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

In population-based optimization methods such as evolutionary algorithms, various information can be obtained from the distribution of good search points. 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 simultaneously along the long axis of the elliptical distribution. A similar distribution also may appear when the search points are far from the optimal solution even in problems with independent variables. In this study, we propose a new crossover CBX which uses correlation coefficients of search points in order to detect such distribution and realizes efficient movement toward the optimal solution. The crossover points are decided so that highly correlated variables are inherited at the same time. However, if only CBX is used, the diversity of the search points tends to be lost rapidly. The adaptive control of the probability for applying CBX is also proposed. The advantage of the proposed method is shown by solving several benchmark problems.