The Influence of Local Search over Genetic Algorithms with Balanced Representations

TL;DR

This paper explores how adding local search to genetic algorithms affects convergence and diversity when evolving balanced Boolean functions, revealing it speeds convergence but unexpectedly increases population diversity.

Contribution

It provides new insights into the effects of local search on GAs with balanced representations, especially regarding convergence speed and diversity.

Findings

Local search improves GA convergence speed.

Adding local search increases population diversity.

Results relate to fitness landscape complexity.

Abstract

We continue the study of Genetic Algorithms (GA) on combinatorial optimization problems where the candidate solutions need to satisfy a balancedness constraint. It has been observed that the reduction of the search space size granted by ad-hoc crossover and mutation operators does not usually translate to a substantial improvement of the GA performances. There is still no clear explanation of this phenomenon, although it is suspected that a balanced representation might yield a more irregular fitness landscape, where it could be more difficult for GA to converge to a global optimum. In this paper, we investigate this issue by adding a local search step to a GA with balanced operators, and use it to evolve highly nonlinear balanced Boolean functions. In particular, we organize our experiments around two research questions, namely if local search (1) improves the convergence speed of GA, and (2) decreases the population diversity. Surprisingly, while our results answer affirmatively the first question, they also show that adding local search actually \emph{increases} the diversity among the individuals in the population. We link these findings to some recent results on fitness landscape analysis for problems on Boolean functions.