Multi-objective memetic optimization for the bi-objective obnoxious p-median problem

Abstract

Location problems have been studied extensively in the optimization literature, the p-median being probably one of the most tackled models. The obnoxious p-median is an interesting variant that appears in the context of hazardous location. The aim of this paper is to formally introduce a bi-objective optimization model for this problem, in which a solution consists of a set of p locations, and two conflicting objectives arise. On the one hand, the sum of the minimum distance between each client and their nearest open facility and, on the other hand, the dispersion among facilities. Both objective values should be kept as large as possible for a convenient location of dangerous facilities.We propose a Multi-Objective Memetic Algorithm (MOMA) to obtain high-quality approximations to the efficient front of the bi-objective obnoxious p-median problem, denoted as Bi-OpM. In particular, we introduce efficient crossover and mutation mechanisms. Additionally, we present several multi-objective local search methods. All the strategies are finally incorporated in a memetic algorithm which limits the search to the feasible region, thus performing an efficient exploration of the solutions space. Our experimentation compares several state-of-the-art procedures with the introduced MOMA emerging as the best performing method in all considered multi-objective metrics.