ROULETTE-TOURNAMENT SELECTION FOR SHRIMP DIET FORMULATION PROBLEM

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1 28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa ( ) ROULETTE-TOURNAMENT SELECTION FOR SHRIMP DIET FORMULATION PROBLEM Rosshary Abd. Rahma 1 ad Razam Raml 2 1,2 Uverst Utara Malaysa, Malaysa, 1 [email protected], 2 [email protected] ABSTRACT. Ths paper ams to propose a ew selecto procedure for real value ecodg problem, specfcally for shrmp det problem. Ths ew selecto s a hybrd betwee two well-kow selecto procedure; roulette wheel selecto ad bary touramet selecto. Shrmp det problem s vestgated to uderstad the hard costrats ad the soft costrats volved. The comparso betwee other exstg selectos s also descrbed for evaluato purposes. The result shows that roulette-touramet selecto s better terms of umber of feasble solutos acheved ad thus sutable for real value ecodg problem. However, the combato wth other crossover or mutato mght be vestgated to fd the most suted combato that ca obta better best so far soluto. INTRODUCTION Keywords: evolutoary algorthm, det problem, selecto, shrmp det Selecto or reproducto s oe of the mportat operators used geetc algorthms (GA). Bascally, the purpose of selecto process s to choose better solutos to be parets for the ext step ad delete the remag worse soluto (Deb, 2000). Svaraj ad Ravchadra (2011) revew several selecto procedures GA. These procedure are roulette wheel selecto, determstc samplg, lear rakg selecto, bary touramet selecto, rage selecto ad may more. Dfferet selecto mechasms work well uder dfferet problem (Svaraj & Ravchadra, 2011). Thus, the most sutable procedure has to be chose for the specfc problem to crease the optmalty of the soluto. Roulette wheel selecto (RWS) has bee proposed by Hollad 1975 ad has bee used wdely the applcato of GA. It becomes oe of the most popular selecto procedures that are based o the cocepts of proportoate. Coceptually, the ftess value of each dvdual the populato s correspods to the area o the roulette wheel proporto. The, the roulette wheel s sp; a soluto marked by the roulette wheel poter s selected. Hgher ftess wth bgger area s lkely to have more chaces to be chose. The segmet sze ad selecto probablty rema the same throughout the selecto phase (Chpperfeld, 1997). The advatage of RWS techque s t gves o bas wth ulmted spread (Chpperfeld, 1997). However, oe of the dsadvatages of RWS s t caot hadle egatve ftess values due to the proportoate cocept (Deb, 2000). Also, RWS caot hadle mmzato problem drectly. However, ths lmtato ca be overcome by trasformg t to equvalet maxmzato problem. Meawhle, competto amog a group of parets s the bass of touramet selecto procedure. Measuremet of ftess of soluto s made amog all parets ad the paret havg the best ftess s selected. The term bary touramet refers to two touramet sze whch s the smplest form of touramet selecto (Deb, 2000). Bary touramet selecto 65

2 28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa ( ) starts by selectg two dvduals radom. The, ftess values of these dvduals are evaluated. The oe havg the better ftess s chose. Oe advatage of touramet selecto s ts ablty to hadle ether mmzato or maxmzato problems wthout ay structural chages. I addto, egatve value s allowed wthout ay restrcto. The ma cocer of ths paper s to develop a ew selecto procedure that combes two establshed selecto schemes; RWS ad bary touramet selecto. GA wth ths ew proposed roulette-touramet selecto s appled for det formulato model for juvele Whteleg shrmp whch satsfy all the costrats wth mmum cost. Whteleg shrmp s chose because ths speces s the most popular cultured shrmp Asa ad Malaysa as well. Whteleg shrmp cotrbutes to early 80% of total shrmp producto Malaysa (FAO, 2012). Several costrats o shrmp det were cosdered cludg rato weght, utrtoal rage, ad gredet rage. These were defe through experts opo ad lterature revew. Nutrtoal rage s classfed to three; sgle utret, combato of utrets, ad rato betwee two utrets. A system prototype s the developed to allow user to put preferred rato weght ad choose the preferred gredets ad search for the most ecoomc det. The fal result s the lst of selected gredets specfc quattes that wll satsfy all the stated costrats. METHODOLOGY The roulette-touramet selecto procedure troduced ths study s a combato of RWS procedure ad bary touramet selecto. The procedure starts wth the same steps as RWS. The, the bary touramet procedure take place by choosg two dvduals as parets. As bary touramet, two dvduals are radomly pcked from all solutos, ad the ftter parets wll be chose as paret oe. The same step s repeated to fd paret two. The hybrdzato of ths procedure wll merge the advatages from both RWS ad bary touramet. The evolutoary model cossts of talzato, roulette-touramet selecto, oe-pot crossover, power mutato ad steady state reproducto as shows Fgure 1. I addto, eltsm procedure s also serted because t ca crease GA performace as t prevets the loss of best foud soluto (López-Pujalte, Bote & Aegó, 2002 ad Sharef, Eldho & Rastog, 2008). However, ths paper specfcally focused o roulette-touramet selecto procedure. I order to develop the model, objectve fucto ad the costrats volved shrmp det problem are llustrated mathematcal formulato the ext subsecto. Meawhle, for comparso purposes, two exstg selecto schemes; RWS ad Quee Bee selecto, are also developed. The results are the evaluated by comparg the results from these selecto schemes. 66

3 28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa ( ) start Geerate populato Icorporatg Power Heurstc Roulette-Touramet selecto Oe-pot crossover Power mutato Repar feasble offsprg usg Power Heurstcs Stoppg crtera met? yes Best dvdual o Fgure 3. Evolutoary Model. Mathematcal Formulato The performace of three GA models wth dfferet selecto schemes are tested usg real data for amal det formulato problem. I ths problem, the am s to satsfy all the utrtoal eeds of farmed shrmps at a mmum cost. The mmzato problem takes to accout 14 gredets ad 18 utrets. The followg are the objectve fucto ad costrats volved ths problem. Objectve fucto of the feed cost s defed as: f ( s) m ( X C ), (1) where C s the cost of gredet, X equals the weght of the th gredet, ad s s cumulatve cost a strg of chromosome. However, the am of ths study s to frstly reduce the pealty fucto value based o all detfed costrats. The costrats cosst of gredets rage, gredet (rato) weght, 67

4 28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa ( ) umber of gredets, sgle utret s rage, combato utrets rage, ad rato of utrets. Igredets rage: X 0 or LX X U X for all X, (2) where L X = lower boud of gredet, Igredet weght: U X = upper boud of gredet, X equals the weght of the th gredet. where Y s a weght predefe by user user terface. Number of gredet: X Y, 1 (3) 14. (4) Sgle utrets rage: L Nk N k X U Nk, (5) where L Nk = lower boud of utret k, U Nk = upper boud of utret k, N = total value of utret k. Combato utrets rage: L N X U, (6) Nk( j) k ( j) Nk( j) where L Nk (+j) = lower boud of combato utret +j, U Nk (+j) = upper boud of combato utret +j. Rato utrets rage: L rato N N k kj U rato, (7) 68

5 28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa ( ) where L rato = lower boud of rato betwee utret ad j, U rato = upper boud of rato betwee utret ad j. Ftess calculato for the GA s bascally based o pealty value for each costrat. There are two types of costrat; hard ad soft costrats. I ths study, hard costrats are gredet (rato) weght, umber of gredet, ad prote rage costrat. Else, for soft costrats, dfferet pealty values are gve for dfferet costrats based o depth dscusso wth experts. Pealty value of 20 s gve for volatg each gredet costrat, except for certa mportat gredets; 30 s gve for sgle utret, 20 for combato of utrets, ad 20 for rato of utret. RESULT AND DISCUSSION I our expermets, GA parameters were set as follow: sze of a populato s 30, umber of geerato s 200, crossover rate s 0.60, ad power value for power mutato s Table 1 llustrates the smulated results of all GA models. From the Table, we summarze the best so far soluto, average ftess, stadard devato ad processg tme ( secod) take to produce the best-so-far soluto. These values are used as a dcator to evaluate the performace of these GA models. Table 1. The Results of GA Models wth Dfferet Selecto Schemes Model Best so far soluto Average Ftess Stadard Devato Ru Tme Roulette- Touramet Roulette Wheel Quee Bee Normalty test s doe wth the teto to check ether the data s ormally dstrbuted or ot. The result from Shapro-Wlk test cofrmed that all the dstrbuto from each model s ormal. From Table 1, Roulette-Touramet Oe-pot gves the worst soluto wth 460 ftess value. However, from 30 rus, Roulette-Touramet Oe-pot obtaed oly 5 feasble solutos, compared to Roulette Wheel-Oe-pot wth 6 feasble solutos, ad Quee Bee Oe-pot wth 16 feasble solutos. Stadard devato for Roulette Wheel Oe-Pot s the lowest value. It s the followed by Roulette-Touramet Oe-pot model ad Quee Bee Oe-pot. Stadard devato shows the devato or dsperso of the data from mea. The lower stadard devato dcates that the model gve stable soluto, whch mea t s always approachg mea. Ru tmes shows that Roulette-Touramet Oe-pot ad Quee Bee-Oe-pot each gve approxmately equal tme. CONCLUSION The performace of basc GA model wth dfferet selecto scheme s descrbed. I ths paper, we exted the basc GA model by troducg the roulette-touramet selecto. The results show that our proposed selecto procedure ca be used problems wth real value 69

6 28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa ( ) ecodg. I future research, ths ew selecto scheme mght be used wth other crossover or mutato scheme to get the most approprate combato for real value ecodg problem. REFERENCES Chpperfeld, A. (1997). Itroducto to geetc algorthms. I A. M. S. Zalzala & P. J. Flemg, Geetc Algorthms egeerg systems. (pp. 1-41). Lodo: The Isttuto of Electrcal Egeers. Food ad Agrculture Orgazato of the Uted Natos (FAO). Retreved September 26, 2012, from Deb, K. (2000). Itroducto to selecto. I T. Bäck, D. B. Fogel, & T. Mchalewcz, Evolutoary Computato 1: Basc algorthms ad operators (pp ). Brstol: Isttute of Physcs Publshg. Food ad Agrculture Orgazato of the Uted Natos (FAO). Retreved September 26, 2012, from López-Pujalte, C., Bote, V. P. G. ad Aegó, F, d., M. (2002). A test of geetc algorthms relevace feedback. Iformato Processg ad Maagemet, 38, Sharef, S., Eldho, T., & Rastog, A. (2008). Eltst GA Based Evolutoary Algorthm for Groudwater. The 12th Iteratoal Coferece of Iteratoal Assocato for Computer Methods ad Advaces Geomechacs (IACMAG). Goa, Ida. Svaraj, R., & Ravchadra, T. (2011). A Revew of selecto methods geetc algorthm. Iteratoal Joural of Egeerg Scece ad Techology, Charkha, P. R. (2008). Stock Prce Predcto ad Tred Predcto Usg Neural Networks. Frst Iteratoal Cofereceo Emergg Treds Egeerg ad Techology (pp ). IEEE. do: /icetet Dzkevčus, A., & Šarada,S. (2010). EMA versus SMA Usage to Forecast Stock Markets: The Case ofs#38;p500 ad OMXBaltc Bechmark. Busess: Theory ad Practce, 11(3), do: /btp Gupta,A., & Dhgra, B. (2012). Stock Market Predcto Usg Hdde Markov Models. IEEE. Hassa,M. R., Nath,B., & Krley, M.(2007). Afuso model of HMM, ANN ad GAfor stock market forecastg. Expert Systems wth Applcatos, 33(1), do: /j.eswa Kamjo, K., & Tagawa, T. (1990). Stock prce patter recogto- a recurret eural etwork approach. 1990I JCNN Iteratoal Jot Coferece o Neural Networks,1(1), do: /ijcnn Lee, K.H., & Jo, G.S.(1999). Expert system for predctg stock market tmg usg a cadle stck chart. Expert Systems wth Applcatos, 16(4), do: /s (99) Makckeė, N., & Makckas, A. (2012). Applcato of Neural Networkf or Forecastg of Exchage Rates ad Forex Tradg. The 7th Iteratoal Scetfc Coferece Busess ad Maagemet Selected papers (pp ). Vlus, Lthuaa: VlusGedmas Techcal Uversty Publshg House Techka. do: /bm Nels,R. (2004). Dyamc Tme Warpg: Atutve way of hadwrtg recogto? Radboud Uversty Njmege. Olay, S. A. S., Adewole, K. S., & Jmoh, R. G. (2011). Stock Tred Predcto Usg Regresso. 70