A Neural Network Based Guidance for a BRKGA: An Application to the Longest Common Square Subsequence Problem

Abstract

In this work we apply machine learning to better guide a biased random key genetic algorithm (Brkga) for the longest common square subsequence (LCSqS) problem. The problem is a variant of the well-known longest common subsequence (LCS) problem in which valid solutions are square strings. A string is square if it can be expressed as the concatenation of a string with itself. The original Brkga is based on a reduction of the LCSqS problem to the LCS problem by cutting each input string into two parts. Our work consists in enhancing the search process of Brkga for good cut points by using a machine learning approach, which is trained to produce promising cut points for the input strings of a problem instance. In this study, we show the benefits of this approach by comparing the enhanced Brkga with the original Brkga, using two benchmark sets from the literature. We show that the results of the enhanced Brkga significantly improve over the original results, especially when tackling instances with non-uniformly generated input strings.