Abstract
This paper considers the p-median problem that consists in finding p-locals from a set of m candidate locals to install facilities minimizing simultaneously two functions: the sum of the distances from each customer to its nearest facility and the sum of costs for opening facilities. Since this is a NP-Hard problem, heuristic algorithms are the most suitable for solving such a problem. To determine nondominated solutions, we propose a multi-objective genetic algorithm (MOGA) based on a nondominated sorting approach. The algorithm uses an efficient elitism strategy and an intensification operator based on the Path Relinking technique. To test the performance of the proposed MOGA, we develop a Mathematical Programming Algorithm, called (-Constraint, that finds Pareto-optimal solutions by solving iteratively the mathematical model of the problem with additional constraints. The results show that the proposed approach is able to generate good approximations to the nondominated frontier of the bi-objective problem efficiently.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alp, O., Erkut, E., Drezner, Z.: An Efficient Genetic Algorithm for the p-Median problem. Annals of Operations Research 122, 21–42 (2003)
Arroyo, J.E.C., Armentano, V.A.: Genetic Local Search for Multi-Objective Flowshop Scheduling Problems. European Journal of Operational Research 167, 717–738 (2005)
Avella, P., Sassano, A.: On the p-Median Polytope. Mathematical Programming 89(3), 395–411 (2001)
Beasley, J.E.: A Note on solving Large p-median problems. European Journal of Operational Research 21, 270–273 (1985)
Chaudhry, S.S., He, S., Chaudhry, P.E.: Solving a class of facility location problems using genetic algorithm. Expert Systems 20, 86–91 (2003)
Chiyoshi, F., Galvão, R.D.: A Statistical Analysis of Simulated Annealing Applied to the p-Median Problem. Annals of Operations Research 96, 61–74 (2000)
Crainic, T., Gendreau, M., Hansen, P., Mladenovic, N.: Cooperative parallel variable neighborhood search for the p-median. Journal of Heuristics 10, 293–314 (2004)
Czyzak, P., Jaszkiewicz, A.: Pareto simulated annealing - a metaheuristic technique for multiple objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 734–747 (1998)
Daskin, M.S.: Network and Discrete Location: Models, Algorithms and Applications. Wiley, New York (1995)
Deb, K., Agrawal, S., Pratab, A., e Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Gandibleux, X., Ehrgott, M.: 1984-2004 - 20 Years of Multiobjective Metaheuristics. But What About the Solution of Combinatorial Problems with Multiple Objectives? In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 33–46. Springer, Heidelberg (2005)
Glover, F.: Tabu search and adaptive memory programming - advances, applications, and challenges. In: Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer Academic Publishers, Dordrecht (1996)
Hansen, P., Mladenovic´, N.: Variable neighborhood search for the p-median. Location Science 5, 207–226 (1997)
Hosage, C.M., Goodchild, M.F.: Discrete Space Location–Allocation Solutions from Genetic Algorithms. Annals of Operations Research 6, 35–46 (1986)
Kariv, O., Hakimi, S.L.: The p-median problems, in An Algorithmic Approach to Network Location Problems. SIAM Journal on Applied Mathematics 37, 539–560 (1979)
Kuehn, A.A., Hamburger, M.J.: A heuristic program for locating warehouses. Management Science 9(4), 643–666 (1963)
Levanova, T., Loresh, M.A.: Algorithms of ant system and simulated annealing for the p-median problem. Automation and Remote Control 65, 431–438 (2004)
Mladenovic´, N., Brimberg, J., Hansen, P., Moreno-Pérez, J.A.: The p-median problem: A survey of metaheuristic approaches. European Journal of Operational Research 179, 927–939 (2007)
Resende, M.G.C., e Werneck, R.F.: A hybrid multistart heuristic for the uncapacitated facility location problem. European Journal of Operational Research 174(1), 54–68 (2005)
Rolland, E., Schilling, D.A., Current, J.R.: An Efficient Tabu Search Procedure for the p-Median Problem. European Journal of Operational Research 96, 329–342 (1997)
Salhi, S.: Defining tabu list size and aspiration criterion within tabu search methods. Computers and Operations Research 29, 67–86 (2002)
Teitz, M.B., Bart, P.: Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph. Operations Research 16, 955–961 (1968)
Whitaker, R.: A fast algorithm for the greedy interchange for large-scale clustering and median location problems. Infor. 21, 95–108 (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arroyo, J.E.C., dos Santos, P.M., Soares, M.S., Santos, A.G. (2010). A Multi-Objective Genetic Algorithm with Path Relinking for the p-Median Problem. In: Kuri-Morales, A., Simari, G.R. (eds) Advances in Artificial Intelligence – IBERAMIA 2010. IBERAMIA 2010. Lecture Notes in Computer Science(), vol 6433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16952-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-16952-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16951-9
Online ISBN: 978-3-642-16952-6
eBook Packages: Computer ScienceComputer Science (R0)