Emrah 70 Ekim kat edilen mesafenin en. mizasyonu (PSO) sezgisel. (PSO), Genetik Algoritma (GA), Optimizasyon, Meta-Sezgisel

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1 METAplam kat edlen mesafenn en mzasyonu (PSO) sezgsel k (PSO), Genetk Algortma (GA), Optmzasyon, Meta-Sezgsel 74

2 OPTIMIZATION OF MULTI- PROBLEM OF ISTANBUL HALK EKMEK A.S. (IHE) BY USING META-HEURISTIC METHODS ABSTRACT The Mult Depot Vehcle Routng Problem (MDVRP) s a well known and complex combnatoral problem whch has receved consderable attenton n recent years. MDVRP can be descrbed as the problem of desgnng optmal routes from several depots to a number of customers. The objectve s to fnd a set of routes whch mnmzes the total dstance traveled. In today's busness world, transportaton cost typcally s an mportant part of the total logstcs costs. An effcent heurstc method combnng the genetc algorthm (GA) and partcle swarm optmzaton (PSO) s proposed for solvng clusterng and VRP subproblems of the MDVRP. Istanbul Halk Ekmek (IHE) A.S. s an economcal organzaton establshed by t dstrbutng cheap, healthy and hgh qualty bread and floury products. The total daly capacty of the IHE factores (Cebec, Edrnekap, Kartal) s the producton of more than 1 mllon breads (13% market share). IHE delvers bread to 1012 customers three tmes a day wth 75 vehcles. The proposed GA-PSO based heurstc technc s used to solve the MDVRP of IHE A.S. and results are compared wth the current delvery strateges. Key words: Vehcle Routng Problem (VRP), Partcle Swarm Optmzaton (PSO), Genetc Algorthm (GA), Optmzaton, Meta-Heurstc Methods 75

3 blnmemektedr. unsurlardan brdr. 1. optmzasyondak - (Laporte, Glbert, Les Cahers du Gerad, 2009, s:6). -Zor) problem a etmektr.. Bast A m lstelenr. q Qk q ve Q k cj 76

4 almaz (Lawler, E. L., v.d., 1992, s: 433). dkkate mevcuttur. H ver G., 2007, s:757). (Crever, B., Cordeau, J. F., Laporte, tp karar almak gerekldr k W., v.d., 2007, s:550). kl (Ho, 77

5 2. (Aarts, E, Lenstra J.K., 1997, s:322). -nokta Ebeveyn jenerasyonu her terasyonda br Probleme at potansyel (Paterln, S., Krnk T., 2006, s: ). Br (Khoo, K. G., Suganthan, P. N., 2002, s:1592). D.R., Martn R.R., 1993, s:60) (Beasley,D., Bull 78

6 (Goldberg, D. E., 1989, s:14). (Coln Reeves, 2003, s:64). (Srwardene, N. R., Perera, B. J. C., 2006, s:417). Shmamoto, H., 2004, s:241). (Tanguch, E., ve 3. (Clerc, M., 2006, s:29). trlen evrmsel 79

7 ( 2006, s:59). (Yuhu Sh, 1999, s:9) sstemde ko (Hassan, R., Cohanm, B., Weck, O., 2005, s:2).. Bunlar s (Kennedy, J. ve Eberhart, R. C., 1995, s:1944). (Yuhu Sh, a.g.e., s:9). resnce s ederler (Sh, Y., Eberhart, R. C., 1999, s:1945). - terasyonda d maddeler L., 2002, s: ). (Xe, X. F., Zhang, W. J., Yang, Z. 80

8 (Hassan, R., v.d., a.g.e., s:3). x0 xmn rand ( xmak xmn) (1) xmn rand( xm ak xmn ) v0 t (2) Konum Zaman (Hassan, R., v.d., a.g.e., s:3). ( p xk ) vk 1 w* vk c1 * rand c2 t (3) * rand ( p g k t x k ) (Momentum) ( vk 1 =. nc -1.4) w* = Mevcut Hareket (Eylemszlk) v k c 1-2) ( p xk ) c1 * rand t c 2-2.5) g ( pk xk ) c2 * rand t alt (x mn ) ve mak x k v k -1 81

9 (Hassan, R., v.d., a.g.e., s:4). (Valle, Y.,v.d., 2008, s:173). g p k vk 1 t hareketten etklenerek v k (atalet k 1, ve s 2 ) Bu 82

10 s belrle Durdurma krter (Tchomte, S. T., Gourgand, M., 2009, s:58) 1 ve c 2 x (4) x v k 1 k k 1 t (Hassan, R., v.d., a.g.e., s:5). 2005, s:11). (Fealko, D. R., (KA) optmzasyonudur. PSOn R ve (10,3, 2,45)] (-3,4, 8), (15, 22) 83

11 (Chen, C.Y., Ye, F., 2004., s:791): x, 1,2,..., N ) j. k C j, j 1,2,..., K x z j x z p, p 1,2,..., K ve j p K N j 1 1 J x z j (5) Uygunluk= k /( J J 0 ) (6) 2 J 0 : P P P P ) P g P g ) daha y se son - 84

12 PSO ve K-ortalamalar n Chu v.d. pazar segmentlern belrleme karar destek sstemnde PSO+K-Ortalamalar ve K- (Chu, C.Y., v.d., 2009, s:4560). 4.UYGULAMA optmzasyonu ve genetk algortma metamevcuttur. 1911,2 km le en uzun seya. Klyos, Durusu, kat etmektedr. Tablo 1: Mevcut rotalara at blgler Toplam Mesafe (km) ,6 756,96 Kartal Fab. (K) ,7 493,62 Cebec Fab. (C) ,2 1146,72 nablr. Programda yer alan PSO n 85

13 Tablo 2: Durdurma Krter Parametre lan kodun grd ve sterlmektedr. PSO le k boyut meleme analzne at ra r. S dek 50 d rastsal st ere sahp d m Daha sonra terasyon say, atalet, ven katsay venme katsay, s b grd parametreler belrlenr. M terlere at GPS matrs yap nda ssteme terasyon boyunca par X ve Y boyutlar ncellenr me merkezlernn da bulunur. me merkezlerne klar er o ana kadark en d er se kaydedlr. Daha z ncellenr. klar me merkezlerne ata r ve merkezlere olan terasyonlar tamamland me merkez erler n hang merkeze atand ve uygunluk r kld uzakl elde edlr. Matlab programlama dlnde kodlanan yaz tek depolu ARP gel. Yaz grd ve da belrtlmektedr. 86

14 say Her rotada zyaret edlecek mnmum m ter say lasyon b terasyon say er d klar matrs En uygun rota Tablo 3: Genetk algortma kontrol parametreler Genetk Algortma Parametre Mutasyon R K T Durdurma Krter terasyon Say m stratejs m say ndan br k say elde edlr. Rotalara at ve k lmalara at rastsal olarak belrlenr. Programda lacak ara de belrlenr. Pop la erlernn elde edlmesn takp eden ndek en uygun rota bulunur. Yen, k e t mutas r. say 1 olarak atand da ARP vermektedr. Bu durumda 87

15 2,5 merkezlerne olan ortalama uzakl 2 1,5 1 0,5 0 Cebec Kartal Tablo 4: Mevcut Rota Yen Rota (km) (TL) 1261, ,6 207, ,2 1288,3 622,9 373,74 822,7 773,8 48,9 29,34 TOPLAM 3995,5 2978,1 1017,4 610,44 88

16 Edrnekap Cebec Kartal Mevcut Rota Uzunluklar (km) Yen Rota Uzunluklar (km) Cebec Kartal 89

17 ve Genetk Algortma meta- nn meta-sezgsel hamlede belrlenmes yerne 10- meta- - bu fabrkalarda mevcuttur. luk ve Cebec larda toplam rota e 1017,.. 90

18 Aarts, E, Lenstra J.K., Sons Ltd, 1997 Beasley,D., Bull D.R., Martn R.R., Computng, 1993, 15(2), s:58-65, Unversty of Chen, C.Y., Ye, F.,, Proceedngs of the 2004 IEEE, Internatonal Conference of Networkng, Sensng and Control, Tape, Tawan, March, 2004, s: Chu, C.Y., Chen, Y.F., Kuo, I.T., Ku, H.C., system usng k- Appcatons, 36, 2009, s: , Expert Systems wth Partcle Swarm Optmzaton Coln Reeves,, Derleycler: Glover, F., Kochenberger, G.A., Kluwer Academc Publshers, 2003, Dordrecht Crever, B., Cordeau, J. F., Laporte, G., -depot vehcle routng problem wth nter-, European Journal of Operatonal Research, 176, 2007, s: Fealko, D. R.,, Graduate School of Computer and Informaton Scences, Nova Southeastern Unversty, Doktora tez, 2005, s:11 Goldberg, D. E., "Genetc Algorthms n Search, Optmzaton and Machne Learnng," Addson-Wesley, 1989 Hassan, R., Cohanm, B., Weck, O., cle Swarm Optmzaton, Structural Dynamcs & Materals Conference Aprl 2005, Austn, Texas. s:

19 Ho, W., v.d., -depot vehcle routng, Engneerng Applcaton of Artfcal Intellgence, 2007, s:550 Kennedy, J. and Eberhart, R. C., Proc. of the IEEE Internatonal Conference on Neural Networks, vol.iv, 1995, s: Khoo, K. G., Suganthan, P. N., Letters, 23, 2002, s: soluton, Pattern Recognton Laporte, Glbert, Les Cahers du GERAD,, G , s:6 Lawler, E. L., Lenstra, J.K., Rnnooy Kan, A.H.G, Shmoys, D. B.,, 1992 Paterln, S., Krnk T.,, Computatonal Statstcs & Data Analyss, 50, 2006, s: Sh, Y., Eberhart, R. C., Proceedngs of the Congress on evolutonary Computaton (CEC99) (July), 1999, s: Srwardene, N. R., Perera, B. J. C., 2006, s: , Mathematcal and Computer Modellng, 44, s:58-68 Tanguch, E., and Shmamoto, H., Transportaton Research Part C: Emergng Technologes, Volume 12, Issues 3-4, June-August 2004, s: Tchomte, S. T., Gourgand, M., Producton Economcs, 121, 2009, s:57-67, Int. J. Valle, Y.,v.d., Vol:12, No:2, Aprl, 2008, s:173 IEEE Transactons on Evolutonary Computaton, Xe, X. F., Zhang, W. J, Congress on Evolutonary Computaton (CEC), Hawa, USA, 2002, s: