Abstract
One of the most common problems in locating obnoxious facilities is the obnoxious p-median problem. This problem seeks to maximize the minimum weighted distance between a set of p facilities and a set of demand points. This work proposes an alternative methodology for the planar obnoxious p-median problem with variable sizes. Variable sizes represents a more realistic variant of the problem in which demand points and facilities are represented using geometric elements rather than atomic points. A greedy randomized adaptive search procedure (GRASP) algorithm is developed as the first proposed approach, which includes a local search that allows the search to traverse the continuous space. Besides, this work defines a discretization based on a Delaunay triangulation and includes an additional local search over it. Finally, a Variable Neighborhood Search (VNS) algorithm is proposed to combine the movements over the continuous space and the discretized space. The computational results show that the proposed algorithm outperforms in the objective function the state-of-art methods while keeping short running times. These results are statistically confirmed through nonparametric statistical tests, becoming the new state-of-the-art method for this problem.
Sergio Salazar
Artificial Intelligence Phd Student
Sergio Salazar graduated in Mathematics and Computer Science from the Rey Juan Carlos University in 2023. He is working here as a predoctoral researcher focusing in Continious Facilities Location Problems.
Abraham Duarte
Full Professor
Abraham Duarte is Full Professor in the Computer Science Department at the Rey Juan Carlos University (Madrid, Spain). He has done extensive research in the interface between computer science, artificial intelligence, and operations research to develop solution methods based on Computational Intelligence (metaheuristics) for practical problems in operations-management areas such as logistics and supply chains, telecommunications, decision-making under uncertainty and optimization of simulated systems.
J. Manuel Colmenar
Full Professor
My research interests are focused on metaheuristics applied to optimization problems. I have worked on different combinatorial optimization problems applying trajectorial algorithms such us GRASP or VNS. Besides, I am very interested in applications of Grammatical Evolution, specifically in model and prediction domain, as alternative to machine learning approaches.