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<p>Global optimization problems in science and engineering are challenging due to their complexity and often Nondeterministic Polynomial-time hard nature. This paper introduces the Adaptive Hybrid Differential Evolution with Local Search (AHDE-LS) algorithm. It uses two phases: a global search with improved Differential Evolution (DE) and a local search via constrained optimization (interior-point or SQP algorithm). AHDE-LS combines global exploration and adaptive local exploitation. It dynamically adjusts DE control parameters—mutation factor (F) and crossover rate (CR)—with an exponential decay function over generations. Generations track evolutionary progress and better reflect long-term trends than iterations or computation time. AHDE-LS reduces the population in later stages and preserves diversity, avoiding premature convergence and improving efficiency and solution quality. Its framework alternates between global and local searches, modulating the intensity of local searches based on the rate of fitness improvement. Tested on 23 benchmarks, AHDE-LS outperforms metaheuristics like PUMA, QIO, SFGWO, IWOA, and Cuckoo Search. Results show superior accuracy, robustness, and speed. Statistical tests, including the Friedman and Wilcoxon signed-rank tests, confirm its dominance, with a mean rank of 2.09 and a significant improvement over competitors. Unlike other DE–LS hybrids with fixed or stagnation-based local search, AHDE-LS adaptively switches based on real-time improvement rate, increasing efficiency and stability. These results highlight AHDE-LS as a strong tool for global optimization.</p>

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Adaptive hybrid differential evolution with local search: a robust global optimization approach

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Eslam Mohamed Ahmed,
  • Andrew Amgad,
  • Ahmed Ragab

摘要

Global optimization problems in science and engineering are challenging due to their complexity and often Nondeterministic Polynomial-time hard nature. This paper introduces the Adaptive Hybrid Differential Evolution with Local Search (AHDE-LS) algorithm. It uses two phases: a global search with improved Differential Evolution (DE) and a local search via constrained optimization (interior-point or SQP algorithm). AHDE-LS combines global exploration and adaptive local exploitation. It dynamically adjusts DE control parameters—mutation factor (F) and crossover rate (CR)—with an exponential decay function over generations. Generations track evolutionary progress and better reflect long-term trends than iterations or computation time. AHDE-LS reduces the population in later stages and preserves diversity, avoiding premature convergence and improving efficiency and solution quality. Its framework alternates between global and local searches, modulating the intensity of local searches based on the rate of fitness improvement. Tested on 23 benchmarks, AHDE-LS outperforms metaheuristics like PUMA, QIO, SFGWO, IWOA, and Cuckoo Search. Results show superior accuracy, robustness, and speed. Statistical tests, including the Friedman and Wilcoxon signed-rank tests, confirm its dominance, with a mean rank of 2.09 and a significant improvement over competitors. Unlike other DE–LS hybrids with fixed or stagnation-based local search, AHDE-LS adaptively switches based on real-time improvement rate, increasing efficiency and stability. These results highlight AHDE-LS as a strong tool for global optimization.