Differential evolution with spherical search algorithm for nonlinear engineering and infectious disease optimization problems

Jongmin Lee

doi:10.1016/j.asoc.2024.112446

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Differential evolution with spherical search algorithm for nonlinear engineering and infectious disease optimization problems

2025-01-01

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DOI：10.1016/j.asoc.2024.112446

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Abstract

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Metaheuristic algorithms for constrained optimization are popular because of their simplicity and ability to find global solutions. However, they can be computationally demanding and may struggle with identifying feasible points. In this study, we propose a new algorithm, Differential Evolution with Spherical Search (DESS), which combines spherical search to explore feasible regions and differential evolution to exploit promising points. Spherical Search (SS) is a recent algorithm that explores a spherical region around each population member and uses gradient repair to guide the solutions towards the feasible region. We incorporate SS into a multi-operator differential evolution with archiving, which uses hierarchical sorting to handle the constraints. Moreover, DESS implements an interior point method as a local search to obtain more accurate solutions. We also introduce an infeasible operator that allows DESS to examine infeasible regions near the global solution. This is particularly helpful for problems where the global solution lies along the boundary of the feasible region. DESS was tested on 57 benchmark objective functions from recent real-world constrained problems, with dimensions ranging from 2 to 158 and up to 148 constraints. It outperformed 18 state-of-the-art methods, achieving a 98% feasibility rate and finding superior solutions. DESS excelled in complex problems, including power systems, power electronics, and livestock feed optimization. It was also applied to a constrained optimization problem involving an ordinary differential equation, demonstrating its practical relevance and versatility.

Keywords:

Spherical search

Differential evolution

Metaheuristic algorithm

Engineering optimization

Infectious disease