Proposal and Evaluation of Adaptive Real-coded Crossover AREX

Abstract

Since once premature convergence happens evolutionary algorithms for function optimization can no longer explore areas of the search space and fail to find the optimum, it is required to handle the notorious drawback. This paper proposes two novel approaches to overcome premature convergence of real-coded genetic algorithms (RCGAs). The first idea is to control the sampling region of crossover by adaptation of expansion rate. The second idea is to cause the acceleration of the movement of population by descending the mean of crossover. Finally, we propose a crossover that combines the adaptation of expansion rate technique and the crossover mean descent technique, called AREX (adaptive real-coded ensemble crossover). The performance of the real-coded GA using AREX is evaluated on several benchmark functions including functions whose landscape forms ridge structure or multi-peak structure, both of which are likely to lead to the miserable convergence phenomenon. The experimental results show not only that the proposed method can locate the global optima of functions on which it is difficult for the existing GAs to discover it but also that our approach outperforms the existing one in number of function evaluations on all functions. Our approach enlarges the classes of functions that real-coded GAs can solve.