## 4 Performance Analysis
### Baseline Methodology  
The TCDE algorithm was compared with the following 15 multimodal optimization algorithms, mainly from highly cited works and authoritative journals (e.g., _IEEE Transactions on Evolutionary Computation_ and _IEEE Transactions on Cybernetics_). Firstly, since this method uses terrain contours to guide multimodal optimization, it is compared with other contour-based approaches. * ANDE (2019) [10]: This method is characterized by utilizing the individual distribution information in each niche to generate contour lines, thereby predicting the approximate positions of potential peaks to accelerate the convergence speed. Secondly, we selected multimodal optimization algorithms using subpopulation strategies as the baseline method to measure the performance of TCDE. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **Name** & **Dimensions** & \
\begin{tabular}{c} **Global** \\ **Optima** \\ \end{tabular} &
\begin{tabular}{c} **Local** \\ **Optima** \\ \end{tabular} \\ \hline F4 & [PERSON] & 2 & 4 & 0 \\ F5 & Six-Hump Camel Back & 2 & 2 & 2 \\ F6 & [PERSON] (2D) & 2 & 18 & many \\ F7 & [PERSON] (2D) & 2 & 36 & 0 \\ F10 & Modified Rastrigin & 2 & 12 & 0 \\ F11 & Composition Func. 1 (2D) & 2 & 6 & many \\ F12 & Composition Func. 2 (2D) & 2 & 8 & many \\ F13 & Composition Func. 3 (2D) & 2 & 6 & many \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Function introduction [39]. * CDE (2004) [22]: This method is characterized by fast convergence and the ability to finely tune the found results. It extends subpopulations via a crowding mechanism, enabling it to track and maintain multiple optimal solutions. * SDE (2005) [23]: In each iteration, the algorithm adaptively forms multiple species (or subpopulations) within its DE population. Each species then operates as an independent DE algorithm, performing successive local improvements to eventually obtain multiple global optima. * PNPCDE (2014) [40]: This method restricts member randomness without compromising exploration, using a parent-centric normalized neighborhood (PCNN) mutation operator combined with a synchronous crowding replacement strategy. This approach effectively prevents niche loss, reduces genetic drift, and maintains optimal solutions, enabling stable and efficient niching behavior. * Self-CSDE (2014) [24]: This method divides the population into subpopulations using clustering and then uses adaptive parameter control to enhance the search capability of the species-based differential evolution (SDE) algorithm, and the method has achieved good results. * NMMSO (2014) [41]: The subpopulations of the algorithm are each responsible for optimizing independent local modes. If individuals within a subpopulation are identified as being near other peaks, they are allowed to migrate from the original subpopulation; if different subpopulations are determined to target the same peak, they are merged. The algorithm achieves optimization by dynamically managing multiple particle swarms in this way. * NCD-DE (2021) [32]: This method designs a fitness-entropy measurement objective function, applies an internal genetic algorithm (GA) to optimize multiple promising niche centers, and globally cooperates with subpopulation niching using these centers to generate new individuals. Differential evolution (DE) is then employed iteratively to refine the results. * RS-CMSA-ESII (2022) [19]: This method proposes a covariance matrix adaptation evolution strategy with repulsive subpopulations. It optimizes the subpopulation initialization process and designs more precise key forbidden regions. Finally, a group of multimodal optimization algorithms using local information was selected as the comparison methods. * R3 PSO (2010) [42]: The main feature of this method is the adoption of a simple and effective parameter-free niching algorithm--namely, using a ring neighborhood topology to induce the formation of stable niches.