Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems
Ni Zhang, Zhiguang Cao
TL;DR
This work addresses the VRP challenge of needing both global trajectory optimization and local transition quality. It introduces Hybrid-Balance GFlowNet (HBG), which unifies TB and DB under a principled, adaptive framework, and adds a VRP-tailored DB objective plus depot-guided inference for CVRP. Empirical results show that integrating HBG into AGFN and GFACS yields significant improvements on CVRP and TSP benchmarks, with strong scalability and generalization, including real-world CVRPLIB XXL data. The framework advances solution quality and robustness by balancing global and local signals, offering a practical path to more effective VRP solvers.
Abstract
Existing GFlowNet-based methods for vehicle routing problems (VRPs) typically employ Trajectory Balance (TB) to achieve global optimization but often neglect important aspects of local optimization. While Detailed Balance (DB) addresses local optimization more effectively, it alone falls short in solving VRPs, which inherently require holistic trajectory optimization. To address these limitations, we introduce the Hybrid-Balance GFlowNet (HBG) framework, which uniquely integrates TB and DB in a principled and adaptive manner by aligning their intrinsically complementary strengths. Additionally, we propose a specialized inference strategy for depot-centric scenarios like the Capacitated Vehicle Routing Problem (CVRP), leveraging the depot node's greater flexibility in selecting successors. Despite this specialization, HBG maintains broad applicability, extending effectively to problems without explicit depots, such as the Traveling Salesman Problem (TSP). We evaluate HBG by integrating it into two established GFlowNet-based solvers, i.e., AGFN and GFACS, and demonstrate consistent and significant improvements across both CVRP and TSP, underscoring the enhanced solution quality and generalization afforded by our approach.