DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909641881944064 |
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| author | Zhao, Hang Yu, Kexiong Huang, Yuhang Yi, Renjiao Zhu, Chenyang Xu, Kai |
| author_facet | Zhao, Hang Yu, Kexiong Huang, Yuhang Yi, Renjiao Zhu, Chenyang Xu, Kai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems Zhao, Hang Yu, Kexiong Huang, Yuhang Yi, Renjiao Zhu, Chenyang Xu, Kai Artificial Intelligence 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. |
| title | DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2406.19705 |