In the many-objective Artificial Physics Optimization (APO) algorithm, the proposed attraction-guided population optimization framework exhibits good convergence properties in the early stages of iteration but suffers from instability in the later stages. This is specifically manifested by the Inverted Generational Distance (IGD) metric oscillating slightly around a suboptimal value, indicating that the particles can neither escape the attraction of suboptimal solutions nor can the algorithm enhance its convergence precision. To overcome these issues, this study proposes a Tri-Cluster Entropy-Guided many-objective Artificial Physics Optimization, abbreviated as TCEG-APO. TCEG-APO partitions the objective space using K-means clustering and, based on the IGD metric, constructs a dynamic hierarchical architecture composed of three cluster layers: elite, intermediate, and exploration. The elite cluster serves as the population’s guiding core, shielded from external forces to maintain the search direction towards the global optimum. The intermediate cluster dynamically decides whether to be guided by the force from the nearest elite cluster based on the decreasing trend of the IGD. The exploration cluster, through a distance-weighting mechanism, prevents ineffective guidance from distant particles, thereby enhancing population diversity. Furthermore, the algorithm incorporates an information entropy mechanism to dynamically adjust the interaction forces within each cluster, preventing particle aggregation and precisely balancing convergence and diversity in the high-dimensional space. To comprehensively evaluate the performance of TCEG-APO, this paper conducts a comparative analysis against several many-objective evolutionary algorithms (MaOEAs) on the DTLZ benchmark test suite with 3, 5, 8, and 15 objectives. The experimental results demonstrate that the TCEG-APO algorithm exhibits superior performance.

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A Study on the Force Mechanism of a Many-Objective Artificial Physics Optimization Algorithm Based on Clustering and Information Entropy

  • Weizhe Li,
  • Liping Xie

摘要

In the many-objective Artificial Physics Optimization (APO) algorithm, the proposed attraction-guided population optimization framework exhibits good convergence properties in the early stages of iteration but suffers from instability in the later stages. This is specifically manifested by the Inverted Generational Distance (IGD) metric oscillating slightly around a suboptimal value, indicating that the particles can neither escape the attraction of suboptimal solutions nor can the algorithm enhance its convergence precision. To overcome these issues, this study proposes a Tri-Cluster Entropy-Guided many-objective Artificial Physics Optimization, abbreviated as TCEG-APO. TCEG-APO partitions the objective space using K-means clustering and, based on the IGD metric, constructs a dynamic hierarchical architecture composed of three cluster layers: elite, intermediate, and exploration. The elite cluster serves as the population’s guiding core, shielded from external forces to maintain the search direction towards the global optimum. The intermediate cluster dynamically decides whether to be guided by the force from the nearest elite cluster based on the decreasing trend of the IGD. The exploration cluster, through a distance-weighting mechanism, prevents ineffective guidance from distant particles, thereby enhancing population diversity. Furthermore, the algorithm incorporates an information entropy mechanism to dynamically adjust the interaction forces within each cluster, preventing particle aggregation and precisely balancing convergence and diversity in the high-dimensional space. To comprehensively evaluate the performance of TCEG-APO, this paper conducts a comparative analysis against several many-objective evolutionary algorithms (MaOEAs) on the DTLZ benchmark test suite with 3, 5, 8, and 15 objectives. The experimental results demonstrate that the TCEG-APO algorithm exhibits superior performance.