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We continue the study of Genetic Algorithms (GA) on combinatorialoptimization problems where the candidate solutions need to satisfy abalancedness constraint. It has been observed that the reduction of the searchspace size granted by ad-hoc crossover and mutation operators does not usuallytranslate to a substantial improvement of the GA performances. There is stillno clear explanation of this phenomenon, although it is suspected that abalanced representation might yield a more irregular fitness landscape, whereit could be more difficult for GA to converge to a global optimum. In thispaper, we investigate this issue by adding a local search step to a GA withbalanced operators, and use it to evolve highly nonlinear balanced Booleanfunctions. In particular, we organize our experiments around two researchquestions, namely if local search (1) improves the convergence speed of GA, and(2) decreases the population diversity. Surprisingly, while our results answeraffirmatively the first question, they also show that adding local searchactually \emph{increases} the diversity among the individuals in thepopulation. We link these findings to some recent results on fitness landscapeanalysis for problems on Boolean functions.

The Influence of Local Search over Genetic Algorithms with Balanced Representations