Integrating Chaotic Evolutionary and Local Search Techniques in Decision Space for Enhanced Evolutionary Multi-Objective Optimization

Abstract

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.

Figures (14)

• Figure 1: Comparison between Decision Space and Objective Space for ZDT3 (Multimodal).
• Figure 2: Exploration in the decision space. The red paths indicate the trajectories followed by the algorithm, illustrating its approach to finding the global optimum within the decision space. The yellow dots represent other individuals in the population, showcasing the algorithm's ability to maintain diversity throughout the search process.
• Figure 3: Improved Deterministic Crowding
• Figure 4: Persistence-based clustering result. The left plot shows the results of K-means clustering, which fails to capture the complex structure of the data. The right plot illustrates the persistence-based clustering results, which successfully identify and preserve the intricate patterns within the data.
• Figure 5: Six-Hump Camel Back Function with Random Points. The top plot shows the 3D surface of the function with randomly generated points within its domain. The bottom plot presents the contour lines of the function on the $X, Y$ plane with the same randomly generated points, illustrating their initial distribution.