A real-coded genetic algorithm using the unimodal normal distribution crossover

TLDR: A real-coded genetic algorithm using the Unimodal Normal Distribution Crossover (UNDX) that can efficiently optimize functions with epistasis among parameters and some improvements of the UNDX under the guidelines are discussed.

Abstract: This chapter presents a real-coded genetic algorithm using the Unimodal Normal Distribution Crossover (UNDX) that can efficiently optimize functions with epistasis among parameters. Most conventional crossover operators for function optimization have been reported to have a serious problem in that their performance deteriorates considerably when they are applied to functions with epistasis among parameters. We believe that the reason for the poor performance of the conventional crossover operators is that they cannot keep the distribution of individuals unchanged in the process of repetitive crossover operations on functions with epistasis among parameters. In considering the above problem, we introduce three guidelines, 'Preservation of Statistics', 'Diversity of Offspring', and 'Enhancement of Robustness', for designing crossover operators that show good performance even on epistatic functions. We show that the UNDX meets the guidelines very well by a theoretical analysis and that the UNDX shows better performance than some conventional crossover operators by applying them to some benchmark functions including multimodal and epistatic ones. We also discuss some improvements of the UNDX under the guidelines and the relation between real-coded genetic algorithms using the UNDX and evolution strategies (ESs) using the correlated mutation.