DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization

TL;DR

DIFUSCO introduces a graph-based diffusion framework utilizing denoising diffusion models to significantly improve neural solutions for NP-complete problems like TSP and MIS, outperforming previous methods.

Contribution

The paper presents a novel graph-based diffusion approach for neural combinatorial solvers, expanding the scope and effectiveness of neural methods for NP-complete problems.

Findings

Outperforms previous neural solvers on TSP and MIS benchmarks.

Reduces performance gap between neural and ground-truth solutions.

Effective diffusion models improve solution quality for complex NP problems.

Abstract

Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural solvers for NPC problems by introducing a new graph-based diffusion framework, namely DIFUSCO. Our framework casts NPC problems as discrete {0, 1}-vector optimization problems and leverages graph-based denoising diffusion models to generate high-quality solutions. We investigate two types of diffusion models with Gaussian and Bernoulli noise, respectively, and devise an effective inference schedule to enhance the solution quality. We evaluate our methods on two well-studied NPC combinatorial optimization problems: Traveling Salesman Problem (TSP) and Maximal Independent Set (MIS). Experimental results show that DIFUSCO strongly outperforms the previous state-of-the-art neural solvers, improving the performance gap between ground-truth and neural solvers from 1.76% to 0.46% on TSP-500, from 2.46% to 1.17% on TSP-1000, and from 3.19% to 2.58% on TSP10000. For the MIS problem, DIFUSCO outperforms the previous state-of-the-art neural solver on the challenging SATLIB benchmark.