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Mathematical Problems in Engineering
Volume 2018, Article ID 2183214, 23 pages
https://doi.org/10.1155/2018/2183214
Research Article

Adaptive Black Hole Algorithm for Solving the Set Covering Problem

1Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
2Escuela de Ingeniería Civil Informática, Universidad de Valparaíso, Valparaíso, Chile
3Universidad Técnica Federico Santa María, Valparaíso, Chile
4Escuela de Ingeniería Industrial, Universidad Diego Portales, Santiago, Chile

Correspondence should be addressed to Rodrigo Olivares; lc.vu@seravilo.ogirdor

Received 5 December 2017; Revised 5 August 2018; Accepted 3 September 2018; Published 16 October 2018

Academic Editor: Georgios Dounias

Copyright © 2018 Ricardo Soto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Evolutionary algorithms have been used to solve several optimization problems, showing an efficient performance. Nevertheless, when these algorithms are applied they present the difficulty to decide on the appropriate values of their parameters. Typically, parameters are specified before the algorithm is run and include population size, selection rate, and operator probabilities. This process is known as offline control and is even considered as an optimization problem in itself. On the other hand, parameter settings or control online is a variation of the algorithm original version. The main idea is to vary the parameters so that the algorithm of interest can provide the best convergence rate and thus may achieve the best performance. In this paper, we propose an adaptive black hole algorithm able to dynamically adapt its population according to solving performance. For that, we use autonomous search which appeared as a new technique that enables the problem solver to control and adapt its own parameters and heuristics during solving in order to be more efficient without the knowledge of an expert user. In order to test this approach, we resolve the set covering problem which is a classical optimization benchmark with many industrial applications such as line balancing production, crew scheduling, service installation, and databases, among several others. We illustrate encouraging experimental results, where the proposed approach is able to reach various global optimums for a well-known instance set from Beasley’s OR-Library, while improving various modern metaheuristics.