An effective deep reinforcement learning-based kernel search heuristic for multimodal transportation planning problem

The growing complexity of global supply chains has made multimodal freight transportation optimization increasingly critical, as businesses seek to balance cost efficiency, service quality, and environmental sustainability across interconnected rail, road, and air networks. This study addresses the capacitated multimodal transportation planning problem (CMTPP) to minimize transportation costs through optimal route selection, mode allocation, and freight consolidation while considering service time constraints. A novel Deep Reinforcement Learning based Kernel Search (DRLKS) framework is developed, integrating deep Q-networks with kernel search mechanisms to efficiently solve this complex optimization problem. The DRL agent learns intelligent policies to identify optimal routing paths for individual freight orders within the network, while the kernel search framework solves the global optimization problem to determine the overall best solution. Extensive numerical experiments on instances up to 500 orders within 20-node networks demonstrate that DRLKS achieves near-optimal solutions with 2.08 %-3.22 % optimality gaps while reducing computational time by 69 %-79 % compared with the exact solutions provided by Gurobi. For large instances, Gurobi provided exact solutions for only 18 of the 50 instances within 7200 seconds. The lower bound obtained from Gurobi was used to evaluate the performance of the DRLKS heuristic, showing an average gap of 2.08 % between the lower bound and near-optimal solution, with a computational time saving of approximately 79 %. Real-world case study validation in inland China confirms the framework’s industrial applicability and demonstrates the promising potential of integrating deep reinforcement learning with classical optimization for complex logistics challenges.