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

• URL: http://arxiv.org/abs/2406.19705v5
• Date: Mon, 21 Oct 2024 13:38:48 GMT
• Title: DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems
• Authors: Kexiong Yu, Hang Zhao, Yuhang Huang, Renjiao Yi, Kai Xu, Chenyang Zhu,
• Abstract summary: DISCO is an efficient DIffusion solver for large-scale Combinatorial Optimization problems. It constrains the sampling space to a more meaningful domain guided by solution residues, while preserving the multi-modal properties of the output distributions. It 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.
• Score: 37.205311971072405
• License:
• 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.

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