aiqbench analysis
This paper introduces ResizeCO, a novel framework that enables diffusion-based solvers to generalize across varying instance sizes in NP-hard routing problems like TSP and CVRP. By combining reinforcement learning with tree search techniques, the method achieves superior performance on instances up to 10,000 nodes while maintaining computational efficiency. This advancement addresses a critical bottleneck in applying generative models to large-scale combinatorial optimization tasks.
Size Generalization for Diffusion Routing Solvers
arXiv:2610.17192v1 Announce Type: new Abstract: Routing problems, like the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP), are NP-hard and slow to solve for large instances. Diffusion-based solvers can be trained in a supervised way using sets of optimal solutions, and then quickly solve new test instances. However, for large instances, optimal solutions are hard to find, and diffusion models fail to generalize to instance sizes outside their training distribution. Here we describe ResizeCO, a label free size-generalization approach that addresses both the change in statistical properties of larger instances, and the computational challenge of solving them quickly. It uses reinforcement learning on large-scale instances to adapt a diffusion model trained on small instances. Specifically, we adapt GRPO to this problem, using route length as the training signal. ResizeCO also formulates k-opt as a tree search, solved by a beam search on the GPU. In size-generalization experiments on TSP and CVRP instances with up to 10000 nodes, ResizeCO achieves a Pareto front over route quality and time that dominates learned solvers, and also outperforms other solvers at short run times, setting a new state of the art.
Abstract:Routing problems, like the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP), are NP-hard and slow to solve for large instances. Diffusion-based solvers can be trained in a supervised way using sets of optimal solutions, and then quickly solve new test instances. However, for large instances, optimal solutions are hard to find, and diffusion models fail to generalize to instance sizes outside their training distribution. Here we describe ResizeCO, a label free size-generalization approach that addresses both the change in statistical properties of larger instances, and the computational challenge of solving them quickly. It uses reinforcement learning on large-scale instances to adapt a diffusion model trained on small instances. Specifically, we adapt GRPO to this problem, using route length as the training signal. ResizeCO also formulates k-opt as a tree search, solved by a beam search on the GPU. In size-generalization experiments on TSP and CVRP instances with up to 10000 nodes, ResizeCO achieves a Pareto front over route quality and time that dominates learned solvers, and also outperforms other solvers at short run times, setting a new state of the art.
Artificial Intelligence (cs.AI)
arXiv:2610.17192 [cs.AI]
(or arXiv:2610.17192v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.17192 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 279 words
