A Scenario-Based Multi-Objective Multimodal Route Optimization Model Considering Demand Uncertainty and Traffic Congestion

Multimodal transport plays an irreplaceable role in international trade due to its cost and efficiency advantages. However, optimizing multimodal transport paths that simultaneously consider economic costs, carbon emissions, demand uncertainty, and traffic congestion remains a critical challenge. This paper establishes a scenario-based multi-objective optimization model to minimize total transportation costs and carbon emissions under uncertain demand and road congestion. To address this complex combinatorial problem, we propose LMSSA, an improved multi-objective salp swarm algorithm that integrates Bernoulli chaotic mapping, adaptive parameter adjustment, and a co-directional leader–follower update strategy. These enhancements significantly improve the balance between global exploration and local exploitation, overcoming premature convergence common in traditional salp swarm algorithms. The algorithm’s effectiveness is validated through extensive experiments on 50 instances of varying scales (8 to 100 nodes) and a real-world case study of multimodal transport in northern China. Results demonstrate that LMSSA outperforms the standard multi-objective salp swarm algorithm in convergence speed, solution quality, and robustness, providing enterprises with more economical, low-carbon, and resilient transportation decisions under uncertain and congested conditions.