Theoretical analysis of the unimodal normal distribution crossover for real-coded genetic algorithms

摘要

Real-coded genetic algorithms attract attention as global optimization methods for nonlinear functions. For real-coded genetic algorithms, there have been proposed many crossover operators so far. Among them, the unimodal normal distribution crossover (UNDX) developed by One et al. shows good performance in optimization of multi-modal and highly epistatic fitness functions. However, the performance of the crossover operators have been evaluated only through numerical experiments with some benchmark problems, and clear guidelines to design operators have not been established. In this paper, first, statistical characteristics of the UNDX are discussed theoretically. The results of the analysis show that the UNDX inherits the statistics of the parent population such as the mean vector and the variance-covariance matrix well. Based on this finding, the authors propose several guidelines to design crossover operators for the real-coded genetic algorithms.