Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems

2025-10-06

AI Summary

To address the imbalance between global and local optimization in the Vehicle Routing Problem (VRP), this paper proposes the first adaptive GFlowNet hybrid framework integrating Trajectory Balance (TB) and Detailed Balance (DB). Methodologically, we design a depot-aware sequence generation strategy that embeds fine-grained local search mechanisms into global trajectory modeling, enabling synergistic global–local optimization. Our key innovation lies in the dynamic coupling of TB and DB within the GFlowNet architecture—first achieved in VRP—and the introduction of depot-oriented inference guidance, which jointly ensures global solution consistency and local structural validity. Experiments on canonical CVRP and TSP benchmarks demonstrate that our approach significantly outperforms state-of-the-art baselines—including AGFN and GFACS—in both solution quality and generalization capability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Integrates global and local optimization for vehicle routing problems
• Proposes adaptive hybrid framework combining Trajectory and Detailed Balance
• Enhances solution quality for both depot-based and depot-less problems

Innovation

• Hybrid-Balance GFlowNet integrates TB and DB adaptively
• Specialized inference strategy leverages depot node flexibility
• Maintains broad applicability across routing problem types