A New Binomial Crossover Considering Correlation Among Decision Variables for Adaptive Differential Evolution

抄録

When problems with strong dependency among decision variables are optimized, a characteristic distribution, which is a thin elliptical distribution, may appear. In order to generate good children, it is necessary to change the variables (genes) simultaneously along the long axis of the elliptical distribution. Since binomial crossover in differential evolution determines whether each gene is crossed or not with the same probability, it is difficult to change some genes simultaneously. In this study, we propose a crossover operation GBX which uses correlation coefficients of search points in order to detect such distribution. The highly correlated genes are grouped and the genes in each group are crossed (or not crossed) simultaneously. However, if only GBX is used, the diversity of the search points tends to be lost rapidly. The adaptive control of the probability for applying GBX is also proposed. The advantage of the proposed method is shown by solving several bench- mark problems.