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A GRASP heuristic with Path-Relinking for a bi-objective p-median problem

This paper deals with the a bi-objective p-median problem that consists in finding p-locals from a set of m candidate locals to install facilities in which two objective functions are simultaneously minimized: the sum of the distances from each customer to its nearest facility and the sum of costs for opening facilities. To determine a set of non-dominated solutions, that is, to find an approximation of the Pareto-optimal solutions is proposed a novel method based on GRASP (Greedy Randomized Adaptive Search Procedure) heuristic that constructs iteratively non-dominated solutions (constructive phase) and some of these solutions are improved by a local search procedure. An intensification strategy based on the Path-Relinking is also applied. To test the performance of the proposed heuristic we develop a Mathematical Programming Algorithm, called e-Restrict, that find Pareto-optimal solutions by solving the Integer Programming model of the problem with additional constraints.