Abstract This paper deals with an interesting facility location problem known as the bi-objective p -Median and p -Dispersion problem ( BpMD problem). The BpMD problem seeks to locate p facilities to service a set of n demand points, and the goal is to minimize the total distance between facilities and demand points and, simultaneously, maximize the minimum distance between all pairs of hosted facilities. The problem is addressed with a novel path relinking approach, called reactive path relinking, which hybridizes two of the most extended path relinking variants: interior path relinking and exterior path relinking. Additionally, the proposal is adapted to a multi-objective perspective for finding a good approximation of the Pareto front. Computational results prove the superiority of the proposed algorithm over the best procedures found in the literature.

Abstract In this paper, a new solution method is implemented to solve a bi‐objective variant of the vehicle routing problem that appears in industry and environmental enterprises. The solution involves designing a set of routes for each day in a period, in which the service frequency is a decision variable. The proposed algorithm, a muti‐start multi‐objective local search algorithm (MSMLS), minimizes total emissions produced by all vehicles and maximizes the service quality measured as the number of times that a customer is visited by a vehicle in order to be served. The MSMLS is a neighbourhood‐based metaheuristic that obtains high‐quality solutions and that is capable of achieving better performance than other competitive algorithms. Furthermore, the proposed algorithm is able to perform rapid movements thanks to the easy representation of the solutions.

Metaheuristic optimization is at the heart of the intersection between computer science and operations research. The INFORMS Journal of Computing has been fundamental in advancing the ideas behind metaheuristic methodologies. Fred Glover’s “Tabu Search—Part I” was published more than 30 years ago in the first volume of the then ORSA Journal on Computing. This article, one of the most cited in the area of heuristic optimization, paved the way for many contributions to the methodology and practice of operations research. As a continuation of this stream of research, we describe a new scatter search design for multiobjective optimization. The design includes a short-term memory tabu search and a path relinking combination method. We show how the strategies and mechanisms within scatter search and tabu search can be combined to produce a highly effective approach to multiobjective optimization.