Robust confidence intervals applied to crossover operator for real-coded genetic algorithms

Abstract

In this work we propose a new approach to crossover operators for real-coded genetic algorithms based on robust confidence intervals. These confidence intervals are an alternative to standard confidence intervals. In this paper, they are used for localising the search regions where the best individuals are placed. Robust confidence intervals use robust localization and dispersion estimators that are highly recommendable when the distribution of the random variables is not known or is distorted. Both situations are likely when we are dealing with the best individuals of the population, especially if the problem under study is multimodal. The performance of the crossovers based on robust intervals is evaluated using a well characterised set of optimisation problems. We have chosen problems with different features of modality, separability, regularity, and correlation among their variables. The results show that the performance of the crossovers based on robust confidence intervals is less dependent on the problem than the performance of the crossovers based on Gaussian confidence intervals. We have also made comparisons between several standard crossovers that show very interesting results, which support the idea underlying the defined operators.