Exploration through Generation: Applying GFlowNets to Structured Search

TL;DR

This paper demonstrates that GFlowNets can be trained to solve classical combinatorial optimization problems like TSP, MST, and shortest path, matching optimal solutions and offering scalable alternatives to traditional algorithms.

Contribution

It introduces the application of GFlowNets to structured graph search problems, showing they can learn to generate optimal solutions efficiently.

Findings

GFlowNets successfully find optimal solutions for TSP, MST, and shortest path.

Generated solutions match classical algorithms like Dijkstra and Kruskal.

Training convergence time increases with problem size.

Abstract

This work applies Generative Flow Networks (GFlowNets) to three graph optimization problems: the Traveling Salesperson Problem, Minimum Spanning Tree, and Shortest Path. GFlowNets are generative models that learn to sample solutions proportionally to a reward function. The models are trained using the Trajectory Balance loss to build solutions sequentially, selecting edges for spanning trees, nodes for paths, and cities for tours. Experiments on benchmark instances of varying sizes show that GFlowNets learn to find optimal solutions. For each problem type, multiple graph configurations with different numbers of nodes were tested. The generated solutions match those from classical algorithms (Dijkstra for shortest path, Kruskal for spanning trees, and exact solvers for TSP). Training convergence depends on problem complexity, with the number of episodes required for loss stabilization increasing as graph size grows. Once training converges, the generated solutions match known optima from classical algorithms across the tested instances. This work demonstrates that generative models can solve combinatorial optimization problems through learned policies. The main advantage of this learning-based approach is computational scalability: while classical algorithms have fixed complexity per instance, GFlowNets amortize computation through training. With sufficient computational resources, the framework could potentially scale to larger problem instances where classical exact methods become infeasible.