PAML: MoE-Based Partitioning and Merging Framework for Solving Large-scale Multi-task VRPs

Yujie Pan, Qingchun Hou

Keywords: Combinatorial Optimization, Large-scale VRPs, Multi-task VRPs, Learning to Optimize, Mixture of Experts (MoE)

Abstract: The Vehicle Routing Problem (VRP) serves as a fundamental optimization problem in modern logistics and supply chain management, where efficient solutions to its large-scale multi-task variants are crucial for reducing transportation costs and improving resource allocation efficiency. Although significant progress has been made in intelligent solving approaches for small- and medium-scale VRPs, current methods still face three major limitations when dealing with real-world large-scale multi-task scenarios: 1) Neural heuristic models trained on small-scale datasets struggle to generalize effectively to larger problem instances; 2) The computation time of traditional optimizers grows nonlinearly with problem scale, making them impractical for real-time decision-making; 3) Current solution approaches lack systematic mechanisms to handle the complex interactions and constraints between multiple concurrent tasks in an integrated manner. To address these challenges, this paper proposes the MoE-Based Partitioning and Merging (PAML) framework, with two key innovations: 1) A learnable and scalable implicit partitioner capable of handling multiple VRP variants, which optimizes partitioning strategies through end-to-end reinforcement learning, effectively overcoming training data scale limitations; 2) A dynamic merging mechanism based on polar angle clustering that enables intelligent control of subproblem sizes. This design allows efficient parallel solving of the partitioned VRP subproblems. Experimental results demonstrate that across various synthetic and real-world multi-task VRP variants of different scales, the PAML method shows remarkable improvements over its base solver model: reducing route length by up to 48.71\% for 2000-node problems and 20.66\% for 1000-node problems. For real-world CVRP-LIB instances, PAML achieves a 16.78\% reduction in routing distance compared to MVMoE while maintaining solution quality within 4.93\% of OR-Tools. Remarkably, PAML requires only one-tenth of OR-Tools' computation time (0.95s vs 14.23s on average).

Primary Area: optimization

Submission Number: 10554