An Analysis of Differential Evolution Population Size

Abstract

The performance of the differential evolution algorithm (DE) is known to be highly sensitive to the values assigned to its control parameters. While numerous studies of the DE control parameters do exist, these studies have limitations, particularly in the context of setting the population size regardless of problem-specific characteristics. Moreover, the complex interrelationships between DE control parameters are frequently overlooked. This paper addresses these limitations by critically analyzing the existing guidelines for setting the population size in DE and assessing their efficacy for problems of various modalities. Moreover, the relative importance and interrelationship between DE control parameters using the functional analysis of variance (fANOVA) approach are investigated. The empirical analysis uses thirty problems of varying complexities from the IEEE Congress on Evolutionary Computation (CEC) 2014 benchmark suite. The results suggest that the conventional one-size-fits-all guidelines for setting DE population size possess the possibility of overestimating initial population sizes. The analysis further explores how varying population sizes impact DE performance across different fitness landscapes, highlighting important interactions between population size and other DE control parameters. This research lays the groundwork for subsequent research on thoughtful selection of optimal population sizes for DE algorithms, facilitating the development of more efficient adaptive DE strategies.

Keywords

• differential evolution DE
• control parameters CP
• population size NP
• functional analysis of variance fANOVA