A Three-Level Radial Basis Function Method for Expensive Optimization.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Machine learning

Background:

• Expensive optimization problems pose significant computational challenges.
• Existing algorithms may struggle with efficiency and accuracy in high-dimensional or complex search spaces.
• Radial basis function (RBF) approximations offer a flexible approach for modeling complex functions.

Purpose of the Study:

• To develop and evaluate a novel three-level radial basis function (TLRBF)-assisted optimization algorithm.
• To address the challenges of computationally expensive optimization problems.
• To improve the efficiency and effectiveness of optimization algorithms in complex scenarios.

Main Methods:

• The proposed algorithm integrates three distinct search strategies within each iteration: global exploration, subregion search using fuzzy clustering, and local exploitation.
• Radial basis function (RBF) approximation models are employed at different levels of the search process.
• The algorithm optimizes RBF approximations under distance constraints and within localized subregions.

Main Results:

• The TLRBF-assisted algorithm demonstrated strong performance on benchmark problems, including scalable problems and CEC2015 computationally expensive problems.
• The algorithm achieved favorable results on a real-world airfoil design optimization task.
• Comparative analysis indicated superior performance against other state-of-the-art algorithms for expensive optimization.

Conclusions:

• The proposed three-level RBF-assisted optimization algorithm is effective for computationally expensive optimization tasks.
• The hybrid approach combining global, subregion, and local searches enhances optimization efficiency.
• The algorithm shows promise for both theoretical benchmark problems and practical engineering design optimization.