# Knowledge-Based Perturbation LaF-CMA-ES for Multimodal Optimization  
[PERSON]  
1 School of Computer and Communication Technology, Lanzhou University of Technology,  
Lanzhou 730050, China; [EMAIL_ADDRESS]  
2 College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China; z  
from performance sensitivity due to multiple parameter-dependent strategies and struggle in higher-dimensional scenarios. The method of multi-objective evolutionary algorithms (MOEAs) is also applied to solve MMOPs [2]. This approach involves constructing objectives for each subproblem to reformulate the optimization problem [8]. [PERSON] introduced a subset selection framework and multi-objective multimodal algorithms [9]. The effectiveness of these algorithms largely depends on the constructed objectives. The performance of EAs in solving MMOPs often surpasses that of classical methods [10; 11]. EAs simulate natural processes by maintaining a population through selection, mutation, and recombination strategies [12]. This evolutionary path approximates the solution's evolutionary trajectory. By extracting hidden information from historical solutions, EAs can uncover problem characteristics and identify the optimum accordingly. Improved EAs have demonstrated strong performance in certain MMOPs [13]. For example, [PERSON] et al. [14] developed an adaptive distributed differential evolution algorithm for MMOPs. [PERSON] [15] introduced a distributed mutation framework along with an elite archive mechanism. [PERSON] et al. [16] proposed an adaptive neighborhood mutation method based on memetic differential evolution for MMOPs. Additionally, [PERSON] et al. [17] developed an enhanced differential evolution algorithm incorporating strategies such as nearest-better clustering (NBC), species balance, and key point-based mutation for MMOPs. Despite their capabilities, these algorithms often rely on multiple search procedures, leading to a somewhat random search process. Additionally, their ability to self-learn problem knowledge is limited. Consequently, researchers have been working to develop EAs that can identify multiple global optima and reliably reach the global optimum in MMOPs, thereby enhancing EA performance. CMA-ES is an effective optimization strategy that is widely utilized across various problems. In the context of MMOPs, CMA-ES incorporates several strategies. [PERSON] et al. [18] utilized small populations to explore the problem space in parallel, designating identified basins as taboo fields to prevent other subpopulations from converging on the same solution. [PERSON] et al. [19] employed opposition learning to investigate unknown regions. [PERSON] et al. [1] proposed an ensemble nearest-better-neighbor clustering method to ensure that solutions are distributed across different basins. In this paper, we propose an enhanced Leader-Follower (LaF) approach to minimize the overexploitation phenomenon and introduce a CMA-ES-based MMOP solver. The method combines the adaptive evolutionary properties of CMA-ES, the powerful overexploitation capability of LaF, and the Knowledge-based Perturbation (KbF) strategy. The algorithm proposed in [20] utilizes some of the algorithmic ideas presented in this paper. However, this paper further proposes a knowledge-driven perturbation-based strategy, which significantly improves the convergence speed and solution accuracy of the algorithm. In addition, this paper not only extends and enriches the experimental content but also adds analyses and discussions not previously covered. Specifically, we incorporate more comprehensive experimental results, refine the methodology, and delve into the implications of the research findings. These improvements significantly enhance the robustness and depth of the study. The structure of this paper is organized around the algorithm's components. Section 2 is an introductory overview of CMA-ES, the LaF strategy, and the KbP method. Section 3 elaborates on an improved algorithm and details the employed strategies.