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<p>Surrogate-assisted evolutionary algorithms (SAEAs) are gaining attention for solving computationally expensive optimization problems, especially in high dimensions where traditional methods struggle. However, their effectiveness often diminishes as dimensionality increases due to challenges in maintaining accurate surrogate models. This research presents the multi-phase ensemble radial basis function assisted differential evolution (MERADE) algorithm, an innovative and efficient approach designed to address these challenges. MERADE utilizes an ensemble of Radial Basis Function (RBF) models, trained through a hybrid strategy that combines K-means clustering and Latin Hypercube Sampling (LHS) for center selection. These ensemble RBFs, constructed in parallel during the global prescreening phase, significantly reduce computational time and provide uncertainty estimates, enhancing the reliability of candidate solution selection. By leveraging uncertainty, MERADE ensures a balance between exploration and exploitation. Furthermore, MERADE incorporates global, semi-local, and local search phases, selectively applied at different iterations to improve convergence. The algorithm also features adaptive adjustments to the Differential Evolution (DE) parameters, specifically tuned to enhance the prescreening phase and avoid local minima. Experimental results on several benchmark functions across multiple dimensions (20D, 30D, 50D, and 100D), totaling thirty-one tests, demonstrate that MERADE achieves faster convergence and significantly reduced computational time compared to several state-of-the-art algorithms, providing an efficient solution for high-dimensional optimization problems.</p>

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Multi-phase ensemble-RBF-assisted differential evolution for high-dimensional expensive optimization

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Majid Ilchi Ghazaan,
  • Parnian Mirghazanfari

摘要

Surrogate-assisted evolutionary algorithms (SAEAs) are gaining attention for solving computationally expensive optimization problems, especially in high dimensions where traditional methods struggle. However, their effectiveness often diminishes as dimensionality increases due to challenges in maintaining accurate surrogate models. This research presents the multi-phase ensemble radial basis function assisted differential evolution (MERADE) algorithm, an innovative and efficient approach designed to address these challenges. MERADE utilizes an ensemble of Radial Basis Function (RBF) models, trained through a hybrid strategy that combines K-means clustering and Latin Hypercube Sampling (LHS) for center selection. These ensemble RBFs, constructed in parallel during the global prescreening phase, significantly reduce computational time and provide uncertainty estimates, enhancing the reliability of candidate solution selection. By leveraging uncertainty, MERADE ensures a balance between exploration and exploitation. Furthermore, MERADE incorporates global, semi-local, and local search phases, selectively applied at different iterations to improve convergence. The algorithm also features adaptive adjustments to the Differential Evolution (DE) parameters, specifically tuned to enhance the prescreening phase and avoid local minima. Experimental results on several benchmark functions across multiple dimensions (20D, 30D, 50D, and 100D), totaling thirty-one tests, demonstrate that MERADE achieves faster convergence and significantly reduced computational time compared to several state-of-the-art algorithms, providing an efficient solution for high-dimensional optimization problems.