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    Area of Science:

    • Computational intelligence
    • Machine learning
    • Optimization algorithms

    Background:

    • Gaussian processes (GPs) are commonly used as surrogate models in data-driven evolutionary algorithms (EAs).
    • Existing methods predominantly utilize stationary GPs (SGPs), which may limit performance on complex optimization tasks.

    Purpose of the Study:

    • To investigate the nonstationary nature of GPs in optimization problems.
    • To propose and evaluate a nonstationary Gaussian process (NSGP) surrogate model for enhanced evolutionary optimization.

    Main Methods:

    • Theoretical analysis of GP nonstationarity in benchmark functions.
    • Development of an NSGP model where the mean varies with decision variables and residue variance follows an SGP.
    • Performance comparison of NSGP-based EAs (NSGP-MAEA) against SGP-based EAs (SGP-MAEA).

    Main Results:

    • GPs in optimization problems exhibit nonstationary behavior with high probability.
    • The proposed NSGP model demonstrated competitiveness against the traditional SGP model.
    • NSGP-MAEA outperformed SGP-MAEA on benchmark problems and an antenna design task.

    Conclusions:

    • Nonstationary GPs are crucial for effectively modeling complex optimization landscapes.
    • The NSGP surrogate model offers a more suitable approach for data-driven evolutionary optimization.
    • Employing NSGP-assisted EAs can lead to improved optimization outcomes.