# An Analysis of Differential Evolution Population Size
## 5 Experimental Setup  
To achieve the objectives, the DE/rand/1/bin strategy was applied to a set of well-known benchmark problems. Since population size determination guidelines have been derived from the original DE, this paper continues to focus on the original DE to analyze the credibility of these guidelines. Also, the CEC provides predefined benchmark suites that are commonly used to test algorithm performance [108; 109; 110; 111]. The standard problems defined in CEC 2014 [109] were chosen for the purpose of experimentation. The selection of the CEC 2014 benchmark suite is primarily attributed to its ability to provide a diverse set of problems that cover a wide range of characteristics, complexities, and dimensions. Despite being over ten years old, the CEC 2014 problems remain widely used due to their diversity and complexity, which continue to benchmark modern algorithms, including advanced variants of the DE algorithm. Moreover, these benchmark problems have been extensively used to provide a consistent testbed for analyzing the population size for DE [16] and other well-known algorithms, like the PSO algorithms recently in 2020 [18], which enables comparisons with previous studies and build upon the existing literature. (The following study demonstrates that there are no significant differences in the fitness landscape characteristics between the CEC 2014 benchmark functions and those in later benchmark sets. Therefore, CEC 2014 remains a sufficient and relevant benchmark suite [112]). The CEC 2014 benchmark suite comprises 30 problems and covers relatively simple unimodal problems (problems 1-3), multimodal problems (problems 4-16), hybrid problems (problems 17-22), and other composition problems (problems 23-30, which are considered extremely complex). All problems are scalable, which were tested using 10, 20, 30, 50, and 100 dimensions. Detailed descriptions of these problems are given in the work by [PERSON] et al. [110]. The CEC 2014 benchmark problems are sufficient to provide evidence supporting the main hypothesis and to draw sound conclusions on the aspects investigated in this study. For each problem, the maximum number of function evaluations was \(10,000\times D\) (where \(D\) is the problem dimension), as previously advised in [PERSON] et al. [109]. Consequently, simulations using 20 individuals were run for 5000 iterations, whereas simulations using 100 individuals were run for 1000 iterations. Moreover, as per the recommendations in [109], a total of 51 independent runs were performed for each problem, per dimension, and parameter setting combination. The obtained results were subjected to rigorous statistical validation, as detailed in the subsequent sections. Two distinct experiments were conducted to achieve the objectives of this paper. The first experiment focuses on assessing the credibility of the proposed guideline used to determine the population size in the DE algorithm and empirically investigates how varying the population size affects DE performance across various fitness landscapes associated with different problem modalities. In this experiment, the population size was the sole control parameter that was varied using a range of values. The other control parameters of DE, i.e., the scale factor \(F\) and the crossover rate \(CR\), were maintained at constant values in accordance with the recommendations by [PERSON] and [PERSON] in [9]. The analysis is conducted for each problem at various specified dimensions. Keeping all other control parameters fixed while changing the population size for diverse problem modalities and various problem dimensions allowed for a comprehensive assessment of the proposed population size guidelines on the performance of the DE algorithm and the effect of various population sizes on problem modalities. In the second experiment, the values of all DE control parameters, including the population size, the crossover rate, and the scale factor, were systematically varied.