Effective inventory management under stochastic demand remains a central challenge in supply chain operations, particularly when multiple items share coupling constraints on the purchasing budget, warehouse capacity, and service level. Although metaheuristic algorithms have been widely applied to such problems, existing approaches typically rely on fixed algorithmic configurations that limit their adaptability and robustness as problem dimensionality and constraint complexity grow. To address this limitation, this paper proposes the adaptive multi-operator differential evolution (AMODE) algorithm, which unifies four complementary mechanisms within a single cohesive framework: opposition-based learning initialization for enhanced population diversity, an adaptive multi-operator mutation pool with success-history-based operator selection, success-history based adaptive differential evolution (SHADE) style parameter self-adaptation for the scaling factor and crossover rate, and a Lévy-flight escape mechanism to counteract premature convergence. AMODE was evaluated on three benchmark instances of increasing dimensionality ($ n = 10, 20, 50 $) derived from the UCI Online Retail Ⅱ dataset, comprising over one million real-world retail transactions. Experiments over 30 independent runs compare AMODE achieved against twelve representative metaheuristic algorithms spanning evolutionary, swarm-based, physics-inspired, and adaptive DE paradigms (including the state-of-the-art DE variants linear success-history based adaptive differential evolution (L-SHADE), adaptive j-strategy self-optimization differential evolution (jSO), and improved multi-operator differential evolution (IMODE)). AMODE the best mean fitness across all instances with a standard deviation not exceeding 0.02—demonstrating near-deterministic convergence. Wilcoxon signed-rank tests confirmed statistical significance ($ p < 0.001 $) against all competitors on all three instances. An ablation study established the independent and synergistic contribution of each component, and an analysis of internal parameter dynamics revealed how the adaptive mechanisms respond coherently to the evolving search landscape. These findings establish AMODE as a robust and scalable optimization framework for practical multi-item inventory management under stochastic demand.
Citation: Zixin Feng, Xingyu Feng, Lupeng Hao, Junming Chen. An adaptive multi-operator differential evolution algorithm for multi-item constrained stochastic inventory optimization[J]. AIMS Mathematics, 2026, 11(5): 14586-14616. doi: 10.3934/math.2026598
Effective inventory management under stochastic demand remains a central challenge in supply chain operations, particularly when multiple items share coupling constraints on the purchasing budget, warehouse capacity, and service level. Although metaheuristic algorithms have been widely applied to such problems, existing approaches typically rely on fixed algorithmic configurations that limit their adaptability and robustness as problem dimensionality and constraint complexity grow. To address this limitation, this paper proposes the adaptive multi-operator differential evolution (AMODE) algorithm, which unifies four complementary mechanisms within a single cohesive framework: opposition-based learning initialization for enhanced population diversity, an adaptive multi-operator mutation pool with success-history-based operator selection, success-history based adaptive differential evolution (SHADE) style parameter self-adaptation for the scaling factor and crossover rate, and a Lévy-flight escape mechanism to counteract premature convergence. AMODE was evaluated on three benchmark instances of increasing dimensionality ($ n = 10, 20, 50 $) derived from the UCI Online Retail Ⅱ dataset, comprising over one million real-world retail transactions. Experiments over 30 independent runs compare AMODE achieved against twelve representative metaheuristic algorithms spanning evolutionary, swarm-based, physics-inspired, and adaptive DE paradigms (including the state-of-the-art DE variants linear success-history based adaptive differential evolution (L-SHADE), adaptive j-strategy self-optimization differential evolution (jSO), and improved multi-operator differential evolution (IMODE)). AMODE the best mean fitness across all instances with a standard deviation not exceeding 0.02—demonstrating near-deterministic convergence. Wilcoxon signed-rank tests confirmed statistical significance ($ p < 0.001 $) against all competitors on all three instances. An ablation study established the independent and synergistic contribution of each component, and an analysis of internal parameter dynamics revealed how the adaptive mechanisms respond coherently to the evolving search landscape. These findings establish AMODE as a robust and scalable optimization framework for practical multi-item inventory management under stochastic demand.
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Zixin Feng, Xingyu Feng, Lupeng Hao, Junming Chen. An adaptive multi-operator differential evolution algorithm for multi-item constrained stochastic inventory optimization[J]. AIMS Mathematics, 2026, 11(5): 14586-14616. doi: 10.3934/math.2026598
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