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<p>This study presents <i>Stochastic Diffusion Adaptive Optimization (SDAO)</i>, a novel metaheuristic algorithm grounded in diffusion dynamics and stochastic modeling. The proposed method replaces traditional gradient descent with a density-driven diffusion mechanism, derived from Fick’s second law, allowing particles to escape densely populated regions and effectively explore sparsely sampled areas. SDAO incorporates global and individual guidance mechanisms, adaptive parameter tuning, opposition-based learning, and periodic bound contraction to enhance convergence behavior. Comprehensive experiments were conducted across four benchmark categories-standard, stochastic, CEC, and real-world problems-under various dimensional settings (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d = 10\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(d = 100\)</EquationSource> </InlineEquation>). The algorithm consistently demonstrated competitive performance and significantly outperformed state-of-the-art methods, including SHADEwithILS, AMSO, and TLPSO, particularly in noisy and high-dimensional environments. Statistical validation using ANOVA, Tukey’s HSD, and Wilcoxon tests confirmed the significance and robustness of the observed performance improvements. These results establish SDAO as a promising solution for complex, high-dimensional, and uncertainty-laden optimization problems, with broad applicability to real-world scenarios.</p>

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Stochastic diffusion adaptive optimization, a novel metaheuristic approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月19日

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  • Ricardo M. Leal Lopez

摘要

This study presents Stochastic Diffusion Adaptive Optimization (SDAO), a novel metaheuristic algorithm grounded in diffusion dynamics and stochastic modeling. The proposed method replaces traditional gradient descent with a density-driven diffusion mechanism, derived from Fick’s second law, allowing particles to escape densely populated regions and effectively explore sparsely sampled areas. SDAO incorporates global and individual guidance mechanisms, adaptive parameter tuning, opposition-based learning, and periodic bound contraction to enhance convergence behavior. Comprehensive experiments were conducted across four benchmark categories-standard, stochastic, CEC, and real-world problems-under various dimensional settings ( \(d = 10\) to \(d = 100\) ). The algorithm consistently demonstrated competitive performance and significantly outperformed state-of-the-art methods, including SHADEwithILS, AMSO, and TLPSO, particularly in noisy and high-dimensional environments. Statistical validation using ANOVA, Tukey’s HSD, and Wilcoxon tests confirmed the significance and robustness of the observed performance improvements. These results establish SDAO as a promising solution for complex, high-dimensional, and uncertainty-laden optimization problems, with broad applicability to real-world scenarios.