Optimizing Low-Carbon Supply Chain Networks: A Dynamic Learning Factor-Based Particle Swarm Optimization Approach

With the tightening of global carbon emission regulations, supply chain enterprises face the challenge of balancing cost optimization with environmental sustainability. This study establishes a low-carbon supply chain network equilibrium model that incorporates carbon footprint constraints into supply chain decision-making. A variational inequality framework is employed to characterize the equilibrium conditions, considering economic costs, carbon emissions from production, transportation, and warehousing, as well as the impact of carbon taxation and trading mechanisms. To enhance computational efficiency, an improved particle swarm optimization (PSO) algorithm is proposed, introducing a dynamic adjustment mechanism for learning factors. The cognitive learning factor decreases linearly, while the social learning factor increases linearly, improving both global exploration and local exploitation capabilities. Experimental results on multi-tier supply chain networks under different carbon policies, including carbon taxes and carbon trading, demonstrate that the proposed method effectively reduces total costs and carbon emissions while achieving faster convergence compared to conventional PSO and other metaheuristic algorithms. These findings provide a quantitative basis for optimizing low-carbon supply chain networks and contribute to the development of more effective decision-making strategies under carbon constraints.