Genetic Algorithms for Optimal Scheduling of Chlorine Dosing in Water Distribution Systems

Transcription

1 oz343 Genetic Algorithm for Optimal Scheduling of hlorine Doing in Water Ditribution Sytem arl Rouhiainen, urtin Univerity, Moe O. Tade, urtin Univerity, EXEUTIVE SUMMARY Thi paper preent a new model uing a genetic algorithm optimiation technique for determining the optimal chedule of chlorine doing within a water ditribution ytem conidering multiple, competing objective: diinfection control and aethetic control. The characteritic of genetic algorithm which olve the optimiation problem in parallel, uing a population of potential candidate olution, make the genetic algorithm a highly uitable technique for olving multi-objective optimiation problem, in particular for generating a et of Pareto-optimal olution (a generating-baed method). A logical proce for multi-objective genetic algorithm development uing generating-baed method i to firt comprehend the ingle-objective genetic algorithm problem. To addre thi, the model formulation i baed on the claic weighted-um approached (a preference-baed method) to convert the multi-objective problem into a ingle-objective problem, by weighting and umming the individual objective function, to create a quai - ingle objective function, for olving uing a ingle-objective genetic algorithm. The model i alo capable of handling improved nonlinear chlorine decay algorithm by eparating the genetic algorithm code from the network imulation code ued to calculate the hydraulic and water quality ytem dynamic. Six different genetic algorithm model were developed and teted againt a hypothetical water ditribution ytem uing a ingle monitoring node, to determine the bet model configuration prior to application on a ytem coniting of 1 monitoring node. Thi wa achieved by mean of ix different cenario: a imple genetic algorithm (SGA), an elitit genetic algorithm (EGA), and a hybrid (with local earch) genetic algorithm (HEGA); each teted uing either binary-parameter or gray-parameter repreentation. Each cenario conited of four imulation with population ize 4, 8, 16 and 32 repectively. Of the 24 model configuration evaluated, the bet model wa determined a the hybrid elitit genetic algorithm uing gray-parameter repreentation, with a population ize of 16 (HEGA GP16 ). Overall the hybrid technique wa found to produce better reult, with 83% of thee making up the top 6 model configuration. Gray-parameter repreentation proved to produce better reult than binary-parameter repreentation, with 67% of thee making up the top 12 model configuration. The bet model configuration (HEGA GP16 ) wa applied to the hypothetical ditribution ytem, with 1 demand node ued a monitoring point. Three cenario were modelled uing weighting factor for diinfection control and aethetic control a.25:.75,.5:.5, and.75:.25 repectively. The reult howed that the model wa capable of producing the optimal doing chedule conidering the varying weighting factor ued. However, the model i enitive to the weighting factor applied to the two primary objective and the bet doing chedule depend on ome prior knowledge of the prioritie

2 of each of the two primary objective function. Solving the multi-objective problem uing the weighted-um approach (a preference-baed method) ha the diadvantage of requiring new run of the model every time prioritie or "preference" change. To addre thi limitation, the development of a new multi-objective genetic algorithm model, uing a Pareto-baed approach (a generating-baed method), i in progre. INTRODUTION ontrolling the level of chlorine within the ditribution ytem i an important area for the water indutry. hlorine doing et point at pot-treatment booter tation are typically contant with adjutment only being made on a weekly or eaonal bai, if at all. Due to the diurnal nature of ytem demand, opportunitie exit to optimie the cheduling of chlorine doing on an hourly bai, via feed-forward predictive optimiation model, to maximie diinfection control and minimie aethetic concern within water ditribution ytem. Exiting reearch clearly demontrate the need for optimal chlorine cheduling model to help maintain chlorine reidual within the ditribution ytem within precribed limit (Levi and Mallevialle, 1995 & Uber et al., 1996). Several tudie have addreed thi problem by developing optimal chlorine booter diinfection cheduling model (Tryby et al., 1997, Boccelli et al., 1998, Tryby et al., 1999 & Nace et al., 21). Reult from thi reearch conclude that there are benefit for indutry of uing uch model. Exiting model have treated the requirement for diinfection control and aethetic control a contraint, by applying lower and upper chlorine bound, to maintain chlorine reidual within the ditribution ytem within precribed limit. By formulating the requirement for diinfection control and aethetic control a two ditinct objective function, the genetic algorithm (GA) model preented in thi paper enable ytem operator to predefine prioritie (preference) for diinfection and aethetic control, in the form of diinfection and aethetic weighting factor. Exiting model have alo aumed a firt-order chlorine decay algorithm, implifying the complex nonlinear optimiation problem. Studie have hown that firt-order chlorine decay algorithm do not adequately repreent the ytem, due to the complex phyical, chemical and biological reaction that occur in water a it travel from treatment plant to cutomer tap. The model preented in thi paper i capable of handling improved nonlinear chlorine decay algorithm by eparating the genetic algorithm code from the network imulation. MODEL FORMULATION The model formulation i baed on a hypothetical water upply cheme. The ditribution ytem (Figure 1) i upplied from a ground water ource, with the water being treated at a ground water treatment plant before being pumped to a high-level excavated ervice reervoir. Long detention time within the ervice reervoir require the addition of pottreatment diinfection, via a chlorine doing tation (node D ) at the outlet of the reervoir. The chlorine-refrehed water gravity feed to ervice (node 1 to 1 ) within the ditribution ytem. The ervice reervoir, doing tation (node D ), and ditribution ytem are modelled uing the EPANET network hydraulic and water quality imulation package (Roman 2). The hydraulic and chlorine decay model are aumed calibrated. For eae of preentation all network detail, uch a pipe ize and chlorine decay coefficient, are omitted. Sytem demand i aumed a a periodic 24-hour demand pattern (1-minute timetep) for the predefined time horizon (72 hour for thi hypothetical ditribution ytem). The model i not limited to a periodic demand pattern,

3 however for eae of preentation the diurnal ytem demand (Figure 2) i aumed to repeat every 24 hour. The doing chedule i alo aumed a a periodic 24-hour pattern, with each one-hour doe rate (1 to 24) repreenting a deciion variable for the optimiation problem. urve fitting i ued to convert the one-hour timetep into 1- minute timetep, for olving uing EPANET. Water ditribution ytem Tranfer main (eg upply high level ditribution ytem) Pot-treatment diinfection (eg chlorine doing tation) D Water ource (eg borefield) Water treatment (eg ground water treatment plant) 8 Demand (L/ per ervice) Figure 1 Hypothetical water upply cheme Time (hour) Figure 2 Diurnal demand curve (applied to ingle equivalent ervice) Diinfection ontrol Diinfection control i achieved by enuring an adequate chlorine reidual, nominally greater than.1mg/l, i maintained at a demand node. Thi i formulated a a minimiation problem (1). Minimie F d where: m = node m TS U N f (1) M e m m m m dc dr d v T m= 1 t= TS = M = number of node monitored for diinfection control m = cot coefficient (uer defined) dc m dr = cot rate ($) per ervice per day (uer defined)

4 TS TS N t = timetep (nominally 1 minute) e m v m = tart timetep for monitoring node m = end timetep for monitoring node m = number of ervice at node m ( ) Ud = min u umin, u = model predicted chlorine reidual (mg/l) at node m at timetep t u min f T = minimimum chlorine reidual (mg/l) deired (uer defined, nominally.1) = fraction of day (nominally 1/144) The cot coefficient i nominally 1., whilt the cot rate per ervice per day reflect the cot to the community aociated with the rik of drinking water containing pathogen. The tart timetep TS, calculated by running EPANET with a hort pule of chlorine at t= for chlorine doing tation D, i the time of the firt non-zero chlorine reidual (plu 12 hour) at monitoring node m. The end timetep TS e i calculated a the um of the tart timetep plu the duration of chlorine doing (nominally 24 hour). The 12 hour delay i an artificial fix and hould be zero, a it wa found that EPANET did not initialie immediately and took everal hour (after the firt non zero value) to tabilie. Aethetic ontrol The goal of aethetic control i to minimie tate and odour problem aociated with high chlorine reidual, nominally greater than.6mg/l. Thi i formulated a a minimiation problem (2). Minimie F a where: n = node n TS UNf (2) N n n e n n ac ar a vt n = 1 t= TS = N = number of node monitored for aethetic control n = cot coefficient (uer defined) ac n ar = cot rate ($) per ervice per day (uer defined) t = timetep (nominally 1 minute) TS TS u N e n a = tart timetep for monitoring node n = end timetep for monitoring node n ( ) U = max u umax, u = model predicted chlorine reidual (mg/l) at node n at timetep t max n v f T = maximum chlorine reidual (mg/l) deired (uer defined, nominally.6) = number of ervice at node n = fraction of day (nominally 1/144) The cot coefficient i nominally 1., whilt the cot rate per ervice per day reflect the cot to the community aociated with complaint for drinking water with tate and odour problem.

5 Minimiing Volume of hlorine Ued The model alo conider cot aociated with operating the chlorine doing tation D, uch a minimiing the total volume of chlorine ued. Limiting the total volume of chlorine ued i formulated a a minimiation problem (3). Minimie F c S T UQt t t 6 = cc cr (3) = 1 t= 11 where: = chlorine doing node S = number of chlorine doing node t = timetep (nominally 1 minute) T = maximum timetep (nominally 144) cc cr t = cot coefficient, for node (uer defined, nominally 1.) = cot rate ($) per kg chlorine ued, for node (uer defined) Q = flow of water (L/) at doing tation node, at time t t U = chlorine doing rate (mg/l) for node, at time t Minimiing Large Variation in hlorine Doe Rate Another cot aociated with operating the chlorine doing tation D would be to minimiing large change in doing rate over hort time interval, which may affect the doing equipment. Thi i formulated a a minimiation problem (4). Minimie F p S T = 1 pcpr U t (4) = 1 t= 1 where: = chlorine doing node S = number of chlorine doing node pc pr = cot coefficient for node (uer defined) = cot rate ($) for exceeding maximum range r, for node (uer defined) t = timetep (nominally 1 minute) T = maximum timetep (nominally 144) U = max ( + ) t u t 1 ut, rmax t + 1 t max max u = chlorine doe (mg/l) for node, at timetep t + 1 r u = chlorine doe (mg/l) for node, at timetep t = maximum change (mg/l) for node (defined by uer) The cot coefficient i nominally 1., whilt the cot rate for exceeding the maximum range depend on local preference and operating cot.

6 Weighted-Sum Approach The weighted-um approach i the implet and mot widely ued claical approach for olving multi-objective optimiation problem, which (a it name ugget) involve weighting and umming the individual objective to create a quai ingle-objective function. If the objective vary ignificantly in their order of magnitude, it may be appropriate to cale them (alo referred to a normaliation) o that each objective ha an equal order of magnitude. It i alo the uual practice to chooe weight uch that their um i equal to one. The multi-objective problem defined in thi paper conit of four different minimiation function. However, the reearcher are mainly intereted in the two primary objective, diinfection control and aethetic control, defined in (1) and (2) repectively. The other two objective, (3) and (4), are not weighted and are treated a contraint, imilar to the "penalty method", a common technique for handling contrained genetic algorithm problem. Normaliation i not required in thi cae, a the reearcher are intereted in minimiing the total cot. For example, it would not be practical to cale up the cot of the volume of chlorine ued, a hown in (3), to give thi equal priority to diinfection control. The compoite function i defined in (5). Minimie F = W F + W F + F + F (5) where: W W d a SOGA d d a a c p = weighting factor for diinfection control (between and 1) = weighting factor for aethetic control ( W 1) SOLUTION PROEDURE The minimiation function (5) i olved uing a new model, developed uing a new genetic algorithm code linked to the exiting EPANET network imulation code (EPANET ver 2, Roman, 2) ued to calculate the hydraulic and water quality ytem dynamic. Roman (1999) developed a programming toolkit for EPANET that allow model developer to implify the tak required to link the EPANET imulation code to other modelling code, uch a a genetic algorithm optimiation model. The independent linked deign developed for the new model enable future, improved chlorine decay algorithm to be ued without changing the genetic algorithm optimiation code. The tructure of the model i hown in Figure 3. The model wa deigned to upport a population of individual, where each individual ha both a phenotype and genotype tructure. Each individual repreent one poible olution. The phenotype hold the deciion variable, in thi cae 24 one-hour doe rate, whilt the genotype hold the genetic algorithm gene (a deciion variable encoded into a erie of and 1 bit). The model upport either binary or gray-parameter repreentation, with adjutable uer defined preciion for each doing rate. The model upport 2-parent tournament election, multi-point croover and bit-wie mutation. Experimentation with the model indicated a population ize ranging between 4 and 32 may lead to the bet convergence rate, when conidering the expenive (time conuming) objective function, olved uing EPANET. The individual of the firt population are initialied randomly. d

7 1. Deign Model (not part of program flow): Define Individual with both Phenotype and Genotype tructure, Define tructure of Phenotype deciion variable, Define tructure of Genotype gene, Define fitne function from objective function (5), Determine appropriate genetic algorithm parameter (popize etc). 2. Initialie Model: Run EPANET hydraulic imulation (once) and ave hyd file, Load firt population ParentPop with popize number of Individual, Randomie each Individual-Phenotype deciion variable. EPANET 3. alculate Objective Function ot (for each Individual): Pa ParentPop-Individual-Phenotype to EPANET alculate cot from objective function (5), Return ParentPop-Individual-Phenotype reult, Save cot reult for current generation. 4. Elitim (optional): alculate elite Individual from ParentPop and ave to ElitePop. 5. Hybrid local earch (optional): Refine elected ParentPop-Individual-Phenetype uing local earch, Update ElitePop. EPANET 6. alculate Fitne (for each Individual): Summarie ParentPop cot, alculate Individual-Genotype fitne, Save fitne reult for current generation. REPEAT: tep 3 to 1 if converged = Fale 7. Select Potential Mating Parent: Encode each Individual- Phenotype into Individual-Genotype, Uing 2-Parent Tournament build MatingPop from ParentPop". 8. Parent Reproduce To Have hildren: Uing Multi-point roover create hildpop from MatingPop, Uing Bit-wie Mutation introduce diverity into hildpop, Decode each Individual-Genotype into Individual-Phenotype. 9. heck onvergence: Save generation data from ParentPop and hildpop, heck convergence. 1. End Generation: Save reult to dik, IF converged = True THEN Exit ELSE lear ParentPop and MatingPop, Age children to parent by copying hildpop to ParentPop, Increment Generation ounter by 1 END IF Figure 3 Model program flow diagram

8 alculating Objective Function ot For each individual in the population, the phenotype repreentation, which conit of 24 one-hour doe rate, i paed to EPANET. Uing the programmer' toolkit provided with EPANET, the chlorine doing chedule i loaded into the EPANET input file, where each input file conit of ditribution ytem hydraulic and water quality data. EPANET i run and the predicted chlorine reidual data for each monitoring node i aved. Given the chlorine doing chedule, cot for objective function (3) and (4) can be calculated. Uing the reult from each monitoring node the cot for objective function (1) and (2) can be calculated. The total cot for each genetic algorithm individual, which repreent a potential optimal olution, i finally calculated uing (5). alculating Fitne In the implet term the genetic algorithm imulate the evolution proce of life, whereby the fittet individual (in thi cae an individual repreent a mathematical olution) are brought together for mating. The concept i that thee fit individual, uing the genetic algorithm reproduction proce, will pa on "good" part of themelve to their children, whilt unfit individual die off. The meaure of fitne for each individual can imply be the cot of the objective function (5), where a lower cot repreent a fitter individual. However, thi can caue confuion for ome, where a high fitne ha a low cot value. To overcome thi, the model ue (6) to calculate the fitne of each individual, uing population cot tatitic, where the lowet cot individual ha a fitne value of 1 and the highet cot individual ha a fitne value of zero. Fitne = 1* ( max ) ( ) max where: = ot of individual min max min = Minumum cot of all individual within population = Maximum cot of all individual within population (6) onvergence riteria The end of the firt genetic algorithm reproduction proce i referred to a the firt generation. Future generation are evolved from thi firt generation, uing tep 2 through 8 of Figure 3, until a uitable (ideally optimal) olution i found. To top the generation proce from continuing infinitum a convergence check i required. The model upport three level of convergence checking. The model top running when one of the following three criteria (7) i met, whichever come firt. heck 1: If heck 2 If r heck 3: If G c min c r top G top top where: G = urrent generation count G c top min top = Uer defined maximum generation count = Minimum cot of all individual within parent population = Uer defined cot (7)

9 r top = Uer defined check ratio (typically.98) X = Uer defined (typically 1) Y = Uer defined (typically 1) G-X G-Y rc = heck ratio for current generation = min X min Y i=g i=g The Elitit Genetic Algorithm The genetic algorithm reproduction proce may not alway lead to better individual. For example, it i poible that the lowet cot of all individual within the parent population of generation X i greater than the lowet cot of all individual within the parent population of generation X-1. To prevent the lo of good olution an elitit trategy wa implemented. The genetic algorithm elitim proce ave a et number (e%*popize) of the bet (lowet cot) individual from each generation into an elite population of ize e%*popize. The elite population of generation X i compared with the elite population of generation X-1 and the bet e%*popize number of individual of both elite population replace the individual within the elite population of generation X. The Hybrid Genetic Algorithm The combination of a local earch technique i ometime referred to a a hybrid genetic algorithm. The model wa developed to upport the option of including a local earch, the objective being to take the bet h%*popize of the parent population and apply a local earch on each individual until a better (if poible) cot i achieved. Thi i done by randomly picking a deciion variable (a one-hour doe rate) and incrementing the value by a mall amount, in a random direction (up or down). The modified chlorine doing chedule i then olved and the cot function (5) calculated. If the cot i lower the proce repeat, moving in the ame direction until there i no more improvement in cot. If the cot i higher (or the ame) the direction of change i revered and the proce repeated in the new direction. MODEL ONFIGURATION Prior to applying the model to a hypothetical ditribution ytem (Figure 1) coniting of 1 demand node, the model wa firt teted againt a ingle demand node, to determine the bet model configuration. Thi wa achieved by mean of ix different cenario: a imple genetic algorithm (SGA), an elitit genetic algorithm (EGA), and a hybrid (with local earch) elitit genetic algorithm (HEGA); each teted with either binary or gray-parameter repreentation. Each cenario conit of four imulation, with each imulation coniting of 5 eparate randomly initialied run. Demand node "1" wa choen a the tet node. The chedule for chlorine doing at node D wa defined a 24 one-hour deciion variable with lower and upper bound of.2 and 6.mg/L repectively and a minimum preciion of.1mg/l. All model configuration ued 2-parent tournament for election and 2-point croover (probability of.8) with bit-wie mutation (probability of.2) for reproduction. The convergence check data, a per (7), wa defined a: top = $5, r top =.98 (X=1, Y=6), and G top =3. The weighting factor for diinfection control and aethetic control were.5 and.5 repectively. Data for each cenario are lited in Table 1 through Table 4. Optional parameter were e= 2 and h= 2. Table 1 Data for diinfection control, objective function (1) Scenario m M m m dc t TS TS e m dr N u v min

10 Table 2 Data for aethetic control, objective function (2) Scenario n N n n ac t TS TS e n ar N u v max Table 3 Data for chlorine volume control, objective function (3) Scenario S cc t T cr 1-6 D Table 4 Data for doe change rate control, objective function (4) Scenario S pc t T pr 1-6 D Scenario 1: Simple GA uing Binary Repreentation (SGA B ) r max hlorine Doe (mg/l) Time (hour) Figure 4 SGA B - doing at node "D" for monitor node "1" Bet Solution Reidual (mg/l) Time (hour) Bet Solution Figure 5 SGA B - reidual at monitor node "1" (target.1mg/l) for doing at node "D" 12 ot ($,) EPANET run Figure 6 SGA B - cot veru EPANET run Bet Solution Scenario 2: Simple GA uing Gray Repreentation (SGA G ) The reult of the doing chedule and monitor node reidual for SGA G follow imilar trend a Figure 4 and Figure 5 repectively.

11 12 ot ($,) EPANET run Figure 7 SGA G - cot veru EPANET run Bet Solution Scenario 3: Elitit GA uing Binary Repreentation (EGA B ) hlorine Doe (mg/l) Time (hour) Figure 8 EGA B - doing at node "D" for monitor node "1" Bet Solution The reult of the monitor node reidual for EGA B follow imilar trend a Figure 5, with light improvement. 12 ot ($,) EPANET run Figure 9 EGA B - cot veru EPANET run Bet Solution Scenario 4: Elitit GA uing Gray Repreentation (EGA G ) hlorine Doe (mg/l) Bet cot found uing EGAGP Time (hour) Figure 1 EGA G - doing at node "D" for monitor node "1" Bet Solution

12 .15 Reidual (mg/l) Time (hour) Bet Solution Figure 11 EGA G - reidual at monitor node "1" (target.1mg/l) for doing at node "D" The reult for cot veru EPANET run follow imilar trend a Figure 9. Scenario 5: Hybrid Elitit GA uing Binary Repreentation (HEGA B ) The reult of the doing chedule and monitor node reidual for HEGA B follow imilar trend a Figure 1 and Figure 11 repectively. ot ($,) EPANET run Figure 12 HEGA B - cot veru EPANET run Bet Solution Scenario 6: Hybrid Elitit GA uing Gray Repreentation (HEGA G ) hlorine Doe (mg/l) P= Time (hour) Figure 13 HEGA G - doing at node "D" for monitor node "1" (Bet Solution) ot ($,) EPANET run Figure 14 HEGA G - cot veru EPANET run (Bet Solution)

13 The reult of the monitor node reidual for HEGA G follow imilar trend a Figure 11. Summary of Model onfiguration The imple genetic algorithm (both binary and grey-parameter model configuration) performed fairly, a compared to the bet olution provided by HEGA GP16. The elitit genetic algorithm model performed better overall, a compared to the imple genetic algorithm model. EGA GP32 produced the lowet cot (refer Figure 16). However, when compared to the reult obtained from HEGA GP16, it wa concluded that HEGA GP16 wa the bet (out of 24) model configuration, when conidering the computational expene, in term of the number of EPANET run. Overall it wa oberved that imulation with a larger population ize were able to obtain a lower final cot. It wa alo noted that model uing grey-parameter repreentation performed better overall, a compared to model uing binary-parameter repreentation, with 67% of thee making up the top12 (out of 24) model configuration. Overall the hybrid technique wa found to produce better reult, with 83% of thee making up the top 6 model configuration. Figure 15 ummarie all model configuration. The top 12 of 24 model configuration are hown in detail in Figure 16. ot ($,) EGAgp32 HEGAgp16 ot HEGAbp32 HEGAgp32 HEGAbp8 HEGAbp16 Ratio EPANET run to (Betot/ot) EGAgp16 HEGAbp4 EGAgp4 EGAgp8 HEGAgp8 HEGAgp4 EGAbp32 EGAbp8 EGAbp4 EGAbp16 SGAgp32 SGAgp16 SGAbp32 SGAbp8 SGAgp8 SGAbp16 SGAgp4 SGAbp4 5, 4, 3, 2, 1, Ratio EPANET run to (Betot/ot) Figure 15 Summary of all model configuration (order of lowet cot) ot ($,) ot Lowet ot Ratio EPANETrun to (Betot/ot) Bet Solution conidering cot veru EPANET run (11% of lowet) 4, 3, 2, 1, Ratio EPANET run to (Betot/ot) EGAgp32 HEGAgp16 HEGAbp32 HEGAgp32 HEGAbp8 HEGAbp16 EGAgp16 HEGAbp4 HEGAgp8 EGAgp8 EGAgp4 HEGAgp4 Figure 16 Detailed view of top 12 (of 24) model configuration

14 MODEL APPLIATION The bet model configuration (HEGA GP16 ) wa applied to the hypothetical ditribution ytem, taking into conideration all node "1" to "1. Three cenario were modelled uing different weighting factor for diinfection control, to ae the impact thi had on the optimal chlorine doing chedule. Figure 17 how the reult for weighting factor W d =.25,.5, and hlorine Doe (mg/l) Wd=.25 Wd=.5 Wd= Time (hour) Figure 17 HEGA GP16 - doing at node "D" for monitoring ALL node "1" to "1" Each cenario converged after approximately 3 EPANET run (Figure 18). The time to run each imulation, uing a Pentium4 (2GHz) peronal computer, wa approximately 25 minute for each cenario. Thi i within uitable time requirement for off-line cheduling, conidering a cheduling period of 24 hour. It i anticipated that the time to converge to an optimal olution, conidering a lightly modified demand pattern at ome future time (ay 2 hour pat firt model run), would be decreaed dramatically if the model were initialied uing reult from a previou run. 3, ot ($,) 2, 1, 75%Di 5%Di 25%Di EPANET run Figure 18 HEGA GP16 - cot veru EPANET run (varying W d ) Figure 19 how the reult, uing W d =.5, for three repreentative node within the ditribution ytem, a node cloet to the doing tation (node "1"), a node midway (node "6"), and a node furthet from the doing tation (node "1"). It wa oberved that node "1" had ome rapid chlorine reidual increae, at around 31 hour. Depending on the degree of change, thi could poe a problem for cutomer a they may notice the change. However, in the cae above, the change i only.2mg/l and thi would not be a great concern for the hypothetical ditribution ytem. However, to avoid thi change rate from becoming too exceive when applying the model to other ditribution ytem, an additional cot function could be added to (5). The additional cot function could be ued to penalie large change in chlorine reidual over a hort period, imilar to cot function (4).

15 1.6 Doe ("D") hlorine (mg/l) Re ("1") Re ("6").4 Re ("1") Time (hour) Figure 19 HEGA GP16 - Doing at "D" with Wd=.5, howing node "1", "6", and "1" ONLUSIONS Thi paper preented a new model uing a genetic algorithm optimiation technique for determining the optimal chedule of chlorine doing within a water ditribution ytem conidering multiple, competing objective: diinfection control and aethetic control. The deign of the model enable future, improved chlorine decay algorithm to be ued with the optimiation model without changing the genetic algorithm optimiation code. The model wa developed to upport either binary or gray-parameter repreentation. Six different model configuration were developed and each configuration wa teted uing a cenario with four different population ize, applied to a ingle demand node within a hypothetical ditribution ytem. The firt two model configuration were developed baed on the "claic" imple genetic algorithm, but lightly modified to include 2-parent tournament for election and multi-point croover with bit-wie mutation for reproduction. The next two model configuration were developed to include elitim, which wa found to increaed the performance of the model, in attaining an optimal chlorine doing chedule. The lat two model configuration were developed a a hybrid genetic algorithm. The hybrid deign included a local earch technique and wa found to outperform all other model configuration. Of the 24 model configuration evaluated, the bet model wa determined a the hybrid elitit genetic algorithm uing-gray parameter repreentation. Overall gray-parameter repreentation wa found to produce better reult, a compared to model configuration uing binary-parameter repreentation. Hybrid model configuration, including the local earch technique, performed the bet overall, with 83% of thee making up the bet 6 configuration. The bet model configuration (HEGA GP16 ) wa applied to the hypothetical ditribution ytem with 1 demand node ued a monitoring point. Three cenario were modelled uing weighting factor for diinfection control and aethetic control a.25:.75,.5:.5, and.75:.25 repectively. The reult howed that the model wa capable of producing the optimal doing chedule conidering the varying weighting factor ued. However, the model i enitive to the weighting factor applied to the two primary objective and the bet doing chedule depend on ome prior knowledge of the prioritie of each of the two primary objective function. Solving the multi-objective problem uing the weighted-um approach (a preference-baed method) ha the diadvantage of requiring new run of the model every time prioritie or "preference" change. To addre

16 thi limitation, the development of a new multi-objective genetic algorithm model, uing a Pareto-baed approach (a generating-baed method), i in progre. AKNOWLEDGEMENTS The author would like to acknowledge the Water orporation (Perth, Wetern Autralia) and the ooperative Reearch entre for Water Quality and Treatment (Adelaide, South Autralia) for their upport. REFERENES Boccelli, D.L., Tryby, M.E., Uber, J.G., Roman, L.A., Zierolf, M.L. and Polycarpou, M.M. (1998) "Optimal cheduling of booter diinfection in water ditribution ytem", Journal of Water Reource Planning and Management, 124(2), Levi, Y. and Mallevialle, J. (1995) "Global trategy and new tool for maintaining water quality in ditribution ytem", Proceeding of the hina Water Supply Aociation - Safety of Water Supply in Tranmiion and Ditribution Sytem, November, Shanghai, hina, Nace, A., Harmant, P. and Villon, P. (21) "Optimization of location and chlorine doage of the booter chlorination in water ditribution network", Proceeding of the World Water & Environmental Reource ongre, Bridging the Gap: Meeting the World' Water and Environmental Reource hallenge, ed. Don Phelp and Gerald Sehlke, May 2-24, Orlando, Florida, pre-conference copy, 11pp. Roman, L.A. (1999) "The EPANET programmer' toolkit for analyi of water ditribution ytem", Proceeding of the 26th Annual Water Reource Planning and Management onference, June 6-9, Tempe, Arizona, 4E, 1-1. Roman, L.A. (2) "EPANET Uer Manual, EPA/6/R-/57", United Stated Environmental Protection Agency, Ver 2. Tryby, M.E., Boccelli, D.L., Uber, J.G., Roman, L.A., Zierolf, M.L. and Polycarpou, M.M. (1997) "Optimal cheduling of booter diinfection", Proceeding of the AWWA Annual onference, June, Atlanta, GA, Vol, Tryby, M.E., Boccelli, D.., Koechling, M.T., Uber, J.G., Summer, R.S. and Roman, L.A. (1999) "Booter diinfection for managing diinfectant reidual", Journal of American Water Work Aociation, 91(1), Uber, J.G., Summer, R.S., Boccelli, D.., Koechling, M.T., Tryby, M.E. and Roman, L.A. (1996) "Booter hlorination", Proceeding of the AWWA Annual onference, June 23-27, Toronto, Ontario, anada, Vol D,