Fitness Landscape Analysis for the Differential Evolution Algorithm

It is crucial to understand how fitness landscape characteristics (FLCs) are associated with the performance and behavior of the differential evolution (DE) algorithm to optimize its application across various optimization problems. Although previous studies have explored DE performance in relation to FLCs, these studies have limitations. Specifically, the narrow range of FLC metrics considered for problem characterization and the lack of research exploring the relationship between the search behavior of the DE algorithm and FLCs represent two major concerns. This study investigates the impact of five FLCs, namely ruggedness, gradients, funnels, deception, and searchability, on DE performance and behavior across various problems and dimensions. Two experiments were conducted: the first assesses DE performance using three performance metrics, i.e., solution quality, success rate, and success speed. The first experiment reveals that DE exhibits stronger associations with FLCs for higher-dimensional problems. Moreover, the presence of multiple funnels and high deception levels are linked to performance degradation, while high searchability is significantly associated with improved performance. The second experiment analyzes the DE search behavior using the diversity rate-of-change (DRoC) behavioral measure. The second experiment shows that the speed at which the DE algorithm transitions from exploration to exploitation varies with different FLCs and the problem dimensionality. The analysis reveals that DE reduces its diversity more slowly in landscapes with multiple funnels and resists deception, but faces excessively slow convergence for high-dimensional problems. Overall, the results elucidate that multiple funnels and high deception levels are the FLCs most strongly associated with the performance and search behavior of the DE algorithm. These findings contribute to a deeper understanding of how FLCs interact with both the performance and search behavior of the DE algorithm and suggest avenues to optimize DE for real-world applications.