Adversarial Generative Flow Network for Solving Vehicle Routing Problems

2025-03-03

AI Summary

Existing Transformer-based neural solvers for the Vehicle Routing Problem (VRP) suffer from poor scalability and insufficient solution diversity. Method: This paper proposes the Adversarial Generative Flow Network (AGFN) framework—the first to integrate Generative Flow Networks (GFlowNets) into VRP solving—establishing an alternating adversarial training paradigm between a generator and a discriminator, augmented by reinforcement learning–driven path generation and a hybrid decoding strategy. Contribution/Results: AGFN overcomes limitations of constructive modeling by jointly optimizing solution quality and diversity. On Capacitated VRP (CVRP) and Traveling Salesman Problem (TSP) benchmarks, AGFN significantly outperforms state-of-the-art constructive neural solvers on both synthetic and real-world datasets, demonstrating superior generalization capability and higher solution quality.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Multiagent Systems: Adversarial Agents

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

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.

Problem

• Address scalability and diversity issues in Transformer-based VRP solvers.
• Introduce Adversarial Generative Flow Networks for diverse route generation.
• Improve solution quality for CVRP and TSP using adversarial training.

Innovation

• Adversarial Generative Flow Networks for VRPs
• Combines GFlowNet with adversarial training
• Hybrid decoding enhances solution construction