TCDE: Differential Evolution for Topographical Contour-Based Prediction to Solve Multimodal Optimization Problems

Multimodal optimization problems represent a category of complex optimization challenges characterized by the presence of multiple global optimal solutions. Addressing these problems requires an algorithm that can not only efficiently locate and identify as many peaks as possible but also pinpoint the precise coordinates of these peaks with a high degree of accuracy. Evolutionary algorithms are frequently employed to tackle multimodal optimization problems, and their heuristic approach often leads to the high-probability discarding of suboptimal individuals generated during the evolutionary process. If all individuals are utilized to depict the contours of the problem space, the contours will be depicted increasingly accurately as the algorithm iterates. By optimizing in this way, the results will become increasingly accurate. Therefore, in this paper, a topographical-contour-based differential evolution (TCDE) method is introduced to address multimodal optimization problems. The method initially applies DE for terrain exploration, followed by the construction of terrain contours to obtain more accurate landform representation, and it finally employs a niching search to investigate the landforms for optimal peaks. Experiments were conducted on a set of eight widely recognized benchmark functions with 15 excellent optimization algorithms, including both DE and non-DE multimodal optimization approaches. The outcomes of these experiments conclusively demonstrate the superior performance of the TCDE algorithm over its counterparts.