Solving Expensive Multimodal Optimization Problem by a Decomposition Differential Evolution Algorithm.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Machine Learning

Background:

• Expensive multimodal optimization problems (EMMOPs) present significant computational challenges due to time-consuming objective functions and multiple global optima.
• Existing methods often struggle with the efficiency and effectiveness required for such complex problems.

Purpose of the Study:

• To propose a novel decomposition differential evolution (DE) method based on radial basis functions (RBF) for solving EMMOPs.
• To enhance the efficiency and effectiveness of global optimization for computationally expensive problems.

Main Methods:

• The D/REM method employs a two-phase approach: promising subregions detection (PSD) and local search phase (LSP).
• PSD utilizes a population update strategy and mean-shift clustering to identify promising subregions.
• LSP constructs local RBF surrogate models for each subregion, with each model tracking a global optimum, effectively decomposing the EMMOP.

Main Results:

• D/REM successfully decomposes EMMOPs into multiple, manageable expensive global optimization subproblems.
• The JADE variant of DE is utilized as the search engine to efficiently handle these subproblems.
• Extensive numerical experiments demonstrate the effectiveness and efficiency of D/REM in solving EMMOPs.

Conclusions:

• The proposed D/REM method offers a robust and efficient solution for expensive multimodal optimization problems.
• The decomposition strategy combined with RBF surrogate models and DE significantly improves optimization performance.