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    Area of Science:

    • Computational Mathematics
    • Artificial Intelligence
    • Optimization Theory

    Background:

    • Existing nonconvex optimization methods struggle with noisy real-world data.
    • Inaccurate results from conventional algorithms can lead to optimization failures.

    Purpose of the Study:

    • To develop a noise-tolerant and robust optimization solution for nonconvex problems.
    • To enhance the stability and convergence of optimization algorithms.

    Main Methods:

    • A coevolutionary neural solution (CNS) integrating a simplified neurodynamics (SND) model and particle swarm optimization (PSO).
    • The SND model avoids time-derivative information for improved stability.
    • The CNS leverages SND's noise tolerance and rapid convergence properties.

    Main Results:

    • The proposed CNS demonstrates superior performance in noisy scenarios compared to existing solutions.
    • Theoretical analysis confirms the CNS's global convergence, robustness, and probabilistic guarantees.
    • Effective application in designing finite impulse response (FIR) filters and pressure vessels.

    Conclusions:

    • The CNS offers a stable and effective approach for nonconvex optimization, even under perturbations.
    • The method provides a reliable tool for complex real-world engineering problems.
    • The CNS significantly improves optimization accuracy and reliability in the presence of noise.