Abstract
Bu çalışmada, talep noktalarının arz noktalarına adil biçimde atanmasını sağlayan ilave bir kısıtı ihtiva
eden p-medyan probleminin çözümü için evrimsel bir algoritma önerilmiştir. Temel haliyle bir p-medyan
problemi toplam n adet nokta içerisinden p adedini tesis yeri olarak seçerek geriye kalan talep
noktalarından her birini tesislerden birine atarken, talep noktaları ile atandıkları tesis arasındaki toplam
mesafeyi enazlamayı amaçlar. Bu makalede incelenen problem, aynı tesise atanan noktaların oluşturduğu
p adet grup için hesaplanan grup değerleri arasındaki azami farkı belirlenmiş bir sınır içerisinde tutan
ilave bir kısıta sahiptir. Bir grubun değeri, o grup içerisindeki tüm noktalar için belirlenmiş değerlerin
toplamına eşittir ve bahsedilen değer satış hacmi, nüfus gibi özellikler olup problemden probleme
farklılık gösterebilir. Söz konusu problemin çözümü için evrimsel bir algoritma geliştirilmiş, ilgili
literatürden alınan test problemleri ile yapılan testlerde iyi çözümler alındığı tespit edilmiştir.
References
- 1. Maniezzo, V., Mingozzi, A., Baldacci, R., 1998. A Bionomic Approach to the Capacitated p-Median Problem, Journal of Heuristics 4(3), 263-280.
- 2. Shieh, H.M., May, M.D., 2001. Solving the Capacitated Clustering Problem with Genetic Algorithms, Journal of the Chinese Institute of Industrial Engineers 18(3), 1-12.
- 3. Lorena, L.A.N., Furtado, J.C., 2001. Constructive Genetic Algorithm for Clustering Problems, Evolutionary Computation 9(3), 309-327.
- 4. Correa, E.S., Steiner, M.T.A., Freitas, A.A., Carnieri, C., 2004. A Genetic Algorithm for Solving a Capacitated p-Median Problem, Numerical Algorithms 35, 373-388.
- 5. Ghoseiri K., Ghannadpour S.F., 2007. Solving Capacitated p-Median Problem using Genetic Algorithm, Proceeding of IEEE International Conference on Industrial Engineering and Engineering Management, 885-889.
- 6. Resurreccion J., 2006. An Opportunity Costbased Genetic Algorithm for a Modified Capacitated p-Median Problem, Philippine Engineering Journal 27(2), 1-26.
- 7. ReVelle, C.S., Swain R., 1970. Central Facilities Location, Geographical Analysis 2(1), 30-42.
- 8. Mulvey, J.M., Beck, M.P., 1984. Solving Capacitated Clustering Problems, European Journal of Operational Research 18(3), 339-348. 9. Osman, I.H., Christofides, N., 1994. Capacitated Clustering Problems by Hybrid Simulated Annealing and Tabu Search, International Transactions in Operational Research 1(3), 317-336.
- 10. Lorena, L.A.N., Senne, E.L.F., 2003. Local Search Heuristics for Capacitated p-Median Problems, Networks and Spatial Economics 3(4), 407-419.
- 11. Franca, P.M., Sosa, N.M., Pureza, V., 1999. An Adaptive Tabu Search Algorithm for the Capacitated Clustering Problem, International Transactions in Operational Research 6(6), 665-678.
- 12.Beasley, J.E., 1990. OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society 41(11), 1990, 1069-1072.
Abstract
In this study, an evolutionary algorithm is proposed for solving the p-median problem with attribute
equity constraint. The basic p-median problem aims to choose p facility locations out of n nodes and
allocate the remaining demand nodes to the selected facility locations in order to minimize the total
distance between demand nodes and assigned facilities. The problem studied in this paper has an extra
constraint which keeps the maximum difference between total attributes of any pair of p clusters within a
specified threshold. Attributes of nodes may represent problem dependent properties, like sales volume or
population of districts. An evolutionary algorithm is developed to solve the problem. The algorithm is
experimented with test problems found in the relevant literature and good results are obtained.
References
- 1. Maniezzo, V., Mingozzi, A., Baldacci, R., 1998. A Bionomic Approach to the Capacitated p-Median Problem, Journal of Heuristics 4(3), 263-280.
- 2. Shieh, H.M., May, M.D., 2001. Solving the Capacitated Clustering Problem with Genetic Algorithms, Journal of the Chinese Institute of Industrial Engineers 18(3), 1-12.
- 3. Lorena, L.A.N., Furtado, J.C., 2001. Constructive Genetic Algorithm for Clustering Problems, Evolutionary Computation 9(3), 309-327.
- 4. Correa, E.S., Steiner, M.T.A., Freitas, A.A., Carnieri, C., 2004. A Genetic Algorithm for Solving a Capacitated p-Median Problem, Numerical Algorithms 35, 373-388.
- 5. Ghoseiri K., Ghannadpour S.F., 2007. Solving Capacitated p-Median Problem using Genetic Algorithm, Proceeding of IEEE International Conference on Industrial Engineering and Engineering Management, 885-889.
- 6. Resurreccion J., 2006. An Opportunity Costbased Genetic Algorithm for a Modified Capacitated p-Median Problem, Philippine Engineering Journal 27(2), 1-26.
- 7. ReVelle, C.S., Swain R., 1970. Central Facilities Location, Geographical Analysis 2(1), 30-42.
- 8. Mulvey, J.M., Beck, M.P., 1984. Solving Capacitated Clustering Problems, European Journal of Operational Research 18(3), 339-348. 9. Osman, I.H., Christofides, N., 1994. Capacitated Clustering Problems by Hybrid Simulated Annealing and Tabu Search, International Transactions in Operational Research 1(3), 317-336.
- 10. Lorena, L.A.N., Senne, E.L.F., 2003. Local Search Heuristics for Capacitated p-Median Problems, Networks and Spatial Economics 3(4), 407-419.
- 11. Franca, P.M., Sosa, N.M., Pureza, V., 1999. An Adaptive Tabu Search Algorithm for the Capacitated Clustering Problem, International Transactions in Operational Research 6(6), 665-678.
- 12.Beasley, J.E., 1990. OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society 41(11), 1990, 1069-1072.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | December 26, 2017 |
| Published in Issue | Year 2017 Volume: 32 Issue: 4 |