DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems

TL;DR

DISCO introduces an efficient diffusion-based solver for large-scale combinatorial optimization problems, improving solution quality and inference speed by constraining sampling space and accelerating denoising, outperforming existing methods on TSP and MIS benchmarks.

Contribution

The paper presents a novel diffusion solver that enhances solution quality and inference speed for large-scale CO problems by constraining sampling space and employing an analytically solvable denoising process.

Findings

DISCO achieves up to 5.28x faster inference than other diffusion methods.

It generalizes well to unseen problem scales, surpassing models trained specifically for those scales.

Strong performance on large TSP and Maximal Independent Set benchmarks.

Abstract

Combinatorial Optimization (CO) problems are fundamentally important in numerous real-world applications across diverse industries, characterized by entailing enormous solution space and demanding time-sensitive response. Despite recent advancements in neural solvers, their limited expressiveness struggles to capture the multi-modal nature of CO landscapes. While some research has shifted towards diffusion models, these models still sample solutions indiscriminately from the entire NP-complete solution space with time-consuming denoising processes, which limit their practicality for large problem scales. We propose DISCO, an efficient DIffusion Solver for large-scale Combinatorial Optimization problems that excels in both solution quality and inference speed. DISCO's efficacy is twofold: First, it enhances solution quality by constraining the sampling space to a more meaningful domain guided by solution residues, while preserving the multi-modal properties of the output distributions. Second, it accelerates the denoising process through an analytically solvable approach, enabling solution sampling with minimal reverse-time steps and significantly reducing inference time. DISCO delivers strong performance on large-scale Traveling Salesman Problems and challenging Maximal Independent Set benchmarks, with inference time up to 5.28 times faster than other diffusion alternatives. By incorporating a divide-and-conquer strategy, DISCO can well generalize to solve unseen-scale problem instances, even surpassing models specifically trained for those scales.