Z. Cao

Ni Zhang, Jingfeng Yang, Zhiguang Cao et al.

Recent research into solving vehicle routing problems (VRPs) has gained significant traction, particularly through the application of deep (reinforcement) learning for end-to-end solution construction. However, many current construction-based neural solvers predominantly utilize Transformer architectures, which can face scalability challenges and struggle to produce diverse solutions. To address these limitations, we introduce a novel framework beyond Transformer-based approaches, i.e., Adversarial Generative Flow Networks (AGFN). This framework integrates the generative flow network (GFlowNet)-a probabilistic model inherently adept at generating diverse solutions (routes)-with a complementary model for discriminating (or evaluating) the solutions. These models are trained alternately in an adversarial manner to improve the overall solution quality, followed by a proposed hybrid decoding method to construct the solution. We apply the AGFN framework to solve the capacitated vehicle routing problem (CVRP) and travelling salesman problem (TSP), and our experimental results demonstrate that AGFN surpasses the popular construction-based neural solvers, showcasing strong generalization capabilities on synthetic and real-world benchmark instances.

Ni Zhang, Zhiguang Cao

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.