Abstract
This paper generalizes the iterated greedy algorithm to solve a multi-objective facility location problem known as the Bi-objective p-Center and p-Dispersion problem ( B p C D ). The new algorithm is coined as Multi-objective Parallel Iterated Greedy (MoPIG) and optimizes more than one objective at the same time. The B p C D seeks to locate p facilities to service or cover a set of n demand points, and the goal is to minimize the maximum distance between facilities and demand points and, at the same time, maximize the minimum distance between all pairs of selected facilities. Computational results demonstrate the effectiveness of the proposed algorithm over the evolutionary algorithms NSGA-II, MOEA/D, and the Strength Pareto Evolutionary Algorithm 2 (SPEA2), comparing them with the optimal solution found by the ϵ -constraint method.
Highlights
Facility location is a family of hard optimization problems that have been in the spotlight of the scientific community in the last few years, from a theoretical point of view, and from practitioners in this field [1,2]
In order to clarify the algorithm proposed for Bi-objective p-Center and p-Dispersion problem (BpCD) resolution, we will break down the different phases that make up the algorithm, from the creation of the initial set of solutions used by the iterated greedy metaheuristic to the improvement of these solutions through the application of different local search algorithms
We included the results provided by an efficient implementation of evolutionary algorithms used in facility location problems: NSGA-II, Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2)
Summary
Facility location is a family of hard optimization problems that have been in the spotlight of the scientific community in the last few years, from a theoretical point of view, and from practitioners in this field [1,2]. A different work was addressed by [11] to solve the bi-objective obnoxious p-median problem in which the objectives are maximizing the distances between each demand point and their nearest facility and the dispersion among facilities They presented a multi-objective memetic algorithm and obtained high quality solutions. The authors presented an integer formulation for each considered problem and an e-constraint algorithm for solving the bi-objective problem They were able to provide high quality solutions for BpCD, the exact nature of the proposal made the development of new metaheuristics necessary, which were able to reach high quality solutions, and in shorter computing times.
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