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<p>The transportation problem is a classical optimization model used in logistics and supply chain management to determine the minimum cost of transporting goods from multiple sources to multiple destinations. Traditional approaches such as the Northwest Corner Rule, Least Cost Method and Vogel’s Approximation Method can generate feasible transportation plans; however, they may face limitations in obtaining optimal solutions when the problem becomes complex or large in scale. To overcome these limitations, metaheuristic optimization techniques have been widely adopted due to their strong exploration capability in complex search spaces. In this study, ten metaheuristic algorithms-Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Firefly Algorithm (FA), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Coyote Optimization Algorithm (COA), Harris Hawks Optimization (HHO), Chimp Optimization Algorithm (ChOA) and Honey Badger Algorithm (HBA)-are applied to solve transportation cost minimization problems. The algorithms are evaluated on ten benchmark transportation instances under identical experimental settings, with each algorithm executed for 30 independent runs. Performance is analyzed in terms of solution quality, stability, and computational runtime to determine which algorithm provides the lowest transportation cost. Statistical validation using the Friedman test, Holm’s post-hoc analysis, Kendall’s coefficient of concordance and the Vargha Delaney <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( A_{12}\)</EquationSource> </InlineEquation> effect size ensures reliable comparison. The results provide a systematic assessment of the effectiveness of modern metaheuristic algorithms in identifying stable and cost-efficient solutions for transportation optimization.</p>

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Statistical performance and stability analysis of ten metaheuristic algorithms for transportation cost minimization

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • A. Sandhya,
  • G. Y. Mythili

摘要

The transportation problem is a classical optimization model used in logistics and supply chain management to determine the minimum cost of transporting goods from multiple sources to multiple destinations. Traditional approaches such as the Northwest Corner Rule, Least Cost Method and Vogel’s Approximation Method can generate feasible transportation plans; however, they may face limitations in obtaining optimal solutions when the problem becomes complex or large in scale. To overcome these limitations, metaheuristic optimization techniques have been widely adopted due to their strong exploration capability in complex search spaces. In this study, ten metaheuristic algorithms-Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Firefly Algorithm (FA), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Coyote Optimization Algorithm (COA), Harris Hawks Optimization (HHO), Chimp Optimization Algorithm (ChOA) and Honey Badger Algorithm (HBA)-are applied to solve transportation cost minimization problems. The algorithms are evaluated on ten benchmark transportation instances under identical experimental settings, with each algorithm executed for 30 independent runs. Performance is analyzed in terms of solution quality, stability, and computational runtime to determine which algorithm provides the lowest transportation cost. Statistical validation using the Friedman test, Holm’s post-hoc analysis, Kendall’s coefficient of concordance and the Vargha Delaney \( A_{12}\) effect size ensures reliable comparison. The results provide a systematic assessment of the effectiveness of modern metaheuristic algorithms in identifying stable and cost-efficient solutions for transportation optimization.