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.

翻译：现有基于生成流网络（GFlowNet）的车辆路径问题（VRP）求解方法通常采用轨迹平衡（TB）实现全局优化，但往往忽视局部优化的重要方面。尽管详细平衡（DB）能更有效地处理局部优化，但单独使用DB不足以解决本质上需要整体轨迹优化的VRP问题。为克服这些局限，我们提出了混合平衡生成流网络（HBG）框架，该框架通过整合TB与DB内在互补的优势，以原则性自适应方式实现二者的独特融合。此外，针对带容量约束的车辆路径问题（CVRP）等以配送中心为核心的应用场景，我们提出了一种专用推理策略，利用配送中心节点在选择后继节点时更高的灵活性。尽管具有此专业化设计，HBG仍保持广泛适用性，可有效扩展至旅行商问题（TSP）等无显式配送中心的问题。我们将HBG集成至AGFN和GFACS两种成熟的GFlowNet求解器中开展评估，实验表明该方法在CVRP和TSP问题上均能带来持续显著的性能提升，印证了我们所提方法在解质量与泛化能力方面的增强效果。