Multi-level graph partition via hierarchical learning for large-scale vehicle routing problems

Abstract Vehicle Routing Problems (VRPs) involve multi-agent route optimization, with the objective of targeting optimal routes for a fleet of vehicles to serve a set of customers. Existing neural solvers based on the divide-and-conquer approach for VRPs in general, and capacitated VRP (CVRP) in particular, integrate the global partition of an instance with the local construction for each resulting subinstance to enhance generalization. However, during the global partition phase, misclusterings within subgraphs have a tendency to progressively compound throughout the multi-step decoding process of the learning-based partition policy. This suboptimal behavior of the partition policy, in turn, may lead to a dramatic deterioration in the performance of the overall decomposition-based system, despite using optimal local constructions. To address these challenges, we propose a versatile Hierarchical Learning-based Graph Partition (HLGP) framework, which is tailored to benefit the partition of CVRP instances by synergistically integrating global and local partition policies. Specifically, the global partition policy is tasked with creating a coarse multi-way partition to generate a sequence of simpler two-way partition subtasks. These subtasks mark the initiation of the subsequent K local partition levels. At each local partition level, subtasks exclusive to this level are assigned to the local partition policy which benefits from the insensitive local topological features to incrementally alleviate the compounded errors. This framework is versatile in the sense that it optimizes the involved partition policies towards a unified objective, which is harmoniously compatible with both reinforcement learning (RL) and supervised learning (SL) paradigms. Additionally, we decouple the synchronized training into individual training of each component to circumvent the instability issue. Furthermore, we point out the importance of treating the subproblems encountered during the partition process as individual training instances. Extensive experiments conducted on various CVRP benchmarks demonstrate the effectiveness and generalization capabilities of the HLGP framework under both scale and distribution shifts. The source code is available at https: //github. com/panyxy/hlgpcvrp.