A multi-objective genetic algorithm with path relinking for the p-median problem

Authors:
José E. C. Arroyo;Paula M. Dos Santos;Michele S. Soares;André G. Santos
Affiliations:
Departamento de Informática, Universidade Federal de Viçosa, Viçosa, MG, Brazil;Departamento de Informática, Universidade Federal de Viçosa, Viçosa, MG, Brazil;Departamento de Informática, Universidade Federal de Viçosa, Viçosa, MG, Brazil;Departamento de Informática, Universidade Federal de Viçosa, Viçosa, MG, Brazil
Venue:
IBERAMIA'10 Proceedings of the 12th Ibero-American conference on Advances in artificial intelligence
Year:
2010

Citing 4
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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 εConstraint, 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.