundwater 0.404 8 0.725 4 0.098 7 0.062 6 0.258 8 0.202 1 0.000 0 0.000 0

Xiangcheng Surface water 0.325 2 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.009 7 0.014 2

Groundwater 0.343 0 0.985 1 1.185 7 1.035 5 0.316 2 0.338 5 0.000 0 0.000 0

Fugou County Surface water 0.134 8 0.235 7 0.000 0 0.000 0 0.000 0 0.000 0 0.005 2 0.007 9

Groundwater 0.089 9 0.157 1 0.840 1 0.764 0 0.183 6 0.219 5 0.000 0 0.000 0

Xihua County Surface water 0.157 6 0.246 7 0.000 0 0.000 0 0.000 0 0.000 0 0.002 1 0.003 2

Groundwater 0.105 0 0.164 4 1.410 2 1.032 9 0.217 5 0.158 6 0.000 0 0.000 0

Shangshui County Surface water 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.003 8 0.006 5

Groundwater 0.224 5 0.361 7 0.703 4 0.807 7 0.280 7 0.165 7 0.000 0 0.000 0

Taikang County Surface water 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.005 6 0.009 9

Groundwater 0.356 3 0.550 9 2.018 0 1.164 8 0.336 0 0.230 5 0.000 0 0.000 0

Luyi County Surface water 0.390 8 0.453 3 0.000 0 0.000 0 0.000 0 0.000 0 0.004 7 0.007 3

Groundwater 0.260 6 0.673 4 1.349 2 0.772 7 0.315 6 0.180 4 0.000 0 0.000 0

Dancheng County Surface water 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.006 3 0.010 4

Groundwater 0.646 3 1.187 6 1.948 7 1.439 1 0.289 7 0.163 0 0.000 0 0.000 0

Huaiyang County Surface water 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.003 9 0.006 8

Groundwater 0.283 1 0.425 9 2.217 1 2.856 2 0.284 6 0.349 6 0.000 0 0.000 0

Shenqiu County Surface water 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.000 0 0.005 6 0.008 3

Groundwater 0.316 5 0.551 5 1.331 8 0.841 3 0.172 9 0.220 8 0.000 0 0.000 0

using PSO algorithm is mainly distributed in agricul-ture and living. The water shortage is 2.654 3×108 m3.The water shortage in the scheme obtained by usingPSO algorithm is 4.054 2 × 108 m3. Therefore, as fortotal water shortage and water shortage distribution,the allocation scheme obtained by using IEA-PSO al-gorithm is superior to PSO allocation scheme.

(2) If analyzed from the water consumption source,the main water consumption source of Zhoukou ismainly groundwater in 2015 and 2025. The agricul-tural water consumption and living water consump-tion in each subarea of Zhoukou are from groundwa-ter, for the water resources of Zhoukou are relativelyinsufficient while the groundwater is relatively abun-dant. Therefore, groundwater is mainly used to assurethe local water consumption demand. The ecologicalwater demands in 2015 and 2025 are mainly suppliedby using surface water. It is also for the protection andreasonable use of groundwater resources.

(3) If analyzed from the water consumption struc-ture, the industrial water consumption has grown veryquickly from 2.776 3×108 m3 in 2010 to 4.038 4×108 m3

in 2015 and 6.718 7 × 108 m3 in 2025 due to the rapideconomic development and continuous expansion of in-dustrial scale. However, with the optimization and ad-

justment of industrial structure, the ratio of primaryindustry has dropped gradually. Meanwhile, with thepromotion of water saving techniques in agriculture,the agricultural water consumption presents a decliningtrend from 1.418 4×108 m3 in 2010 to 1.310 3×108 m3 in2015 and 1.077 7× 108 m3 in 2025. Since the ecologicalenvironment draws increasingly attention from people,the ratio of ecological water consumption has also beenincreased gradually in order to enhance the compre-hensive benefits of water consumption. The ecologicalwater consumption has increased from 6.540 × 106 m3

in 2010 to 9.850× 106 m3 in 2015 and 1.712× 107 m3 in2025.

(4) IEA-PSO algorithm is used to solve the alloca-tion issue of regional water resources. The diversityof population in the initial evolutionary stage of PSOis relatively favorable. The evolutionary processes oftwo algorithms are almost consistent. However, withthe promotion of evolution, the phenomenon of con-vergence of the best individual occurs relatively earlierin PSO algorithm due to the decline of population di-versity. In IEA-PSO algorithm, due to the functionof immune self-regulation mechanism, the diversity ofpopulation has been maintained in a favorable man-ner. Meanwhile, the premature convergence of the best

640 J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(5): 634-640

individual hasn’t taken place. Instead, it continuouslyapproaches the optimal solution of the problem to besolved. Furthermore, the immune component drawn inthe late stage of evolution has already approached theequipotential component of optimal solution, and theimmunization effect becomes increasingly good, whichhas a certain promoting effect on the improvement ofconvergence precision of IEA-PSO algorithm and ac-celeration of the convergence speed in the late stage ofalgorithm.

6 Conclusion

The optimal allocation of regional water resources is amain approach to solve the shortage of water resources.This paper has introduced IEA in particle swarm algo-rithm and fully utilized the global search characteris-tics of IEA and local search capacity of particle swarmalgorithm to solve the defects of PSO including the de-pendence on initial population and vulnerability to lo-cal optimum. The study of optimal allocation of waterresources has been carried out on Zhoukou, a city se-riously lack of water, to obtain a practical and feasiblewater resource allocation scheme with the combinationof the actual local conditions. The results indicate thatthe PSO algorithm based on IEA proposed in this pa-per can better solve various kinds of multi-objectiveand multi-constraint complicated nonlinear optimiza-tion problems. The optimization results are obviouslybetter than those obtained by using regular PSO algo-rithm, thus providing a new high-efficiency method forthe optimal allocation of regional water resources.

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