Recent Advances n Computer Scence Evolutonary Mult-objectve Optmzaton Algorthms To Envronmental Management and Plannng Wth Water Resources Case Studes ANDRE A. KELLER Laboratore d Informatque Fondamentale de Llle/ secton SMAC (UMR80:CNRS) Unversté de Llle Scences et Technologes Cté Scentfque, 5900 Llle FRANCE andre.eller@unv-llle.fr; http://www.unv-llle.fr Abstract: - Envronmental management and plannng problems cover mportant real lfe areas. These problems may nclude the scarcty of groundwater resource, the optmalty of a mult-reservor system, the management of forest resources, the ar qualty montorng networs, the muncpal sold waste polces, etc. Management and plannng targets by authortes consst n allocatons at approprate places and tmes, protecton from dsasters, mantenance of qualty (e.g., water qualty, water polluton control, ntrate concentraton dmnshng), sustanable development of the groundwater resources. The formalzaton of such optmzaton problems ncludes multple objectves and constrants. The multple objectves consst n maxmzng/mnmzng of varous aspects of envronmental management, e.g., maxmzng of rrgaton releases, maxmzng the hydropower producton, maxmzng net returns, mnmzng costs, mnmzng the nvestment n water development, mnmzng groundwater qualty deteroraton, etc.. Physcal, bologcal, economc and envronmental constrants are e. g., constrant of surface water balance, water supply constrants, water qualty constrants, economc constrants (demand, resource costs, etc.), reservor storage constrants. The eco-envronmental objectves are often conflctng (e.g., the optmum use of water resources under conflctng demands. The use of mult-objectve optmzaton allows a smultaneous treatment of all the objectves and constrants. The solutons tae the form of non-domnated Pareto solutons, whch enable the decson maers to study the tradeoffs between the objectves (e.g., between proftablty and rss). Most of the envronmental domans are faced to uncertantes due to varablty (e.g., clmate, ranfalls, hydrologc varablty, envronmental polcy, marets, etc.), mprecson and lac of data, vagueness of judgments by decson maers. These uncertantes lead to extend the analyss to fuzzy envronments. Ths presentaton s then concerned wth decson-mang methods n an envronmental management and plannng, where multple conflctng objectves are used under a fuzzy envronment by usng a nched Pareto algorthm. Key-Words: mult-objectve optmzaton evolutonary algorthm genetc search method - fuzzy data - envronmental management water resources and forest plannng. Introducton Ths paper ntroduces to the envronmental management and plannng problems by usng evolutonary mult-objectve optmzaton algorthms. Natural genetc and natural selecton based algorthms (GA s) belong to ths class of methods and consst n search procedures. GA s are Evolutonary approaches refer to search optmzaton algorthms nspred by the process of natural evoluton. They nclude evolutonary programmng, evoluton strateges, genetc algorthms and genetc programmng. A bees algorthm has been also proposed by Tapan, et al. [5] for solvng multple objectve programs. It s a flexble and effectve methods for solvng complex real lfe optmzaton problems. GA s have been adapted to mult-objectve optmzaton problems where all objectves are optmzed smultaneously and where a Pareto front of optmal solutons s approxmated (e.g., the tradeoff between the sustanablty of groundwater use and economc development [5]). Evolutonary methods have been used to solve large scale real world eco-envronmental problems, such as the rrgaton water resource for determnng optmal crop patterns and rrgaton water resources allocaton, the optmzaton of swarm based optmzaton algorthm nspred by the foragng behavour of honey bees. ISBN: 978-960-474-354-4 5
Recent Advances n Computer Scence mult-reservor systems for hydropower and rrgaton purposes (n Reddy and Kumar, 006 [9]), water qualty management, forest plannng, etc. Ths study s focused on water resources and forest management 3, wth applcatons usng mostly GA s. An example problem s drawn from Reddy and Kumar [9] to llustrate the techncal pattern of such formulaton. The case studes for ths paper have been selected only for water resources management problems, such as wth Shyang rver and Ha rver basn n Chna, and Godavar rver n Inda 4. Uncertantes are n water resources and forest data and plannng decsons. They are due to numerous factors, such as, a lac of nformaton, nexact or mperfect data, statstcal estmaton errors, mprecsons, vagueness of qualtatve jugments by the decson maers (DM s), etc. For ths context, fuzzy optmzaton technques have been developed n water resources and forest management [4,8,33]. Fuzzness n multobjectve optmzaton problems may be the aspraton values of the objectves, the lmt values for resources n the constrants wth tolerance threshold, fuzzy coeffcents n the objectves and constrants. Mult-Objectve Optmzaton. Nonfuzzy mult-objectve optmzaton The classcal maxmzng lnear programmng (LP) problem states T n maxmze z = cx, ( cx, ) s.t. x X where the feasble regon n X = x Ax b, x 0, { } wth ( A m n, b m, x ), s defned by all the constrants. 3 In the lterature, other mult-objectve envronmental applcatons are wth energy problems, sold waste management, ar qualty, fsheres management, agrcultural land use, etc. 4 Other case studes are the Fengman reservor (Sonhua rver) n Chna by Chuntan and Chau [3], the Xngahu Lae Irrgaton Dstrct n Chna by Zhou, et al. [34], the Bhadra reservor system n Inda by Reddy and Kumar [9], the Bagmat rver basn n Nepal by Onta, et al. [7], the Ro Colorado rver n Argentna ([4], pp. 43-80), etc. The groundwater management n ard regons s analysed by Dawoud (006)[5]... Multple objectve formulaton and soluton In practce, the decson maers (DM s) are confronted to multple objectves. The multobjectve lnear problem (MOLP) s maxmze Z x = C x s.t. x ( ) X, n where Z( x ) states a -vector valued objectve T functon ( ( x), ( x),, ( x) ). z z z Defnton. Let { maxmze Z( x) x X} be a vector-maxmum problem, x ˆ X s an effcent Pareto optmal soluton, f and only f, there s no x X such that z ( x) z ( xˆ ) ( ) and z x > z x ˆ for at least one. ( ) ( ).. Pareto optmal soluton search usng genetc algorthms Genetc algorthms (GA s) are stochastc search technques. Ther procedures are nspred from the genetc processes of bologcal organsms by usng encodngs and reproducton mechansms [6,8]. These prncples may be well adapted to more complex real-world optmzaton problems. Let P( t) be a populaton of potental solutons at generaton t, and new ndvduals (or offsprng) C( t ), the pseudo-code of a smple algorthm s the followng. 3 4 5 6 7 8 9 0 3 4 5 6 begn /* ntal random populaton */ t:=0 generate ntal P(t) evaluate ftness of P(t) whle (NOT fnshed) do begn /* new generaton */ for populaton Sze/ do begn /* reproducton cycle */ select two ndvduals for matng; recombne P(t) to yeld offsprng C(t); evaluate P(t+) from P(t) and C(t); t:=t+; end f populaton has converged then fnshed:=true end end An ntal populaton of ndvduals (chromosomes) s generated at random, and wll evolve over successve mproved generatons towards the global optmum. Usually, a gene has converged when 95% of the populaton has the same ISBN: 978-960-474-354-4 6
Recent Advances n Computer Scence value, and the populaton has converged when all the genes have converged. There are three types of operators for the reproducton phase: the selecton operator for more ftted ndvduals, the crossover operator that creates new ndvduals by combnng parts of strngs of two ndvduals and the mutaton that mae one or more changes n a sngle ndvdual strng. Real optmzaton problems often requre the dentfcaton of multple optma due to multvarate objectve functons and multple objectve functons. In ths study, the evolutonary GA s are used to approxmate the Pareto-optmal set n the objectve functon space...3 Nched Pareto genetc algorthm To sample non-domnated solutons from the Pareto-optmal set t s mportant to mantan the dversty of solutons whch can be lost due to the stochastc selecton process of a smple GA procedure. Nchng methods have been ntroduced to reduce the effect of the random genetc drft and to preserve the genetc dversty of the optmal solutons. Nchng s based on the mechancs of natural ecosystems 5. Goldberg and Rchardson [9] suggested the use of a sharng functon to estmate the number of solutons belongng to each optmum, such as ( ) ( d σ j share d ) j /, f d < σ share sh = j 0, otherwse where d s a smlarty metrc between ndvduals and j, j share α σ the threshold of dssmlarty and α, a constant whch regulates the shape of the functon. The nche count m approxmatng the number of ndvduals that share the ftness f s m N =, where N s the populaton sze. j= sh ( d ) j The Nched Pareto Genetc Algorthm (NPGA) extends the basc GA to multple objectves optmzaton problem wth two addtonal genetc operators: the Pareto domnaton ranng and ftness sharng [7,9,0]. The Pareto domnaton ranng 6 5 A nche can be vewed as a subspace n the envronment that can support dfferent types of lfe [3]. 6 A desgn domnates another desgn f t s at least equal n all the objectves and better than one another n at least one objectve. The Pareto domnaton ran of an ndvdual desgn s the number of desgns that domnate t [7]. and tournament compettons help for decdng whch canddates should go to the next generaton. The ftness sharng operator contrbutes to mantan dversty n the populaton of solutons. Ercson, et al. [7] show a modfed flowchart correspondng to the NPGA. Thereafter, the modfed algorthm s appled to groundwater qualty management problems.. Fuzzy Multobjectve Optmzaton.. Fuzzy LP problem A fuzzy sngle objectve FLP may be T maxmze c x s.t. A x d b, x 0, ( ) m where maxmze means mprove reachng some aspraton level and where the fuzzy nequalty d means roughly smaller than. More generally, we may ntroduce fuzzy b s coeffcents, such that we may wrte: T maxmze c x s.t. A x d b, x 0... Solvng a fuzzy multobjectve LP by usng crsp equvalent models Gven the fuzzy mult-objectve problem maxmze C x t Z s.t. A x b, x 0 wth fuzzy objectves and crsp constrants. The lnear objectve functons are maxmzed smultaneously, subject to m lnear constrants for the n decson varables. The coeffcents are the n matrx C, the m n matrx A and the m vector b. The m vector C s the frst lne of the matrx C. The resoluton may consst n solvng successve sngle objectve LP s by usng each objectve: maxmze Cx( ). Usng the payoff Table, we can obtan lower and upper bounds L s and U s such that { ( xˆ ) ( xˆ ) ( xˆ )} { ( xˆ ) ( xˆ ) ( xˆ )} L = mn z, z,, z, U = max z, z,, z. Soluton Table : Payoff table wth objectves Objectve value z ( x ) z ( x ) z ( x ) ˆx ( ) z ˆ x z ( x ˆ ) z ( ˆ x ) ˆx ( ) z ˆ x z ( x ˆ ) z ( ˆ x ) ISBN: 978-960-474-354-4 7
Recent Advances n Computer Scence ˆ z x x z ( x ˆ ) z ( x ˆ ) ( ˆ ) The lnear membershp functons (MF s) µ ( ) are expressed by µ G, Cx U ( x) = ( Cx L) /( U L), Cx ( L, U) 0, Cx L G The fuzzy set of the objectves 7 s ( x) ( ) µ = = µ G G G = G and = x. The decson set s defned by D = G X. The optmal soluton s an effcent soluton, whch s obtaned for the greatest degree α of satsfacton for whch the program s maxmze λ s.t. Cx L / U L λ, ( ) ( ) wth, x X, λ ( 0,]. In the constraned method, the problem s transformed to a partally FLP problem wth only one of the objectve functons, the remanng fuzzy objectves beng placed nto the set of constrants. Choosng the frst objectve and transferrng the other objectves yelds maxmze z ( x) = Cx U s.t. Cxt z ( j \ { }), j j Ax b, x 0, where the aspraton level equals the upper value of U U L z wth a tolerance of z z. The MF s of the objectves are defned by, Cx z L U L L U µ ( ) ( ) /( ), (, G Cx = Cx z z z Cx z z ) L 0, Cx z Then we have to solve the parametrc programmng problem maxmze z ( x) = Cx U U L s.t. Cx z λ ( z z ) ( j \ { }), j j j j A x b, x 0. 7 Other real-valued functons have been proposed n the lterature : a weghted sum of objectves β α z ( x ), α, β > 0 or a product of objectves = ( ) ( z ) α. Ths aggregaton may also be based on the = DM s preferences wth utlty functons. Ths programmng technque wll provde a fuzzy decson dependent on the preference parameter λ...3 Drect soluton method va meta-heurstc algorthms Bayasoglu and Göçen [,] proposed a drect soluton method (DSM) for solvng fuzzy multobjectve optmzaton problems to avod the nconvenences of a transformaton nto equvalent crsp programs. A ranng method s used for fuzzy numbers to ran the objectve values and to determne the feasblty of the constrants. Thereafter, a meta-heurstc algorthm s carred out for searchng effcent solutons [5]..3 Mult-objectve water resource example problem The followng model for water resources management s drawn from Reddy and Kumar (006) [9] 8. Ths model s for the Badra dam. It s stuated n Chmagalur dstrct of Karnataa State, Inda. The reservor s multpurpose, provdng for rrgaton and for hydropower producton. The two rrgaton areas are of 87,5 ha and 6,367 ha, respectvely. There are three hydropower turbnes. One turbne s at the bed of the dam. Fg. shows the flowchart of the reservor system. Fg. : The Badra multpurpose reservor system n Inda. The model formulaton conssts n three objectves and sx constrants [9]. There are two conflctng objectves whch consst n mnmzng the devaton of releases from demands and n maxmzng the total producton of energy. Physcal 8 The formulaton of a water polluton control problem was presented by Saawa and Seo, 980 [], wth applcaton to Osaa Cty, Japan. (See also, La and Huang, 994 [3], pp. 9-3). ISBN: 978-960-474-354-4 8
Recent Advances n Computer Scence and envronmental constrants are mposed on the system:.e., a storage contnuty equaton, the storage lmts, the maxmum power producton lmts, the canal capacty lmts, the rrgaton demand lmtatons and the water qualty requrements. Table : Water resource management example problem [9] Objectves: ζ ( D R,, ) + t t ( D R, t, t) ( ) mnmze t= t= t= ( + +, t, t, t, t 3, t 3, t) ( ) ζ maxmze p R H R H R H Constrants: ΰ S t S t I t ( R, t R, t R 3, t E + t Ot) (3) ΰ St [ Smn, Smax ] (4) ΰ prjt, Hjt, Ej,max, j=,,3 (5) ΰ Rjt, Cj,max, j =, ΰ Rjt, Dj,mn, D j,max, j =, (6) (7) ΰ R MDT (8) 3, t t Lst of parameters: C max : canal carryng maxmum capacty D, D : rrgaton demand Dmn, D max : mnmum and maxmum demands E : evaporaton losses E max : turbne capacty H, H, H 3: net heads avalable I : nflow to the reservor; MDT : mnmum release to meet downstream water qualty O : overflow from the reservor; p: power producton coeffcent R, R, R 3: releases nto ban canals S : actve reservor storage. The non-domnated sortng genetc algorthm (NSGA II) s used to derve operatng polces for the reservor operaton problem. The parameters used are selected after a senstvty analyss. The populaton sze s of 00 ndvduals and the maxmum generaton number s of,000. The tradeoff between rrgaton and hydropower n the objectve space s shown n [9]. At ths Pareto front, the decson maer may choose a soluton correspondng to hs preferences. 3 Modelng Envronmental management Problems In ths study, the management and plannng problems are llustrated for two man envronmental areas: water resources and forest [,8,30]. 3. Model formulaton The standard formulaton of the model concerns the varables (or parameters), the multple objectves and the constrants. A dstncton s made between the state and the decson varables. The set of the state varables (state vector) for a gven system ams at descrbng the system and all ts elements (e.g., area of forest land, machnery, plant speces, labor force, budget, etc.) [33]. The varable decsons are under the control of the DM s and can nfluence the system. Ths set of feasble parameters s constraned by budget lmts, avalable labor force and machnery, etc. The multple objectves for water resources and forest management are descrbed n Table 3. Dfferent types of objectves are consdered: the economc objectves (e.g., output of groundwater, benefts and costs, labor employment, hydropower producton n water resources, tmber producton n forestry); physcal objectves (e.g., rrgaton releases); envronmental and ecologcal objectves (e.g., aqufer yeld, BOD dscharge, TDS concentraton, groundwater salnty n water resources, wldlfe habtat condton, n forest management; socal health and educaton objectves (e.g., food producton, employment possbltes, health rs, envronmental awareness). The constrants are nequaltes and equaltes that determne the set of the admssble decsons. The constrants can be dvdes nto physcal, economc and envronmental constrants as n Table 3. Thus, the physcal constrants are lmtatons such as water level, turbne releases for mult-reservor systems. ISBN: 978-960-474-354-4 9
Recent Advances n Computer Scence ISBN: 978-960-474-354-4 0 Table 3: Objectves and constrants n water resources and forest management problems Lterature Objectves Constrants Water resources management problem Onta, et al. (99) Economc objectves : ) maxmze economc output of [7] ; Maows & groundwater use ; ) maxmze economc output of ndustres; Somlyody (000) [5]; Yang, et al. (00) [3]; Ercsson, et al. (00) [7]; Cohon (003) [4]; 3) maxmze GDP; 4) maxmze benefts from hydropower generaton; 5) maxmze net benefts from agrcultural; 6) maxmze the rato benefts to costs; 7) maxmze employment of labour; 8) maxmze food grans producton; 9) mnmze Raju & Ducsten cost; 0) mnmze nvestment n water development; ) (003) [8]; Weng mnmze net value of groundwater depleton mtgaton cost. (005) [9]; Dawoud Physcal objectves (n mult-reservor systems): ) (006) [5]; Reddy & maxmze rrgaton releases; ) maxmze hydropower Kumar (006) [9] producton; 3) maxmze the rrgated cropped area; 4) Steuer & Schuler, (979) [4] ; Mendoza, et al. (993) [6] ;Tecle, et al. (998) [6] ; Raju & Ducsten (003) [8] ;Wentraub & Romero (006) [7] ; Zadn Strn (006) [33]; Kennedy, et al. (008) [] mnmze the rrgaton defct. Envronmental objectves: ) maxmze aqufer yeld; ) maxmze cleanup tme; 3) mnmze BOD (bologcal oxygen demand) dscharge; 4) mnmze concentraton (n total dssolved solds (TDS)) ncrement n groundwater; 5) mnmze the ar polluton (total amount of SO ); 6) mnmze the water polluton (dssolved oxygen ( DO ) and ammona ( NH ) concentratons); 7) mnmze groundwater salnty. 4 Socal, health and educatonal objectves: ) maxmze food producton; ) mnmze health rs. Economc objectves : ) maxmze net present value ; ) maxmze tmber producton ; 3) maxmze on-ste merchandable tmber volume ; 4) maxmze forage producton ; 5) maxmze herbage producton ; Envronmental objectves : ) maxmze water yeld ; ) maxmze wld lfe habtat condton ; 3) mnmze sedment yeld. Socal and educatonal objectves: ) promoton of envronmental awareness; ) educaton about flora and fauna. Physcal constrants: ) water level; ) water resources; 3) maxmum surface avalablty; 4) maxmum groundwater avalablty; 5) crop water requrement; 6) maxmum area avalablty; 7) crop area contnuty; 8) forestry; 9) drawdown; 0) surface water balance; ) turbne release (for multreservor system); ) rrgaton release; 3) reservor storage; 4) hydrologc contnuty for all reservors. Economc constrants: ) water demand; ) mcroeconomc constrants; 3) expendtures; 4) agrcultural producton requrement. Envronmental constrants: ) anmal husbandry and fshery; ) BOD dscharge; 3) water qualty. Forest management problem Physcal constrants: ) acreage lmtatons; ) tmber harvestng yeld. Economc constrants: ) budget lmtaton. Envronmental constrants: ) brd habtat; ) land; 3) sedment yeld; 4) fre danger.
Recent Advances n Computer Scence ISBN: 978-960-474-354-4 Table 4: Envronmental selected case studes n water resources management Case study Programmng method: mult-objectve Locaton and characterstcs Problems and drawbacs Polces and programmng method Shyang Locaton: northwestern Chna Problems: ) Extensve water uses begn n Polces: ) mantan the current water Rver, Chna Characterstcs: ) a sedment fllen the 950s; ) overexplotaton of groundwater utlzaton; ) perform a conjunctve Yang, et al., graben of 30,000 m area; ) annual Drawbacs: ) conflcts between water management of groundwater and surface (00) [3] average precptaton of 00-50 mm; 3) supply and water demand; ) contnuous water; 3) mnmze the groundwater potental evaporaton of 000-3000 mm; drawdown of the groundwater level; 3) deteroraton; 4) meet the ncreasng water 4) about 65% of water comng from the deteroraton of water qualty; 4) wtherng of demand of human, lvestoc, ndustry and precptaton and 35% from groundwater. vegetaton; 5) sol desertfcaton and forestry users; 5) acheve economc, best salnzaton. socal and ecologcal values of water uses. Ha Rver, Chna Weng, (005) [9] Godavar Rver, Inda Regulwar & Raj, (008) [0] Locaton: northern part of Chna Characterstcs: ) basn area of 89,000 m ; ) sem-humd clmate wth uneven ranfall dstrbuton (average precptaton of about 550 mm) ; 3) about 0% of Chna gran output, a center of varous ndustral actvtes, a populaton of 0 mllons n 994. Locaton: Maharashtra State, n Inda. Characterstcs: The physcal water system conssts of fve reservors (one s a barrage): the Jayawad project stages I and II, the Yeldar project, the Sddheshwar project and the Vshnupur project. Problems: ) rapd economc growth wde varety of ndustres; ) substantal changes n the water demand; 3) few water treatment facltes Drawbacs: ) water defct; ) scarce of water resources; 3) ncrease n of water area; 4) competton of other uses; 5) water polluton (urban populaton growth and ndustry); 6) wastewater dscharged to the rver. Problems: ) scarcty of water for rrgaton and hydropower producton, ndustral requrement and domestc purposes; ) ncreasng water demands; 3) the complexty of water resources domans, of rver basn plannng under uncertanty. Drawbacs: ) water qualty deteroraton; ) water defct; 3) competton between uses. optmzaton model Polces: ) water savng polcy (controllng, leaage, promotng re-use of water, etc.); ) protecton of water resources (reducng water polluton, buldng waste water nfrastructure, chargng ratonal prces); 3) South-north water transfer project Programmng method: ) mcroeconomc multobjectve water resource model; ) multobjectve optmzaton component; 3) a stepwse multobjectve programmng algorthm; 4) scenaros. Polces: ) maxmze the rrgaton releases; ) maxmze the hydropower producton; 3) consder other ncrease alternatves for rrgaton and hydropower demands. Programmng method: mult-objectve optmzaton by usng genetc algorthms wth fuzzfed objectves. Soluton surface coverng the whale range of polces for dfferent levels of satsfacton.
Recent Advances n Computer Scence 3. Envronmental water resources case studes Envronmental case studes n water resources have been selected for ths ntroductory approach: two are rver basns northern of Chna and the other case study s a multreservor system on the Godavar rver n Inda. In Table 4, the characterstcs of the case studes are compared. The man problems and drawbacs are mentoned. The chosen polces by authortes result wth some detals. 3.3 Multreservor Case Study n Maharashtra Sub Basn The real-world case study by Regulwar and Raj (008, 009) [0,] llustrates a multreservor management problem for rrgaton and hydropower producton. The physcal system s shown n Fg. whch has been adapted from []. It conssts of four reservors and a barrage. Each reservor s descrbed n terms of gross storage, lve storage, nstalled capacty for power generaton 9. The rrgable area s also defned. The monthly rrgaton demand and nflow are gven for all the reservors. The decson maer ams at maxmzng two objectves: the rrgaton releases and the hydropower producton. The constrants are due to the turbnes for power producton, to rrgaton releases, to the reservor storage capactes. There are also hydrologc contnuty constrants for all reservors []. Only the two objectves are supposed to be fuzzy, all other parameters beng crsp n nature. The membershp functons (MFs) of the two objectves are supposed to have a lnear formulaton, for whch the best and worst values are determned for each MF 0. The two fuzzfed objectves are maxmzed by defnng, and then maxmzng a level of satsfacton (ranged from 0 to 00%). The resultng crsp equvalent sngle objectve programmng problem s solved by usng GA. The genetc operators are: a stochastc remander selecton, a one pont crossover and a bnary mutaton. The crossover probablty s 0.7 for the frst objectve and 0.9 for the second. In both cases, the mutaton probablty s set to 0.. The parameter values are a populaton of 30 and 500 generatons. The results for an exstng demand are: a level of satsfacton of 60%, rrgaton releases 6 3 (objectve ) of, 054. 0 m and a hydropower producton (objectve ) of 4 0, 475 0 Wh [0]. 4 Concluson The mportance of water resources and forest management s proved by numerous applcatons n the envronmental lterature. DM s am at sustanable solutons. They are faced to long term mult-objectve plannng problems for whch data are mprecse and judgments are vague. Therefore most decson-mang systems are based on fuzzy evolutonary mult-objectve optmzaton methods. Ths ntroductory study s used adequate methods Fg.. Multreservor system n Godavar sub basn n Mahharashtra State, Inda. 9 All the data are gven n []. The reservor R s the 6 3 largest reservor wth a gross storage of,909 0 m, an nstalled capacty for power generaton of.mw and for an rrgable area of, 46.40 m. Consderng the gross storage, the reservor are raned as R < R < R < R < R. Monthly hstorcal flow data 5 4 3 have been collected over 3 years. 0 For the rrgaton releases frst objectve the worst and best values are respectvely,807.97 and 6 3, 8.36 0 m respectvely. For the hydropower producton second objectve the worst and best values are 4 respectvely,739.5 and 8, 559.5 0 Wh respectvely []. The results for an ncreased demand of 0 % are the followng [] : a level of satsfacton of 5%, rrgaton 6 3 releases (objectve ) of,95.34 0 m and a 4 hydropower producton of, 06 0 Wh. ISBN: 978-960-474-354-4
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