###### Abstract  
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. differential evolution; multimodal optimization problems; niching; solving topographic contours of spatial data distribution 2025202 were originally designed for optimization problems with a single global optimum, they often struggle to find optimal solutions in more complex landscapes. In scenarios involving a large number of peaks, their performance may degrade due to issues such as limited population diversity. Researchers accordingly divide the entire population into distinct niches [6] and uncover multiple global optima through the coevolution of these niches. This method has been successfully applied and is a research hotspot in the field of multimodal optimization problems such as AM-ACO [7], lbestPSO [8], and MOMMOP [9]. However, the parameters of the niching method tend to be highly sensitive and it often requires the upfront specification of the niching size and quantity. If these parameters are not set suitably, the results of the algorithm may have significant errors. The exact number of peaks that exist in the current multimodal optimization function is unknown. Achieving precise parameter settings in multimodal optimization problems therefore remains a challenging task. Even following the adoption of various strategies, multimodal optimization problems in complex scenarios are still open and require extensive research. It is observed that the two-dimensional plane figure of a multimodal function often resembles a geographical contour map. The benchmark two-dimensional combined test function F13 from CEC2013 for multimodal optimization problems is presented in Figure 1. Its corresponding two-dimensional plan view, depicted in Figure 1, is analogous to a geographical contour map. [PERSON] et al. first proposed the contour prediction approach (CPA) in the adaptive niche differential evolution (ANDE) algorithm [10], achieving promising results. However, their method only uses a few current optimal individuals in each generation to construct local contour lines for the prediction of peak locations. Due to the lack of global topographic information, this approach fails to capture comprehensive peak details. To address these limitations, the TCDE method is proposed. By constructing terrain contours to obtain a complete global landscape, TCDE enables more accurate micro-niche subdivision and demonstrates superior performance.