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

Kexiong Yu, Hang Zhao, Yuhang Huang, Renjiao Yi, Kai Xu, Chenyang Zhu

Keywords: combinatorial optimization, diffusion models

TL;DR: We propose an efficient diffusion solver for large-scale combinatorial optimization problems that excels in both solution quality and inference speed.

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 **DI**ffusion **S**olver for large-scale **C**ombinatorial **O**ptimization 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.

Primary Area: optimization

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Submission Number: 6285