The ɛ-constraint as a learning strategy in the population-based algorithm: The case of Bi-Objective Obnoxious p-Median Problems - Aïder, Méziane; Azzi, Aida-Ilham; Hifi, Mhand (Knowledge-based systems, 2023)
The obnoxious p-median problem occurs in real-world applications, where facilities have features that induce a dangerous influence on the surrounding area. Therefore, this study aims to investigate a variant of this problem: the bi-objective version, where the two functions are related to the sum of the distances between each customer and its nearest open facility, and to the dispersion between facilities. For this purpose, a population-based algorithm is designed to solve it, where it starts by determining an initial reference archive set of diversified solutions and sequentially enriching the archive set by combining the dominating sorting local search with exchange and drop/reassign operators. Next, a series of ɛ-constraints is added as a learning strategy for iteratively highlighting the final approximate Pareto front. The performance of the method is evaluated on a set of instances, where its provided results are compared to those reached by more recent methods in the literature. Encouraging results are observed. •An NP-hard bi-objective obnoxious p-median problem is studied.•A new population-based algorithm is proposed.•The ɛ-constraint is used as a learning strategy fo highlighting the approximate Pareto front.•Quantitative and qualitative analysis are considered for evaluating the performance of the algorithm.•New dominated solutions with high approximate Pareto fronts are reached.