Theoretical Analysis of Phenotypic Diversity in Real-Valued Evolutionary Algorithms With More-Than-One-Element Replacement

This paper investigates the evolutionary dynamics of steady-state real-valued evolutionary algorithms (RVEAs) with more-than-one-element replacement theoretically, whereas most theoretical studies of RVEAs have considered single-or all-element replacement. The subject RVEAs are of interest because they appear in various fashions, such as real-coded genetic algorithms (RCGAs) and island RVEAs. The analysis is conducted to deepen the understanding of how RVEA components and their parameters influence the phenotypic diversity in the parental pool. First, the diversity evolution is modeled mathematically and then a constraint of diversity control is derived from this model. The control method is demonstrated and the accuracy of the theoretical predictions is evaluated through experiments. The shortest convergence time is estimated. The analysis requires few assumptions about either the variation operators or selection schemes, and therefore is applicable to various RVEAs. As such an application in RCGAs, the influence on the diversity evolution of offspring-population size, parental-pool size, crossover-operator parameter, and selection-pressure parameters of two selection mechanisms is quantified. The computational efficiency, search stability, and selection-pressure controllability are then evaluated. The analysis results are discussed from a practical point of view in parameter settings for preventing premature convergence.