# An Analysis of Differential Evolution Population Size
## 2 Background and Related Work
### Challenges in Selecting the Initial Population Size in DE  
It is of utmost importance to highlight that the adaptive population size strategies within the DE algorithm still rely on the utilization of initial populations either as a problem dimension-related factor or a predetermined fixed value. [PERSON] et al. [47], who proposed a novel self-adaptive DE variant, mentioned that _\"Recently, some works are related to changing population size during the optimization process, but there are still no general guidelines how to set the population size at the beginning of the optimization process, when to change (question if to increase or decrease remains open, too), etc. Since all parameters are related to each other and they are depending on the optimization problem being solved, further works are necessary\"_. [PERSON] et al. [57] wrote that _\"the relationship between population size and the problem dimension still remains to be deeply studied, while for the third type, the simple ignorance of all characteristics of a specific problem may result in ineffectiveness\"_. However, the initial population size in [PERSON] et al. [57] was selected as a function of the problem dimension, as they wrote _\"in this paper, the population size varies in a given range, and the upper and lower bounds of the population size are initialized as \(10\times D\) and \(D\), respectively, while the initial population size \(PS_{init}\) is set at 100, and these settings have referred to some conclusions in [PERSON] [16]\"_. In 2017, [PERSON] published a comprehensive and informative review [16] that thoroughly investigated the nuances of the DE population size as a crucial control parameter. The review not only shed light on previously unexplored research areas surrounding the population size, but also emphasized the pressing need for further investigation to optimize the DE population size. Areas such as considering problem-specific characteristics when setting the DE population size, the relative importance of \(N_{P}\), \(F\), and \(CR\), and the interrelationship between DE control parameters were overlooked in [16]. Furthermore, several applications have yielded evidence that some control parameters tend to be more critical than others [94; 95]. This is further corroborated by research investigating the relative importance of control parameters in the particle swarm optimization (PSO) algorithm applying the functional analysis of variance (fANOVA) [96]. However, research on the relative importance and interrelationships of DE control parameters using fANOVA has never been reported in the existing literature. Additionally, a clue into the interaction between DE control parameters was reported in [97], where the overall optimization and the relationship between DE control parameters were investigated. The findings in [97] demonstrated a close correlation between DE control parameters, and the optimal population sizes were observed to range between 30 and 40 individuals [97]. However, the results in [97] were specifically derived from experiments conducted on the unmanned aerial vehicle (UAV) path planning problem. Further research concerning the population size within the DE algorithm was reported by [PERSON] et al. [98] who analyzed the effect of population size on the performance of the DE algorithm and proposed an adaptive DE variant. The adaptive DE proposed in [98] utilized a population re-setting strategy, in which the population is reinitialized upon reaching a certain threshold of population diversity, and concluded that further increment of the population size detrimentally affects the overall performance of the DE algorithm. However, the study in [98] omits key information, such as the correlation between the population size and the problem dimension, the interrelationships between DE control parameters, and the link between problem-specific characteristics and the DE population size.