Evaluating the Effects of Chaos in Variable Neighbourhood Search

Abstract

Metaheuristics are problem-solving methods which try to find near-optimal solutions to very hard optimization problems within an acceptable computational timeframe, where classical approaches usually fail, or cannot even been applied. Random mechanisms are an integral part of metaheuristics, given randomness has a role in dealing with algorithmic issues such as parameters tuning, adaptation, and combination of existing optimization techniques. In this paper, it is explored whether deterministic chaos can be suitably used instead of random processes within Variable Neighbourhood Search (VNS), a popular metaheuristic for combinatorial optimization. As a use case, in particular, the paper focuses on labelling graph problems, where VNS has been already used with success. These problems are formulated on an undirected labelled graph and consist on selecting the subset of labels such that the subgraph generated by these labels has, respectively, an optimal spanning tree or forest. The effects of using chaotic sequences in the VNS metaheuristic are investigated during several numerical tests. Different one-dimensional chaotic maps are applied to VNS in order to compare the performance of each map in finding the best solutions for this class of graph problems.