This study modifies the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm for multi-modal optimization problems. The enhancements focus on addressing the challenges of multiple global minima, improving the algorithm's ability to maintain diversity and explore complex fitness landscapes. We incorporate niching strategies and dynamic adaptation mechanisms to refine the algorithm's performance in identifying and optimizing multiple global optima. The algorithm generates a population of candidate solutions by sampling from a multivariate normal distribution centered around the current mean vector, with the spread determined by the step size and covariance matrix. Each solution's fitness is evaluated as a weighted sum of its contributions to all global minima, maintaining population diversity and preventing premature convergence. We implemented the algorithm on 8 tunable composite functions for the GECCO 2024 Competition on Benchmarking Niching Methods for Multi-Modal Optimization (MMO), adhering to the competition's benchmarking framework. The results are presenting in many ways such as Peak Ratio, F1 score on various dimensions. They demonstrate the algorithm's robustness and effectiveness in handling both global optimization and MMO- specific challenges, providing a comprehensive solution for complex multi-modal optimization problems.

翻译：本研究针对多模态优化问题，对协方差矩阵自适应进化策略（CMA-ES）算法进行了改进。增强措施主要着眼于应对多个全局最小值的挑战，提升算法在维持多样性和探索复杂适应度地形方面的能力。我们引入了小生境策略和动态适应机制，以优化算法在识别和优化多个全局最优解方面的性能。该算法通过以当前均值向量为中心、以步长和协方差矩阵决定分布范围的多变量正态分布进行采样，生成候选解群体。每个解的适应度被评估为其对所有全局最小值贡献的加权和，从而保持群体多样性并防止早熟收敛。我们在GECCO 2024多模态优化基准测试方法竞赛的8个可调复合函数上实现了该算法，并遵循了竞赛的基准测试框架。结果通过峰值比率、多维F1分数等多种方式呈现，证明了该算法在处理全局优化和多模态优化特定挑战方面的鲁棒性和有效性，为复杂的多模态优化问题提供了全面解决方案。