A new real-coded genetic algorithm for implicit constrained black-box function optimization

Abstract

In this paper, we propose a new real-coded genetic algorithm (RCGA) for implicit constrained black-box function optimization. On implicit constrained problems, there often exist active constraints of which the optima lie on the boundaries, which makes the problem more difficult. Almost all of conventional constraint-handling techniques cannot be applied to implicit constrained black-box function optimization because we cannot get quantities of constraint violations and preference order of infeasible solutions. The resampling technique may be the only available choice to handle the implicit constraint. AREX/JGG is one of the most powerful RCGAs for non-constrained problems. However, AREX/JGG with resampling technique deteriorates on implicit constrained problems because few individuals are generated near the boundaries of active constraints and, thus, a population cannot approach the boundaries quickly. In order to find these optima, we believe that it is necessary to locate the mode of a distribution for generating new individuals nearer the boundaries. Since solutions around the optima on boundaries of active constraints may have better evaluation values, our proposed method employs the weighted mean of the best half individuals in a population as the mode of the distribution. We assess the proposed method through experiments with some benchmark problems and the results show the proposed method succeeds in finding the optimum with about 40-85% of function evaluations compared to AREX/JGG with resampling technique.