multi-objective waste load allocation model for optimizing waste load abatement and inequality among...

Multi-objective Waste Load Allocation Model for OptimizingWaste Load Abatement and Inequality Among WasteDischargers

Jae Heon Cho & Jong Ho Lee

Received: 10 October 2013 /Accepted: 29 January 2014# Springer International Publishing Switzerland 2014

Abstract In allocating the waste load of a river basin,the first priority is to achieve a given water quality goalfor that river by utilizing several water quality manage-ment methods. Minimizing the waste load abatementcost within the river basin through appropriate, efficientwater quality management is an important aspect of thisprocess. In the past, it was common to concentrate oneconomic factors when constructing a waste load allo-cation (WLA) model. However, environmental re-sources (e.g., sub-basin area, population, wastewaterflow, etc.) vary in each region of a river, and the fairnessin the distribution of the treatment efforts among wastedischargers must be considered. TheWLAmodel in thisstudy was constructed as a multi-objective optimizationproblem and was established to achieve the economicgoal of minimizing waste load abatement and to consid-er the inequality among waste dischargers. Two types ofinequality were introduced into the WLA model. Thefirst type is the inequality in the waste load dischargeregarding the environmental resources in each regionwas computed with the environmental resource-basedGini coefficient. The second type of inequality is the

fairness in the distribution of the treatment effortsamong waste dischargers. The suitability of this WLAmodel was verified with its application in a heavilypolluted total maximum daily load subject river inSouth Korea. Furthermore, Pareto-optimal solutionsdrawn from the multi-objective genetic algorithm wereanalyzed to infer the least cost solution, the least in-equality solution, and the compromise solutions and toverify critical pollution sources.

Keywords WLA . Inequality . ER-Gini .Multi-objective genetic algorithm . Pareto-optimal solutions .

Critical pollution sources

1 Introduction

The control of the water quality in large river basins withextensive pollution requires effective waste load alloca-tions. In the past, the main objective of waste loadallocation (WLA) was to minimize the waste load abate-ment and wastewater treatment cost, thereby achievingeconomic efficiency. In this article, the term “waste loadabatement” refers to the amount of reduction of wasteloading that is proposed, and the term “allocation” refersto the amount of reduction in loading that will be re-quired. The optimization problem of such WLA modelswas interpreted using optimization techniques such aslinear programming (Arbabi and Elzinga 1975), integerprogramming (Burn 1989), nonlinear programming(Fujiwara 1990), and dynamic programming(Klemetson and Grenny 1985). Recently, genetic

Water Air Soil Pollut (2014) 225:1892DOI 10.1007/s11270-014-1892-2

J. H. Cho (*)Department of Health and Environment, KwandongUniversity, Naegok-Dong, Gangneung, Gangwon-Do210-701, South Koreae-mail: [email protected]

J. H. LeeDepartment of Urban Planning, Cheongju University,Daeseongro, Sangdang-Gu, Cheongju, Chungbuk 360-764,South Korea

algorithms (GAs) (Gen and Cheng 1997; Goldberg1989) have been applied to waste load allocation in riverbasins (Burn and Yulianti 2001; Cho et al. 2004;Kerachian and Karamouz 2007). Burn and Yulianti(2001) developed an optimization model that interpretsthe waste load allocation problem with a GA. The trade-off curves developed for the multi-objective optimiza-tion problem can be used by a water quality agency toidentify an appropriate solution for implementationwhile considering the conflicting objectives inherent tothe problem. Cho et al. (2004) developed a water qualitymanagement model that minimizes the cost of wastewa-ter treatment within a river basin by integrating a GAand the QUAL2E water quality model. Kerachian andKaramouz (2007) demonstrated the methodology ofcombining a water quality simulation model with astochastic GA-based optimization model to generateimproved operational strategies for water quality man-agement in reservoir–river systems.

Most of these optimization techniques have focusedon optimization problems for a single objective func-tion, and even in the case of a multi-objective function,optimization problems have been constructed with theabove-listed optimization techniques by transformingthe multi-objective function into single-objective func-tions with weighted values. A single-objective optimi-zation problem searches for a unique optimal solutionfrom among numerous feasible solutions. A multi-objective optimization problem, in contrast, generallysearches for a set of trade-off solutions involving a largenumber of optimal solutions, providing a trade-off curveknown as the Pareto front (Singh and Chakrabarty2010). To overcome potential drawbacks (such as thehigh computational complexity of nondominatedsorting, a lack of elitism, and the need to specify asharing parameter) of the earlier nondominated,sorting-based, multi-objective evolutionary algorithms,the computationally fast, elitist, Nondominated SortingGenetic Algorithm-II (NSGA-II) was proposed (Bashi-Azghadi and Kerachian 2010; Deb 2001; Murty et al.2006a, b). This algorithm uses the crowding techniqueto ensure diversity among nondominated solutions.This method is computationally efficient and is capableof finding a good spread of Pareto-optimal solutions(Deb 2001; Murty et al. 2006b). NSGA-II has beenfurther modified using the concept of jumping genes,and the new algorithm, called NSGAII-JG, has beenfound to more rapidly converge to the Pareto solution(Kasat and Gupta 2003; Sankararao and Gupta 2007).

More recently, another adaptation of the jumping gene,NSGA-II-aJG, has been developed by Bhat et al.(2006). This fixed-length, JG adaptation convergesmore rapidly than the more random NSGA-II-JG(Khosla et al. 2007). In the multi-objective optimizationproblem of the present study, Pareto-optimal solutionswere obtained with NSGA-II-aJG (Guria et al. 2005;Ramteke and Gupta 2009).

Several recent studies have generated optimizationsolutions to WLA problems by utilizing the afore-mentioned multi-objective evolutionary algorithmNSGA-II. Murty et al. (2006a, b) constructed amulti-objective optimization problem to minimize thetotal cost of wastewater treatment and the inequitymeasure among the waste dischargers. The inequitymeasure is calculated by summing the results of thefollowing calculation for each point in the basin: thelevel of waste removal at a given point divided by theaverage amount of waste removed from the entirebasin minus the level of waste added at a given pointdivided by the average amount of waste input into theentire basin.

The probabilistic nature of river flow and water qual-ity has been incorporated into manyWLAmodels. Burnand McBean (1985) and Fujiwara et al. (1986) appliedchance-constrained programming to a WLA optimiza-tion problem to convert the probabilistic constraints totheir deterministic equivalents. Kerachian andKaramouz (2007) used a stochastic form of the Nashbargaining theory to incorporate the utility functions ofdecision-makers/stakeholders that are related to thequantity or quality of water in a reservoir–river system.Ghosh and Mujumdar (2006) performed a first-orderreliability analysis and Monte–Carlo simulations tocompute the fuzzy risk of low water quality and usedfuzzy multiobjective programming for risk minimiza-tion in a river water quality management problem. Liuet al. (2008) applied a Bayesian model using theMarkovchain Monte Carlo sampling method to estimate theload and the respective parameters in river water qualitymodeling.

A total maximum daily load (TMDL) was conductedon water quality management for four large rivers inKorea. The TMDL is applied to achieve water qualitygoals that are established at target points, which repre-sent the boundaries between local governments. Theallowable waste load in each sub-basin to achieve thegoal must be estimated. The target water quality param-eter was the biochemical oxygen demand (BOD), and

1892, of 17 Water Air Soil Pollut (2014) 225:1892

the standard flow in the WLA for the TMDL was fixedat Q275 low flow (i.e., stream flows of 275 days are notless than this flow). The probabilistic nature of the flowand the water quality are not considered in the WLA inthe Korean TMDL.

The main task of the WLA in the TMDL is tooptimize economic efficiency while maintaining theequality of the pollution discharge for each region.This study utilizes the Gini coefficient, which representsincome inequality and considers the variation in envi-ronmental resources in each region to maintain equalityamong the waste load discharges. Recently, the Ginicoefficient has been applied in various fields concerningresources and the environment. Druckman and Jackson(2008) expanded the range of applications of the Ginicoefficient and developed AR-Gini, an inequality indextailored to resource utilization. AR-Gini is an index thatevaluates the inequality of consumption of a certainproduct among neighboring regions. Heerink et al.(2001) analyzed the correlation between individual in-come and environmental degradation by utilizing theEKC (environmental Kuznets curve). The environmen-tal parameters that were considered included SO2,suspended particulate matter, CO2, and depletion of soilnutrition in Sub-Saharan Africa. The Gini coefficientwas used to estimate the total impact of income inequal-ity on the environment. Jacobson et al. (2005) surveyedthe distribution of residential electricity consumption infive nations to calculate the Gini coefficient for energyconsumption and to estimate energy equity. White(2007) conducted research on the global distribution ofecological footprints by utilizing the Atkinson index anda Gini coefficient of energy, food, forest land, and built-up land. Sun et al. (2010) introduced an environmentalGini coefficient (EGC) into a WLA model to considerthe inequality of environmental resources. The EGCwas based on multiple criteria, including land area,population, GDP, and water environmental capacity,and it was applied to a COD allocation within a water-shed. As a result, the EGC method was verified as anappropriate decision-making tool in environmentalmanagement to ensure a balance between environmentalequality and efficiency. In their study, waste load allo-cation was treated as a single-objective optimizationproblem aiming to minimize the total EGC within abasin. An objective function regarding the economicefficiency of waste load abatement was not considered.Furthermore, the constraints on the river water qualitygoal were not established.

In addition to the inequality in the waste load dis-charge using the Gini coefficient, the fairness in thedistribution of the treatment efforts among waste dis-chargers (Burn and Yulianti 2001; Murty et al. 2006a,2006b) is also important in the WLA. The optimizationproblem in this study not only considered the economicefficiency goal of minimizing the waste load abatementbut also the objective function used to represent thesetwo inequalities. Therefore, two WLA models using amulti-objective genetic algorithm were developed tooptimize the waste load abatement within the entirebasin and to maintain equality among different regions.This model utilizes the NSGA-II-aJG to calculate themulti-objective optimum solutions.

2 Methods

2.1 Establishing WLA Model Using a Multi-objectiveGenetic Algorithm

2.1.1 Inequality Measures

The multi-objective waste load allocation model includ-ed two inequality measures: the environmentalresource-based Gini coefficient (ER-Gini) inequalityand the inequality in the waste load abatement. Theinequality of environmental resources was included asone of the objective functions in this study’s first multi-objective optimization problem, and the environmentalresource-based Gini coefficient (ER-Gini) was used tocalculate the index of inequality. The environmentalresources with currently available data used in the cal-culation of inequality were the sub-basin area and thewastewater flow in the sub-basins. The calculation ofthe ER-Gini was based on the Gini coefficient calcula-tion methods of Lerman and Yitzhaki (1985) with thewaste load discharge data regarding the environmentalresources at each sub-basin.

The ER-Gini calculation method was integrated withthe multi-objective genetic algorithm (MOGA) and wasthen written as a program. The ER-Gini coefficient forthe waste load discharge inequality can be derived direct-ly from the following formula for the mean differences inthe Gini coefficient (Boisvert and Ranney 1991):

ER−Gini ¼ 1

μ

Za

b

F yð Þ 1−F yð Þ½ �dy ð1Þ

Water Air Soil Pollut (2014) 225:1892 of 17, 1892

where y is the waste load discharge in each sub-basin (a≤y≤b), F(y) is the cumulative distribution, and μ is meanwaste load discharge. Through integration by parts andvariable transformations, the above equation becomes thefollowing:

ER−Gini ¼ 2 cov y; F yð Þ½ �μ

ð2Þ

The objective functions of the second multi-objectiveoptimization problem included the inequality measureof the fairness in the distribution of the waste loadabatement, which is similar to the fairness in the distri-bution of treatment efforts and the associated cost pro-posed by Burn and Yulianti (2001). The inequality isgiven as follows:

Inequality in waste load abatement ¼ WiXm

i¼1Wi

−X iXm

i¼1X i

��

ð3Þ

where m is the number of pollution sources (i.e., sub-basins, WWTPs, and tributaries), Wi is the waste loaddischarge of the pollution source i, and Xi is the wasteload abatement of the pollution source i.

2.1.2 Multi-Objective Waste Load Allocation ModelFormulation

The following multi-objective optimization problemwas established to achieve the economic goal of mini-mizing the waste load abatement and to consider theequality of the waste load discharge and the waste loadabatement for each region. Equation 4 is the objectivefunction minimizing the total waste load abatement inthe basin. Equation 5 is the objective function minimiz-ing inequality, in other words, minimizing the total ER-Gini for each environmental resource. Equation 6 is theobjective function that minimizes the inequality in thewaste load abatement among the waste dischargers.Equation 7 is a constraint equation regarding the mini-mum and maximum limits of the waste load abatementfor each pollution source. Equation 8 is a constraintequation regarding the attainment of the water qualitygoal. In the first multi-objective allocation model inwhich the ER-Gini inequality is considered, Eqs. 4 and5 are used as the objective functions. In the secondmulti-objective allocation model in which the fairnessin the distribution of the waste load abatement is

considered, Eqs. 4 and 6 are used as the objectivefunctions.

MinimizeXi¼1

m

X i ð4Þ

MinimizeXj¼1

l

ER−Gini j ð5Þ

MinimizeXm

i¼1

WiXm

i¼1Wi

−X iXm

i¼1X i

�� ð6Þ

Subject to:

Umini≤X i≤Umaxi i ¼ 1; 2;…;m ð7Þ

Xk j

i¼1Tij X i ≤ ⊿C j j ¼ 1; 2;…; n ð8Þ

where

l No. of environmental resourcesm No. of pollution sourcesn No. of target points for TMDLXi Waste load abatement of pollution source i,

in kilograms per daykj No. of pollution sources until point jTij The transfer coefficient (water quality

variation of point j caused by the pollutionsource i), (milligrams per liter)/(kilogramsper day)

ΔCj The difference between the water qualitygoal and present water quality at point j, inmilligrams per liter

Umaxi,Umini

The maximum and minimum pollutionload, respectively, at pollution source i, inkilograms per day

The multi-objective optimization models were devel-oped by integrating the optimization problem, i.e.,Eqs. 1 and 2 were used for the ER-Gini inequality, andEq. 3 was used for the inequality of the fairness in wasteremoval and the multi-objective optimization algorithm(NSGA-II-ajG).


2.2 Application of the WLA Model

The subject region of theWLAmodel was the upper andmiddle reaches of the Yeongsan River located in south-western South Korea. The water in this region is con-taminated, and the region is one of the target areas of thegovernment’s TMDL. The target points of the TMDLare Yeongbon A, Yeongbon B, and Whangyong A. Thefirst design period for the TMDL covered 2004–2010,and the target parameter for water quality was the BOD.The river basin map for the study area is shown in Fig. 1,and a schematic diagram of the water quality modelingis shown in Fig. 2. There are 44 point and non-pointsources discharging pollutants into the study area. Thecalculation of the water quality for the WLA usesQUAL2Kw and was introduced in a previous study(Cho 2013). The optimum parameters for multiple

reaches of the Yeongsan River were determined withthe QUAL2Kw model (Pelletier and Chapra 2008;Pelletier et al. 2006), which employs a user-definedauto-calibration function in the rates worksheet. Thetransfer coefficient is calculated with the water qualityvariations of Yeongbon A, Yeongbon B, andWhangyong A, which comply with the level of pollu-tion load abatement in each sub-basin.

Numerous researchers have referred to previous stud-ies and have therefore interpreted the optimization prob-lem with a fixed value for the MOGA parameter.However, other studies have chosen an optimizedMOGA parameter via a sensitivity analysis. The selec-tion of MOGA parameters depends upon the character-istics of the optimization problem, and the MOGAparameters greatly affect the Pareto-optimal solutions.In the present study, the first multi-objective allocation

0 5 10 km

Gwangjucheon

Whangyonggang

Yeongbon AWhangyong A

Yeongbon B

Orecheon

Pyungrimcheon

Gaecheon

Jeongamgang

Pungyoungjeongcheon

Fig. 1 The Yeongsan River Basin study area. This figure shows the upper and middle reaches of the Yeongsan River watershed. The targetpoints of the TMDL in the study area are Yeongbon A, Yeongbon B, and Whangyong A


model in which the ER-Gini inequality is consideredwas used in a sensitivity analysis of the population size,the crossover probability (Pc), the mutation probability(Pm), the length of chromosome (lchrom), the jumpinggene probability (PJG), and the fixed length of the JG(fb). Optimum solutions for each categorywere analyzedin the range of 30–150 for population size; 0.5–0.95 forPc; 1.0/lchrom; 0.005, 0.01, 0.02, and 0.1 for Pm; 1,100,1,320, 1,540, and 1,760 for lchrom; and 0.1–0.95 for PJG.

3 Results and Discussion

3.1 The Sensitivity Analysis of the MOGA Parameter

The two objective functions in the first multi-objectiveWLA in this study minimize the waste load abatementand minimize the ER-Gini inequality. The sensitivityanalysis focused mainly on finding the MOGA param-eter that minimizes the total waste load abatement in thebasin, although the distribution of the optimal solutions

was also considered. The sensitivity analysis of thepopulation size is shown in Fig. 3, and the optimalpopulation size for the WLA was found to be 50.Although the population size was not large, it was fairlywell distributed. Moreover, the optimum WLA resultsfor Pc, Pm, lchrom, PJG, and fb were found at 0.9, 0.005,1320, 0.7, and 25, respectively.

The Pareto-optimal solutions for the increasing gen-eration number are shown in Fig. 4. In Fig. 4, the Pareto-optimal solutions for generation 50 are much betterdistributed than the Pareto-optimal solutions for gener-ation 10, whereas the distribution of the Pareto-optimalsolutions from generation 50 to generation 500 gradu-ally improved. The optimal solutions for generation 500and generation 2,000 were almost identical. Therefore, itcan be concluded that the solutions in generation 2,000converged. The maximum spread value from the resultsfor generation 2,000 was high and was well distributedcompared with the other results. This trend can also beobserved in the box plots (Fig. 5) for the total waste loadabatement and discharge load inequality. As the

Y1

R1 1

2

3

4

5Y2,Y3 6

7 Y4

Y5 8

9

10

11 Y6

12

13

R2 14 Y7,8

15 Y9

Y10 16Y11 17

18 Y12

19Y13 20

21

22

23

24

25

26 Y14

27

28

29 Y15

30 Y16

Y17 31 Y18,Y19

R5 44

45

46

47 Y20

48 Y21

49

50Y22 88Y23 89Y24 90

91 Y25

Y26 92

G3,G4 G2

R4

43 42 41 40 39 38 37 36 35 34 33 32 G1

G5W2 W3 W8 W13

W1 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87

R6 R7 R8W4,W5 W9 W10 W11 W12

W6,W7

W1 Whangyonggang Head Y5 Subukcheon

W2 Deokjincheon Y6 Orecheon

W3 Jangseongcheon Y7 Yeongbon A07

W4 Gaecheon Y8 Jeongamgang

W5 Whangyong A08 Y9 Yeongbon A13,A14

W6 Whangyong A11 Y10 Yeongbon A12

W7 Chewamcheon Y11 Dejeoncheon

W8 Jangseong WWTP Y12 Yongjeoncheon

W9 Dangwangcheon, Dongwhacheon Y13 Yongsancheon, Hakrimcheon

W10 Guryongcheon Y14 Yeongbon B04

W11 Wangdongcheon Y15 Yeongbon B05

W12 Pyungrimcheon Y16 Yeongbon B16

W13 Seobongcheon, Seonamcheon Y17 Pungyoungjeongcheon

G1 Gwangjucheon Head Y18 Gwangju WWTP1-1,2

G2 Donggyecheon Y19 Yeongbon B17

G3 Yeongbon B10 Y20 Mareukcheon, Seochangcheon

G4 Seobangcheon Y21 Songjeongcheon

G5 Geukrakcheon Y22 Yongbon B32

Y1 Yeongbon Head Y23 Gwangju WWTP2

Y2 Yeongbon A03 Y24 Pyungdongcheon

Y3 Yongcheon Y25 Yeongbon B27

Y4 Damyang WWTP Y26 Yeongbon B29

Yeongsan River

W hangyonggang Stream

G wang jucheon Stream

R3

R9

Fig. 2 A schematic diagram for the river water quality modeling.This figure shows nine reaches and 92 computational elements inthe main stream of the Yeongsan River, and the Whangyonggang

and Gwangjucheon streams that were used in the application of thewater quality model. There are 44 point and non-point sourcesdischarging pollutants into the study area


generation number increased, the maximum spread ofthe two parameters gradually increased; the differencebetweenQ2 (median) and mean became smaller, and thedistribution (spacing) grows better. The two box plotsfor generations 500 and 2,000 are almost identical.Therefore, the maximum generation number was con-sidered to be 2,000 in the WLA model. Figure 6 showsthe Pareto-optimal solutions for the increasing genera-tion number obtained using the second multi-objectiveallocation model in which the fairness in the distributionof the waste load abatement was considered. Althoughthe solutions to this model converged more slowly than

those of the first model (Fig. 4), the optimal solutionsaround generation 2,000 were almost identical.

3.2 The WLA Results

The final Pareto-optimal solutions for the waste loadabatement and the ER-Gini inequality for the first ap-plication of the WLA are shown in Fig. 7. The Pareto-optimal solutions were not concentrated in a narrowrange but were well distributed. In the trade-off curve,A is the solution point at which the waste load abate-ment is at a minimum and inequality is at a maximum. B

0.4

0.5

0.6

0.7

0.8

0.9

0 1000 2000 3000 4000 5000

Ineq

ualit

y m

easu

re

Total pollution load abatement (kg/day)

Population size 30

Population size 50

Population size 70

Population size 100

Population size 150

Fig. 3 Sensitivity analysis for the population size using the multi-objective allocation model in which the ER-Gini inequality is considered:Pareto-optimal solutions of the multi-objective WLA are shown for a population size range from 30–150

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ineq

ualit

y m

easu

re


Generation 10

Generation 50

Generation 100

Generation 500

Generation 2000

Fig. 4 Pareto-optimal solutions calculated using the ER-Gini inequality measure for increasing generation numbers: The distributions of theoptimal solutions are compared for generations 10, 50, 100, 500, and 2,000


is the solution point at which inequality is at a minimumand the waste load abatement is at a maximum. Withregard to the distribution of the Pareto-optimal solu-tions, the slope between point A and E is approximately2.5 times larger than the slope between point F and B. Inthe A–E interval, the ratio of the inequality reduction interms of the increase in the waste load abatement ishigher than that in the F–B interval. However, economicefficiency is the primary goal in traditional WLA prob-lems. Thus, the points between A and E are moredesirable than the points between F and B. At point E,the slope of the Pareto-optimal curve changes, andtherefore, point E can be considered to be the appropri-ate WLA solution. Of the solutions between A and E,

the solution characteristics between both end points ofthe disjointed portion of the Pareto front are quite dif-ferent, and the end points are inflection points at whichthe slope changes. Therefore, points C and D can beconsidered to be typical solutions. Hence, an environ-mental manager can select a compromiseWLA solutionamong points A, C, D, and E after thoroughly consid-ering the sociopolitical and economic factors of theregion. Table 1 shows the allocated waste load abate-ment for the ER-Gini inequality measure.

Figure 8 shows the final Pareto-optimal solutions forthe waste load abatement and the fairness in the distri-bution of the waste load abatement in the second WLA.The Pareto solutions are divided into three parts, the

0

1000

2000

3000

4000

5000

10 50 100 500 2000

Generation

Tot

al p

ollu

tion

load

aba

tem

ent (

kg/d

ay)

a

0.4

0.5

0.6

0.7

0.8

0.9

1

10 50 100 500 2000

Generation

Ineq

ualit

y m

easu

re

b

Fig. 5 Box plots according to theincrease in generation number. aA box plot for the total pollutionload abatement. b A box plot forthe discharge load inequality. Boxplots for the total waste loadabatement and discharge loadinequality are shown forgenerations 10, 50, 100, 500, and2,000. The bottom and top of thebox are the first and thirdquartiles; the band inside the boxis the second quartile (median),and the dotted line inside the boxis the mean. Awhisker is drawnfrom the first quartile to theminimum, and the other whiskeris drawn from the third quartile tothe maximum


slope of which change at two points, E and F. The slopeof the solutions in Fig. 8 is generally larger than those inFig. 7. As the total allocated load abatement increases,the fairness in the distribution of the waste loadabatement improves rapidly. The A–E interval hasthe largest slope of the three parts, and a compro-mise WLA solution to the second WLA model can

be chosen among the points A, C, D, and E. Table 2shows the allocated waste load abatement for the in-equality measure of the waste load abatement in thesecond WLA model.

A social agreement between the region and the coun-try regarding the type of inequality that is important fortheWLA is necessary for selecting between the ER-Gini

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Ineq

ualit

y m

easu

re


Generation 10

Generation 50

Generation 100

Generation 500

Generation 2000

Fig. 6 Pareto-optimal solutions calculated using the inequality measure of the waste load abatement for increasing generation numbers: Thedistributions of the optimal solutions are compared for generations 10, 50, 100, 500, and 2,000

AC

D

E F

B

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ineq

ualit

y m

easu

re


Fig. 7 Pareto-optimal solutions calculated using the ER-Giniinequality measure in the WLA model application. In the trade-off curve, A is the solution point at which the waste load abatementis at a minimum and inequality is at a maximum. B is the solutionpoint at which inequality is at a minimum and the waste load

abatement is at a maximum. Points C, D, and E can be consideredas a compromiseWLA solution. In the F–B interval, the inequalityreduction ratio in terms of the increase in the waste load abatementis lower than that in the interval A–E. The points between F and Bare not considered to be a compromise solution


inequality and the inequality in the waste load abate-ment for the WLA of a certain river. After deciding

which inequality is suitable for the WLA, the environ-mental manager can select an appropriate solution for

Table 1 Allocated waste loadabatement for the six optimal so-lutions obtained using the ER-Gini inequality measure in theWLA model

Pollution source Allocated BOD load abatement (kg/day)

A B C D E F

W1 0.003 0.003 0.006 0.003 0.003 0.003

W4 131.03 131.04 131.01 131.03 131.04 131.04

W6 1.16 1.26 1.25 1.16 1.16 1.22

W7 10.19 10.17 10.25 10.19 10.22 10.25

W8 19.32 19.3 19.29 19.32 19.31 19.30

W9 110.76 110.77 110.72 110.76 110.77 110.72

W11 0.46 6.01 0.48 0.46 0.48 0.67

W12 0.076 247.34 0.077 0.076 0.066 122.20

W13 1.92 202.96 6.79 1.92 1.72 0.30

G1 0.001 0.21 0.028 0.001 0.001 0.002

G2 0.340 0.13 0.027 0.34 0.34 0.30

G3 0.32 0.002 1.66 0.32 0.32 0.10

G4 0.42 126.61 0.41 0.42 0.42 0.41

G5 0.13 319.48 0.13 0.13 0.13 0.13

Y1 54.04 0.46 54.05 54.04 54.04 54.04

Y2 0.43 0.015 0.13 1.36 0.43 0.43

Y3 0.62 2.21 0.76 0.62 0.62 0.67

Y4 0.17 0.62 0.97 0.17 0.17 0.81

Y5 0.38 0.12 0.44 0.53 0.38 0.38

Y6 1.70 59.47 1.72 1.7 1.90 1.70

Y7 2.75 0.73 2.38 3.28 2.34 2.75

Y8 323.43 427.23 323.43 323.53 323.45 323.43

Y9 1.45 0.39 1.45 1.45 1.58 1.45

Y10 12.37 0.068 12.37 12.37 12.37 12.11

Y11 1.77 0.30 1.78 1.77 1.77 5.05

Y12 0.38 1.16 0.38 5.79 0.35 2.40

Y13 0.15 64.34 0.15 0.45 0.16 1.33

Y14 1.20 0.30 1.20 1.18 1.18 1.49

Y15 1.74 63.69 1.74 0.42 0.42 0.79

Y17 0.15 1,118.06 143.27 379.19 789.89 816.49

Y18 12.51 546.19 1.32 5.56 2.30 2.30

Y20 220.71 647.04 220.71 215.52 202.83 202.83

Y21 9.43 364.12 9.43 0.43 0.29 0.29

Y22 1.45 0.98 1.78 0.12 0.12 5.44

Y23 3.56 2.20 0.86 1.36 2.71 2.71

Y24 0.023 0.05 0.15 0.15 0.068 0.14

Y25 1.23 0.027 0.16 0.16 1.23 0.16

Total 927.77 4,475.1 1,062.7 1,287.3 1,676.4 1,835.8


implementation from the WLA application while con-sidering the chosen inequality.

The comparison of the water quality distributionbetween the calibrated water quality in year 2010 andthe two waste load allocations via the least cost solutionat point A is shown in Fig. 9. The results of the waterquality calculation by the least cost solution clearly meetthe water quality goal of the TMDL, as shown in thefigure. The water quality in the upper part of theYeongsan River that was obtained using the secondWLA model (which uses the inequality measure of thewaste load abatement) was better than that obtainedusing the first WLA model (which uses the ER-Giniinequality measure). This result was obtained becausethe waste load abatement of the second WLA modelwas larger than that in the first model in the upper part ofthe river where the river flow is low. However, the waterquality distributions were almost identical in most of thereaches of the Yeongsan River and theWhangyonggangStream.

3.3 Critical Pollution Sources

The mean, standard deviation, and covariance of thewaste load abatement for the Pareto-optimal solutionsup to generation 2,000 and at each pollution source are

shown in Table 3. For the pollution sources with smallstandard deviations of waste load abatement, the calcu-lated decision variables were generally consistent anddid not have a significant effect on the Pareto-optimalsolution. However, pollution sources with large standarddeviations and covariances displayed steep fluctuationsof abatement load and had an observable effect on thedecision process for the Pareto-optimal solution.Therefore, the critical pollution sources within a basincan be found according to the standard deviations andthe covariances of waste load abatement in this table.

Among the pollution sources in Whangyonggang,W4 and W9 have small standard deviations and largetransfer coefficient values and allocate relatively largeamounts of waste load abatement under most optimalsolutions. Pollution sources W12 and W13 have largedischarge loads. Among the pollution sources inWhangyonggang, W12 and W13 have the largest trans-fer coefficient toward Yeongbon B and show large stan-dard deviations and covariances compared with themean allocation loads. Therefore, W12 and W13 arethe critical pollution sources in Whangyonggang. Inthe upper reach of the Yeongsan River, Y8 has a largetransfer coefficient and discharge load and is thereforethe subject of intensive abatement. In the middle reachof the Yeongsan River, Y17, Y20, and Y21 display large

A

B

D

C

F

E

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Ineq

ualit

y m

easu

re


Fig. 8 Pareto-optimal solutions calculated using the inequalitymeasure of the waste load abatement in the WLA model applica-tion. In the trade-off curve, A is the solution point at which thewaste load abatement is at a minimum and the inequality is at a

maximum. B is the solution point at which the inequality is at aminimum and the waste load abatement is at a maximum, andpoints C and D can be considered to be a compromise WLAsolution


standard deviations and mean abatement loads and aretherefore the critical pollution sources. Similar trends for

the statistics of the two WLA applications can be ob-served in the table.

Table 2 Allocated waste loadabatement for the six optimal so-lutions obtained using the in-equality measure of waste loadabatement in the WLA model

Pollution source Allocated BOD load abatement (kg/day)

A B C D E F

W1 3.44 42.22 27.89 27.89 27.89 27.9

W4 121.99 112.64 81.28 81.28 81.74 111.89

W6 18.44 30.57 17.79 17.77 19.82 18.16

W7 20.38 24.96 21.69 21.69 21.69 21.7

W8 18.92 17.34 19.01 19.01 19.02 19.01

W9 97.99 83.75 117.28 116.36 116.36 96.15

W11 7.56 74.13 7.56 7.56 7.56 45.84

W12 7.1 143.54 11.35 7.19 7.19 77.79

W13 4.2 155.98 47.13 55.81 55.81 89.77

G1 1.25 29.99 7.79 0.38 0.17 20.32

G2 5.88 34.7 13.77 7.68 7.68 3.3

G3 2.81 52.05 2.81 5.63 5.44 48.25

G4 21.21 126.35 21.21 63.87 63.87 95.52

G5 27.57 186.04 10.95 20.91 20.91 121.26

Y1 60.42 39.07 60.81 60.93 60.93 56.83

Y2 0.46 34.85 12.06 14.09 14.09 11.55

Y3 46.78 64.53 39.52 39.51 39.21 44.07

Y4 0.05 1.53 2.72 1.87 1.87 0.12

Y5 20.54 40.36 18.1 18.15 19.86 28.78

Y6 41.68 89.13 41.78 40.92 41.71 56.93

Y7 10.59 30.43 13.72 13.45 14.56 17.38

Y8 269.16 261.2 272.57 268.52 268.7 262.24

Y9 4.01 21.41 6.26 6.26 4.28 14.52

Y10 14.17 33.94 7.4 14.21 15.18 21.36

Y11 6.69 75.8 16.53 16.9 17.8 54.12

Y12 3.1 31.7 2.47 1.14 12.89 3.76

Y13 11.99 93.08 23.24 23.93 7.5 64.68

Y14 5.04 34.78 2.36 7.68 15.42 12.83

Y15 7.75 108.74 11.29 14.97 36.67 38.11

Y17 0.55 435.36 2.79 92.23 163.82 293.83

Y18 1.72 3.39 29.39 1.72 0.33 12.39

Y20 85.54 299.96 98.09 91.16 142.35 167.89

Y21 100.11 207.27 77.26 77.73 86.32 113.81

Y22 8.12 13.96 8.9 6.29 8.02 8.96

Y23 0.93 12.98 0.19 2.19 0.76 2.21

Y24 17.45 66.98 19.93 18.59 20.03 19.93

Y25 12.12 15.08 7.83 5.02 4.87 7.98

Total 1,087.66 3,129.76 1,182.71 1,290.49 1,452.31 2,111.09


3.4 Correlation Among Allocated Waste LoadAbatement, Inequality, and Resulting WaterQuality and Analysis of ER-Gini ResultsBefore and After Allocation

Table 4 shows the correlation coefficients among theallocated waste load abatement, the inequality, and theresulting water quality that are obtained using data fromthe six optimal solutions to the two applications of theWLA model in Section 3.2. In the first WLA applica-tion, the correlation coefficient between the total allo-cated waste load abatement and the ER-Gini inequalityis −0.973, and the correlation coefficient between the

total allocated waste load abatement and the resultingwater quality was −0.970. However, the correlationcoefficient between the ER-Gini inequality and the wa-ter quality was 0.889, which was relatively low com-pared with those for the other factors. The behavior ofthe correlation coefficients obtained for the secondWLA application was similar to that obtained for thefirst WLA application. The correlation coefficient be-tween the total allocated load abatement and the fairnessof the waste treatment among the waste dischargers was−0.934, and the correlation coefficient between the totalallocated load abatement and the resulting water qualitywas −0.990. For both applications, there was a strong

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35 40C

BO

Du

(mg/

L)

Distance (km)

Least abatement (inequality of ER-Gini)

Least abatement (inequality of waste load abatement)

2010 calibrated

Water quality goal

a

0

2

4

6

8

0 5 10 15 20 25 30 35

CB

OD

u (m

g/L)

Distance (km)

Least abatement (inequality of ER-Gini)

Least abatement (inequality of waste load abatement)

2010 calibrated

Water quality goal

b

Fig. 9 Comparison of the waterquality distribution between thecalibrated water quality in 2010and the water quality of the twoapplications of the WLA afterallocation according to the leastcost solution. aYeongsan River. bWhangyonggang Stream. TheQUAL2Kw results derived fromthe twoWLA results are shown inthe figure. The square points inthe figures indicate the waterquality goals at the target points ofthe TMDL of Yeongbon A andYeongbon B (a), andWhangyongA (b)


negative correlation between the total allocated wasteload abatement and the resulting water quality, and therewas also a strong negative correlation between the totalallocated waste load abatement and the inequality. Thisresult shows that the higher the treatment cost, thehigher the river water quality, and the higher the equityamong the waste dischargers.

The inequality measure before and after waste loadallocation was compared for the first WLA applicationin which the ER-Gini inequality was used. In solution Aof Fig. 7, the ER-Gini for the wastewater flow in thesub-basins slightly decreased after allocation, indicatinga decrease in inequality. The ER-Gini for the sub-basinarea slightly increased, indicating an increase in

Table 3 Mean, standard devia-tion, and covariance of the allo-cated waste load abatement ateach pollution source in the basinfor two applications of the WLAmodel

Statistics for second WLA appli-cation are shown in parentheses

Pollution source Mean Standard deviation Covariance

W1 0.082 (28.518) 0.404 (11.191) 4.926 (0.392)

W4 131.031 (105.109) 0.010 (14.877) 0.000082 (0.141)

W6 1.476 (21.129) 1.263 (5.507) 0.856 (0.261)

W7 10.548 (22.379) 1.860 (1.629) 0.176 (0.073)

W8 19.306 (18.657) 0.017 (0.634) 0.00089 (0.034)

W9 110.761 (98.051) 0.030 (12.330) 0.00027 (0.126)

W11 0.977 (31.467) 1.718 (22.365) 1.758 (0.711)

W12 63.018 (67.667) 82.161 (55.790) 1.303 (0.824)

W13 34.773 (82.373) 66.718 (50.520) 1.918 (0.613)

G1 0.124 (13.028) 0.535 (13.167) 4.289 (1.011)

G2 0.624 (15.824) 0.904 (12.841) 1.449 (0.811)

G3 0.404 (25.229) 0.593 (21.606) 1.465 (0.856)

G4 44.504 (82.976) 56.870 (35.591) 1.277 (0.429)

G5 102.982 (95.038) 113.237 (66.938) 1.099 (0.704)

Y1 38.204 (53.739) 21.764 (9.946) 0.569 (0.185)

Y2 1.426 (21.413) 2.619 (10.828) 1.836 (0.506)

Y3 1.028 (47.566) 1.246 (13.685) 1.212 (0.288)

Y4 0.915 (1.885) 0.891 (0.975) 0.973 (0.517)

Y5 2.290 (27.541) 5.325 (9.922) 2.325 (0.360)

Y6 15.389 (59.462) 22.732 (20.865) 1.477 (0.351)

Y7 3.012 (18.803) 2.808 (7.072) 0.932 (0.376)

Y8 356.438 (265.997) 43.516 (4.030) 0.122 (0.015)

Y9 2.253 (10.834) 4.782 (8.209) 2.122 (0.758)

Y10 8.078 (21.706) 5.600 (10.053) 0.693 (0.463)

Y11 1.784 (38.201) 2.894 (28.387) 1.621 (0.743)

Y12 2.695 (16.103) 2.606 (11.420) 0.967 (0.709)

Y13 8.403 (47.834) 19.085 (28.793) 2.271 (0.602)

Y14 0.895 (18.451) 0.439 (11.157) 0.490 (0.605)

Y15 5.026 (49.303) 15.205 (31.056) 3.024 (0.630)

Y17 761.033 (229.443) 336.217 (145.101) 0.441 (0.632)

Y18 16.931 (5.814) 77.300 (8.520) 4.565 (1.465)

Y20 374.257 (164.910) 166.683 (68.466) 0.445 (0.415)

Y21 97.928 (122.343) 125.930 (48.232) 1.285 (0.394)

Y22 2.133 (9.423) 5.277 (3.378) 2.473 (0.358)

Y23 2.378 (3.825) 4.616 (6.092) 1.940 (1.593)

Y24 0.323 (34.262) 0.626 (21.737) 1.938 (0.634)

Y25 0.299 (7.990) 0.687 (3.785) 2.294 (0.474)


inequality. The overall inequality measure slightly in-creased, possibly because the ER-Gini was calculatedaccording to the Pareto-optimal solution in which thewaste load abatement was at a minimum, whereas theinequality was at a maximum. In solutions for points C,D, E, F, and B (excluding solution A), the allocated loadabatement became larger, but the overall equality im-proved. As the allocated load abatement increased, theER-Gini for the wastewater flow, the ER-Gini for thesub-basin area, and the inequality measure, which is thesum of the two, all gradually decreased. The ER-Gini forpoints C, D, E, F, and B after allocation all improved incomparison with the ER-Gini before allocation.

4 Conclusions

Along with the economic goal of minimizing the cost,two types of inequality among waste dischargers wereintroduced to consider the regional differences in theWLA for water quality management in a river basin.The first type of inequality was calculated with the ER-Gini coefficient, utilizing the environmental resourceand the discharge load for each sub-basin. The secondtype of inequality is the fairness in the distribution of thetreatment efforts among waste dischargers. The WLAmodel was developed by integrating the MOGA, con-straints on the water quality goal achievement, andequations for the inequality measure.

In terms of the WLA, the minimization of the costand waste load abatement are the most prioritized fac-tors. For the first WLA application in which the inequal-ity measure of ER-Gini was used, the least cost solutionof point A in Fig. 7 can be considered to be the optimalsolution. However, considering the discharge inequalitydepending on sub-basin and regional differences, pointE (where the slope of the trade-off curve changes) canalso be considered the optimal WLA solution. When

placing an emphasis on the economic goal rather thanthe discharge inequality, an environmental decisionmaker could choose the appropriate WLA solution fromamong points between points A and E, depending onregional factors. In comparing the ER-Gini inequalitymeasure before and after allocation, solution A, which isthe minimum abatement load, displayed a slight in-crease after allocation. However, for solutions C, D, E,F, and B, the inequality measure gradually decreasedand eventually displayed a significant improvement af-ter allocation. For the second WLA application, inwhich the inequality measure of the fairness of the wastetreatment among waste dischargers was used, the fair-ness in the distribution of the treatment effort amongwaste dischargers improved rapidly as the total allocatedload abatement increased. The slope of the A–E intervalwas the largest among the three intervals; thus, an ap-propriateWLA solution could be chosen from the pointsbetween points A and E. After selecting the inequalitythat is suitable for the WLA, that is, between the in-equality in the waste load discharge regarding the envi-ronmental resources in each region and the fairness inthe distribution of the treatment efforts, the environmen-tal manager can select an appropriate solution for im-plementation from the WLA application based on thechosen inequality.

The mean, standard deviation, and covariance of thewaste load abatement were calculated for each pollutionsource regarding the final Pareto-optimal solutions. Thepollution sources with large standard deviations andcovariances displayed rapid fluctuations in abatementload and influenced the decision process of the Pareto-optimal solution. W12 and W13 in Whangyonggangdisplayed large discharge loads and transfer coefficients,and their standard deviations and covariances were alsolarge. Therefore, W12 and W13 were the critical pollu-tion sources. In the middle stretch of the YeongsanRiver, Y17, Y20, and Y21, which displayed large

Table 4 Correlation coefficients among allocated waste load abatement, inequality, and water quality using data from the six optimalsolutions for the two applications of the WLA model

Total allocated waste load abatement Inequality Water quality

Total allocated waste load abatement 1 −0.973 (−0.934) −0.970 (−0.990)Inequality 1 0.889 (0.885)

Water quality 1

Correlation coefficients obtained from the second WLA model using the inequality measure of the waste load abatement are shown inparentheses


discharge loads and standard deviations, were the criti-cal pollution sources.

Acknowledgments This research was supported by the BasicScience Research Program through the National Research Foun-dation of Korea (NRF) funded by the Ministry of Education (grantnumber 2010-0024879).

References

Arbabi, M., & Elzinga, J. (1975). A general linear approach tostream water quality modelling. Water Resources Research,11(2), 191–196.

Bashi-Azghadi, S. N., & Kerachian, R. (2010). Locating monitor-ing wells in groundwater systems using embedded optimiza-tion and simulationmodels. Science of the Total Environment,408(10), 2189–2198.

Bhat, S. A., Gupta, S., Saraf, D. N., &Gupta, S. K. (2006). On-lineoptimizing control of bulk free radical polymerization reac-tors under temporary loss of temperature regulation:Experimental study on a 1-L batch reactor. Industrial &Engineering Chemistry Research, 45(22), 7530–7539.

Boisvert, R. N., & Ranney, C. K. (1991). The budgetary implica-tions of reducing U.S. income inequality through incometransfer programs. Ithaca: Department of AgriculturalEconomics, Cornell University.

Burn, D. H. (1989). Water-quality management through combinedsimulation-optimization approach. Journal of EnvironmentalEngineering, 115(5), 1011–1024.

Burn, D. H., & McBean, E. A. (1985). Optimization modeling ofwater quality in an uncertain environment. Water ResourcesResearch, 21(7), 934–940.

Burn, D. H., & Yulianti, J. S. (2001). Waste-load allocation usinggenetic algorithms. Journal of Water Resources Planning andManagement, 127(2), 121–129.

Cho, J. H. (2013). Waste load allocation method for total maxi-mum daily load program of a polluted river. Journal ofEnvironmental Impact Assessment, 22(2), 157–170.

Cho, J. H., Sung, K. S., & Ha, S. R. (2004). A river water qualitymanagement model for optimising regional wastewater treat-ment cost using a genetic algorithm. Journal ofEnvironmental Management, 73(3), 229–242.

Deb, K. (2001). Multi-objective optimization using evolutionaryalgorithms. Chichester, UK: Wiley.

Druckman, A., & Jackson, T. (2008). Measuring resource inequal-ities: The concepts and methodology for an area-based Ginicoefficient. Ecological Economics, 65(2), 242–252.

Fujiwara, O. (1990). Preliminary optimal design model for waste-water treatment plant. Journal of EnvironmentalEngineering, 116(1), 206–210.

Fujiwara, O., Gnanendran, S. K., & Ohgaki, S. (1986). Riverquality management under stochastic streamflow. Journalof Environmental Engineering, 112(2), 185–1986.

Gen,M., &Cheng, R. (1997).Genetic algorithms and engineeringdesign. New York: John Wiley & Sons.

Ghosh, S., & Mujumdar, P. P. (2006). Risk minimization in waterquality control problems of a river system. Advances in WaterResources, 29(3), 458–470.

Goldberg, D. E. (1989). Genetic algorithms in search, optimiza-tion and machine learning. Reading, MA: Addison-Wesley.

Guria, C., Bhattacharya, P. K., & Gupta, S. K. (2005). Multi-objective optimization of reverse osmosis desalination unitsusing different adaptations of the non-dominated sortinggenetic algorithm (NSGA). Computers and ChemicalEngineering, 29(9), 1977–1995.

Heerink, N., Mulatu, A., & Bulte, E. (2001). Income inequalityand the environment: Aggregation bias in environmentalKuznets curves. Ecological Economics, 38(3), 359–367.

Jacobson, A., Milman, A. D., & Kammen, D. M. (2005). Lettingthe (energy) Gini out of the bottle: Lorenz curves of cumu-lative electricity consumption andGini coefficients asmetricsof energy distribution and equity. Energy Policy, 33(14),1825–1832.

Kasat, R. B., & Gupta, S. K. (2003). Multiobjective optimizationof an industrial fluidized-bed catalytic cracking unit (FCCU)using genetic algorithm with the jumping genes operator.Computers and Chemical Engineering, 27(12), 1785–1800.

Kerachian, R., & Karamouz, M. (2007). A stochastic conflictresolution model for water quality management inreservoir-river systems. Advances in Water Resources,30(4), 866–882.

Khosla, D. K., Gupta, S. K., & Saraf, D. N. (2007). Multi-objective optimization of fuel oil blending using the jumpinggene adaptation of genetic algorithm. Fuel ProcessingTechnology, 88(1), 51–63.

Klemetson, S. L., & Grenny, W. J. (1985). Dynamic optimizationof regional wastewater treatment systems. Journal of WaterPollution Control Federation, 57(2), 128–134.

Lerman, R., & Yitzhaki, S. (1985). Income inequality effects byincome source: A new approach and applications to theUnited States. The Review of Economics and Statistics,67(1), 151–156.

Liu, Y., Yang, P., Hu, C., & Guo, H. (2008). Water qualitymodeling for load reduction under uncertainty: A Bayesianapproach. Water Research, 42(13), 3305–3314.

Murty, Y. S. R., Murty, B. S., & Srinivasan, K. (2006a). Non-uniform flow effect on optimal waste load allocation in rivers.Water Resources Management, 20(4), 509–530.

Murty, Y. S. R., Srinivasan, K., & Murty, B. S. (2006b).Multiobjective optimal waste load allocation models for riv-ers using nondominated sorting genetic algorithm-II. Journalof Water Resources Planning and Management, 132(3), 133–143.

Pelletier, G. J., & Chapra, S. C. (2008). QUAL2Kw theory anddocumentation (version5.1): A modeling framework for sim-ulating river and stream water quality. Olympia, WA:Washington State Department of Ecology.

Pelletier, G. J., Chapra, S. C., & Tao, H. (2006). QUAL2Kw–Aframework for modeling water quality in streams and riversusing a genetic algorithm for calibration. EnvironmentalModelling & Software, 21(3), 419–425.

Ramteke, M., & Gupta, S. K. (2009). Multi-objective geneticalgorithm and simulated annealing with the jumping geneadaptation. In G. P. Rangaiah (Ed.), Multi-objective optimi-zation: Techniques and applications in chemical engineering(pp. 91–129). Singapore: World Scientific Publishing.


Sankararao, B., & Gupta, S. K. (2007). Multi-objective optimiza-tion of an industrial fluidized-bed catalytic cracking unit(FCCU) using two jumping gene adaptations of simulatedannealing. Computers and Chemical Engineering, 31(11),1496–1515.

Singh, T. S., & Chakrabarty, D. C. (2010). Multi-objective opti-mization for optimal groundwater remediation design andmanagement system. Geoscience Journal, 14(1), 87–97.

Sun, T., Zhangm, H.,Wang, Y.,Meng, X., &Wang, C. (2010). Theapplication of environmental Gini coefficient (EGC) in allo-cating wastewater discharge permit: The case study of water-shed total mass control in Tianjin, China. Resources,Conservation and Recycling, 54(9), 601–608.

White, T. J. (2007). Sharing resources: The global distribu-tion of ecological footprint. Ecological Economics,64(2), 402–410.


multi-objective waste load allocation model for optimizing waste load abatement and inequality among...

Documents