This paper presents innovative approaches to optimization problems, focusing on both Single-Objective Multi-Modal Optimization (SOMMOP) and Multi-Objective Optimization (MOO). In SOMMOP, we integrate chaotic evolution with niching techniques, as well as Persistence-Based Clustering combined with Gaussian mutation. The proposed algorithms, Chaotic Evolution with Deterministic Crowding (CEDC) and Chaotic Evolution with Clustering Algorithm (CECA), utilize chaotic dynamics to enhance population diversity and improve search efficiency. For MOO, we extend these methods into a comprehensive framework that incorporates Uncertainty-Based Selection, Adaptive Parameter Tuning, and introduces a radius \( R \) concept in deterministic crowding, which enables clearer and more precise separation of populations at peak points. Experimental results demonstrate that the proposed algorithms outperform traditional methods, achieving superior optimization accuracy and robustness across a variety of benchmark functions.

翻译：本文针对单目标多模态优化（SOMMOP）与多目标优化（MOO）问题提出了创新的优化方法。在SOMMOP中，我们融合了混沌进化与小生境技术，以及基于持久性的聚类结合高斯变异。所提出的算法——确定性拥挤混沌进化（CEDC）与聚类算法混沌进化（CECA）——利用混沌动力学增强种群多样性并提升搜索效率。对于MOO，我们将这些方法扩展为一个综合框架，该框架融合了基于不确定性的选择、自适应参数调优，并在确定性拥挤中引入了半径 \( R \) 的概念，从而能够在峰值点处实现更清晰、更精确的种群分离。实验结果表明，所提出的算法优于传统方法，在多种基准函数上实现了更优的优化精度与鲁棒性。