# 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 interrelations 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. differential evolution DE; control parameters CP; population size NP; functional analysis of variance fANOVA  
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of the DE algorithm are its control parameters, namely, the crossover rate (\(CR\)), the scale factor (\(F\)), and notably, the population size (\(N_{P}\)). While a substantial amount of research has been dedicated to the optimization of \(CR\) and \(F\) due to their pronounced impact on the performance of the DE algorithm [10; 11; 12; 13], the pivotal role of (\(N_{P}\)) in determining DE success cannot be overlooked. The influence of the population size on the performance of the DE algorithm has been widely acknowledged in the existing body of research [5; 14; 15]. Since the inception of the DE algorithm, conventional guidelines have been proposed to provide users with recommendations for determining the population size. These guidelines suggest the selection of the population size either as a function of the problem dimension or the adoption of a fixed value as clearly highlighted in previous review studies [16]. Conventional guidelines suggesting population sizes based on problem dimensions often stem from limited experimental investigations, which may not be generalizable. Concrete evidence about a linear relationship between the population size and the problem dimensionality has never been found [17; 18]. The study by [PERSON] in 2020 reveals a nonlinear relationship between the population size and the problem dimension in the context of the particle swarm optimization (PSO) algorithm [18]. There appears to be a lack of comprehensive research in the literature related to the DE algorithm that investigates the link between population size and problem-specific characteristics across various dimensions and complexities. Nevertheless, the practice of the adoption of a fixed value for the population size, based on experimental analysis, seems primarily applicable to the specific problems investigated. Determining the appropriate population size within the DE algorithm remains a daunting task, critically influencing DE performance. Acknowledging the significance of the population size on the performance of the DE algorithm, researchers have increasingly explored adaptive DE strategies that provide more flexible and dynamic approaches.