ILS-Perturbation Based on Local Optima Structure for the QAP Problem

Abstract

Many problems in AI can be stated as search problems and most of them are very complex to solve. One alternative for these problems are local search methods that have been widely used for tackling difficult optimization problems for which we do not know algorithms which can solve every instance to optimality in a reasonable amount of time. One of the most popular methods is what is known as iterated local search (ILS), which samples the set of local optima searching for a better solution. This algorithm’s behavior is achieved by some mechanisms like perturbation which is a key aspect to consider, since it allows the algorithm to reach a new solution from the set of local optima by escaping from the previous local optimum basis of attraction. In order to design a good perturbation method we need to analyze the local optima structure such that ILS leads to a good biased sampling. In this paper, the local optima structure of the Quadratic Assignment Problem, an NP-hard optimization problem, is used to determine the required perturbation size in the ILS algorithm. The analysis is focused on verifying if the set of local optima has the “Big Valley (BV)” structure, and on how close local optima are in relation to problem size. Experimental results show that a small perturbation seems appropriate for instances having the BV structure, and for instances having a low distance among local optima, even if they do not have a clear BV structure. Finally, as the local optima structure moves away from BV a larger perturbation is needed.