iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908023755112448 |
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| author | Guo, Yifan Ren, Zhongqiang Wang, Chen |
| author_facet | Guo, Yifan Ren, Zhongqiang Wang, Chen |
| contents | This paper considers a Min-Max Multiple Traveling Salesman Problem (MTSP), where the goal is to find a set of tours, one for each agent, to collectively visit all the cities while minimizing the length of the longest tour. Though MTSP has been widely studied, obtaining near-optimal solutions for large-scale problems is still challenging due to its NP-hardness. Recent efforts in data-driven methods face challenges of the need for hard-to-obtain supervision and issues with high variance in gradient estimations, leading to slow convergence and highly suboptimal solutions. We address these issues by reformulating MTSP as a bilevel optimization problem, using the concept of imperative learning (IL). This involves introducing an allocation network that decomposes the MTSP into multiple single-agent traveling salesman problems (TSPs). The longest tour from these TSP solutions is then used to self-supervise the allocation network, resulting in a new self-supervised, bilevel, end-to-end learning framework, which we refer to as imperative MTSP (iMTSP). Additionally, to tackle the high-variance gradient issues during the optimization, we introduce a control variate-based gradient estimation algorithm. Our experiments showed that these innovative designs enable our gradient estimator to converge 20% faster than the advanced reinforcement learning baseline and find up to 80% shorter tour length compared with Google OR-Tools MTSP solver, especially in large-scale problems (e.g. 1000 cities and 15 agents). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning Guo, Yifan Ren, Zhongqiang Wang, Chen Artificial Intelligence Machine Learning Robotics This paper considers a Min-Max Multiple Traveling Salesman Problem (MTSP), where the goal is to find a set of tours, one for each agent, to collectively visit all the cities while minimizing the length of the longest tour. Though MTSP has been widely studied, obtaining near-optimal solutions for large-scale problems is still challenging due to its NP-hardness. Recent efforts in data-driven methods face challenges of the need for hard-to-obtain supervision and issues with high variance in gradient estimations, leading to slow convergence and highly suboptimal solutions. We address these issues by reformulating MTSP as a bilevel optimization problem, using the concept of imperative learning (IL). This involves introducing an allocation network that decomposes the MTSP into multiple single-agent traveling salesman problems (TSPs). The longest tour from these TSP solutions is then used to self-supervise the allocation network, resulting in a new self-supervised, bilevel, end-to-end learning framework, which we refer to as imperative MTSP (iMTSP). Additionally, to tackle the high-variance gradient issues during the optimization, we introduce a control variate-based gradient estimation algorithm. Our experiments showed that these innovative designs enable our gradient estimator to converge 20% faster than the advanced reinforcement learning baseline and find up to 80% shorter tour length compared with Google OR-Tools MTSP solver, especially in large-scale problems (e.g. 1000 cities and 15 agents). |
| title | iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning |
| topic | Artificial Intelligence Machine Learning Robotics |
| url | https://arxiv.org/abs/2405.00285 |