Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Machine Learning

Background:

• Existing niching methods for multimodal optimization often rely on restrictive assumptions about search space characteristics.
• These assumptions limit their applicability in real-world optimization problems where basin properties are often unknown.

Purpose of the Study:

• To develop a novel, assumption-free niching strategy for multimodal optimization.
• To enhance the covariance matrix self-adaptation evolution strategy (CMSA-ES) with this new strategy, creating the repelling subpopulations covariance matrix self-adaptation (RS-CMSA) method.

Main Methods:

• The RS-CMSA method employs parallel subpopulations that are repelled by identified basins (taboo points) to prevent premature convergence.
• It incorporates normalized Mahalanobis distance and Ursem's hill-valley function, adapting repelling power for varying basin sizes and approximating local basin shapes.
• A systematic parameter setting procedure and the robust mean peak ratio are introduced for performance evaluation.

Main Results:

• RS-CMSA demonstrated superior performance compared to state-of-the-art niching methods on a standard multimodal optimization test suite.
• The method shows high robustness and efficiency, particularly when considering the accuracy of the estimated number of minima.
• Performance sensitivity analysis confirmed the method's reliability across different parameter settings.

Conclusions:

• The proposed RS-CMSA method offers a robust and efficient solution for multimodal optimization without requiring prior assumptions about the search space.
• It effectively handles challenges posed by dissimilar basin sizes and complex search landscapes.
• RS-CMSA represents a significant advancement in niching strategies for global optimization problems.