Dual-Objective Optimization Model for Low Carbon Cold-Chain Logistics

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Abstract
Cold-chain logistics plays a crucial role in maintaining the quality of temperature-sensitive products. However, it generates high energy consumption and carbon emissions due to refrigeration and complex routing operations. Therefore, this study proposes a dual-objective optimization model for low carbon cold-chain vehicle routing that simultaneously minimizes total logistics and carbon emission costs. The model comprehensively integrates transportation, refrigeration, cargo damage, and holding costs, as well as emissions from fuel consumption and refrigeration energy use. To solve the proposed model, two multi-objective evolutionary algorithms, the non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective particle swarm optimization (MOPSO), were employed and compared under the same experimental framework. Numerical experiments based on Solomon benchmark instances demonstrate that both algorithms can effectively generate Pareto-optimal solutions. NSGA-II shows superior convergence and better diversity maintenance, whereas MOPSO achieves faster early-stage convergence and stronger global exploration. The comparative analysis, supported by quantitative performance metrics and visual results, confirms the reliability of the proposed optimization model and highlights the complementary characteristics of the two algorithms. The findings provide theoretical and practical insights for designing sustainable, cost-efficient, and environmentally friendly cold-chain logistics systems.

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