A Dynamic Optimization Algorithm Based on Energy Level Collaboration Mechanism.

Complex multimodal optimization problems are widespread in machine learning, engineering design, and data science, where multiple local optima often trap conventional algorithms. Balancing global exploration and local exploitation remains a fundamental challenge for population-based optimization algorithms when solving such problems. This paper proposes a dynamic search framework optimization algorithm based on an energy level collaboration mechanism, termed DSF-ELC. The algorithm introduces two synergistic strategies. First, a population dynamic reorganization strategy adaptively adjusts particle migration between two fitness-stratified subpopulations based on real-time diversity measurements, effectively balancing exploration and exploitation. Second, a comprehensive learning strategy enables each dimension of inferior solutions to learn from the corresponding dimension of superior solutions in a randomized manner, thereby enhancing search capability on complex multimodal functions. The two strategies work synergistically to achieve an adaptive exploration-exploitation balance. Experimental validation on the CEC 2017 benchmark suite demonstrates that DSF-ELC achieves superior solution accuracy and stability compared to six representative algorithms on the vast majority of functions. Wilcoxon signed-rank tests, box plot visualization, and convergence curve analysis further validate the effectiveness of the proposed strategies. The results indicate that DSF-ELC has significant advantages and broad application prospects for complex multimodal optimization problems.