Aránzazu Gila Arrondo

A two-level evolutionary algorithm for solving the facility location and design (1|1)-centroid problem on the plane with variable demand

In this work, the problem of a company or chain (the leader) that considers the reaction of a competitor chain (the follower) is studied. In particular, the leader wants to set up a single new facility in a planar market where similar facilities of the follower, and possibly of its own chain, are already present. The follower will react by locating another single facility after the leader locates its own facility. Both the location and the quality (representing design, quality of products, prices, etc.) of the new leader’s facility have to be found. The aim is to maximize the profit obtained by the leader considering the future follower’s entry. The demand is supposed to be concentrated at n demand points. Each demand point splits its buying power among the facilities proportionally to the attraction it feels for them. The attraction of a demand point for a facility depends on both the location and the quality of the facility. Usually, the demand is considered in the literature to be fixed or constant regardless the conditions of the market. In this paper, the demand varies depending on the attraction for the facilities. Taking variable demand into consideration makes the model more realistic. However, it increases the complexity of the problem and, therefore, the computational effort needed to solve it. Three heuristic methods are proposed to cope with this hard-to-solve global optimization problem, namely, a grid search procedure, a multistart algorithm and a two-level evolutionary algorithm. The computational studies show that the evolutionary algorithm is both the most robust algorithm and the one that provides the best results.

Approximating the Pareto-front of a planar bi-objective competitive facility location and design problem

A bi-objective competitive facility location and design problem is considered. The problem of obtaining a complete representation of the efficient set and its corresponding Pareto-front has been previously tackled through exact general methods, but they require high computational effort. In this work, we propose a new evolutionary multi-objective optimization algorithm, named FEMOEA, which deals with the problem at hand in a fast and efficient way. It combines ideas from different multi-objective and single-objective optimization evolutionary algorithms, although it also incorporates new devices which help to reduce the computational requirements, and also to improve the quality of the provided solutions. The performance of the algorithm is analyzed by comparing it to other (meta)heuristics previously proposed in the literature. In particular, the reference algorithms MOEA/D, SPEA2 and NSGA-II have been considered. A comprehensive computational study shows that the new heuristic method outperforms, on average, the three heuristic algorithms. Additionally, it reduces, on average, the computing time of the exact methods by approximately 99%, and this offering high-quality discrete approximations of the true Pareto-front. HighlightsA new multi-objective evolutionary algorithm, called FEMOEA, is presented.Its aim is to obtain a discrete approximation of the Pareto-front of multi-objective optimization problems.It combines ideas from different multi-objective and single-objective optimization evolutionary algorithms.It also incorporates a new improving method and a new stopping rule. It has been applied to a hard-to-solve bi-objective continuous competitive facility location and design problem.Computational studies show that the new method outperforms, on average, both SPEA2 and NSGA-II.

Parallelization of a non-linear multi-objective optimization algorithm

Real-life problems usually include conflicting objectives. Solving multi-objective problems (i.e., obtaining the complete efficient set and the corresponding Pareto-front) via exact methods is in many cases nearly intractable. In order to cope with those problems, several (meta) heuristic procedures have been developed during the last decade whose aim is to obtain a good discrete approximation of the Pareto-front. In this vein, a new multi-objective evolutionary algorithm, called FEMOEA, which can be applied to many nonlinear multi-objective optimization problems, has recently been proposed. Through a comparison with an exact interval branch-and-bound algorithm, it has been shown that FEMOEA provides very good approximations of the Pareto-front. Furthermore, it has been compared to the reference algorithms NSGA-II, SPEA2 and MOEA/D. Comprehensive computational studies have shown that, among the studied algorithms, FEMOEA was the one providing, on average, the best results for all the quality indicators analyzed. However, when the set approximating the Pareto-front must have many points (because a high precision is required), the computational time needed by FEMOEA may not be negligible at all. Furthermore, the memory requirements needed by the algorithm when solving those instances may be so high that the available memory may not be enough. In those cases, parallelizing the algorithm and running it in a parallel architecture may be the best way forward. In this work, a parallelization of FEMOEA, called FEMOEA-Paral, is presented. To show its applicability, a bi-objective competitive facility location and design problem is solved. The results show that FEMOEA-Paral is able to maintain the effectiveness of the sequential version and this by reducing the computational costs. Furthermore, the parallel version shows good scalability. The efficiency results have been analyzed by means of a profiling and tracing toolkit for performance analysis.

Solving a leader---follower facility problem via parallel evolutionary approaches

A leader–follower facility problem is considered in this paper. The objective is to maximize the profit obtained by a chain (the leader) knowing that a competitor (the follower) will react by locating another single facility after the leader locates its own facility. A subpopulation-based evolutionary algorithm called TLUEGO was recently proposed to cope with this hard-to-solve global optimization problem. However, it requires high computational effort, even to manage small-size problems. In this work, three parallelizations of TLUEGO are proposed, a distributed memory programming algorithm, a shared memory programming algorithm, and a hybrid of the two previous algorithms, which not only allow us to obtain the solution faster, but also to solve larger instances.

An approach for solving competitive location problems with variable demand using multicore systems

A planar competitive location and design problem with variable demand is considered. The assumption that the demand may vary depending on the conditions of the market makes the problem more realistic, but it also increases its complexity, and therefore, the computational effort needed to solve it. In this paper, a modification of a heuristic recently proposed to cope with the problem is presented, which allows, on the one hand, to obtain the same solutions as the original heuristic more quickly and, on the other hand, to handle larger size problems. Furthermore, a parallel version of the algorithm, suitable for being run in most of today’s personal computers, has also been proposed. The parallel algorithm has been implemented using the OpenMP library and the results show an ideal efficiency up to at least eight processors (the largest number of available processing elements). The effectiveness of the parallel algorithm has also been measured. From the computational results, it can be inferred that the proposed parallelization is robust.

A Triobjective Model for Locating a Public Semiobnoxious Facility in the Plane

A new mathematical model for locating a single semiobnoxious facility in the plane is proposed. Three objectives are taken into consideration. The first one maximizes the efficiency of the service provided by the facility to some users, by minimizing the sum of weighted distances between the facility and those users. The second one minimizes the social cost caused by the undesirable effects produced by the facility, by minimizing the sum of the repulsions of the affected people (as they feel it). The third one aims to distribute the repulsions fairly (as equal as possible) among the affected people. To prove that the new model can be tackled in practice, two recent general-purpose multiobjective evolutionary algorithms, MOEA/D and FEMOEA, are suggested to obtain a discrete approximation of its Pareto-front. A computational study shows that both algorithms are suitable to cope with the problem.