Learning to Deliver: a Foundation Model for the Montreal Capacitated Vehicle Routing Problem
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| Format: | Preprint |
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2024
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| _version_ | 1866909123897982976 |
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| author | Chin, Samuel J. K. Winkenbach, Matthias Srivastava, Akash |
| author_facet | Chin, Samuel J. K. Winkenbach, Matthias Srivastava, Akash |
| contents | In this paper, we present the Foundation Model for the Montreal Capacitated Vehicle Routing Problem (FM-MCVRP), a novel Deep Learning (DL) model that approximates high-quality solutions to a variant of the Capacitated Vehicle Routing Problem (CVRP) that characterizes many real-world applications. The so-called Montreal Capacitated Vehicle Routing Problem (MCVRP), first formally described by Bengio et al. (2021), is defined on a fixed and finite graph, which is analogous to a city. Each MCVRP instance is essentially the sub-graph connecting a randomly sampled subset of the nodes in the fixed graph, which represent a set of potential addresses in a real-world delivery problem on a given day. Our work exploits this problem structure to frame the MCVRP as an analogous Natural Language Processing (NLP) task. Specifically, we leverage a Transformer architecture embedded in a Large Language Model (LLM) framework to train our model in a supervised manner on computationally inexpensive, sub-optimal MCVRP solutions obtained algorithmically. Through comprehensive computational experiments, we show that FM-MCVRP produces better MCVRP solutions than the training data and generalizes to larger sized problem instances not seen during training. Even when compared to near-optimal solutions from state-of-the-art heuristics, FM-MCVRP yields competitive results despite being trained on inferior data. For instance, for 400-customer problems, FM-MCVRP solutions on average fall within 2% of the benchmark. Our results further demonstrate that unlike prior works in the literature, FM-MCVRP is a unified model, which performs consistently and reliably on a range of problem instance sizes and parameter values such as the vehicle capacity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_00026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning to Deliver: a Foundation Model for the Montreal Capacitated Vehicle Routing Problem Chin, Samuel J. K. Winkenbach, Matthias Srivastava, Akash Machine Learning Artificial Intelligence Optimization and Control In this paper, we present the Foundation Model for the Montreal Capacitated Vehicle Routing Problem (FM-MCVRP), a novel Deep Learning (DL) model that approximates high-quality solutions to a variant of the Capacitated Vehicle Routing Problem (CVRP) that characterizes many real-world applications. The so-called Montreal Capacitated Vehicle Routing Problem (MCVRP), first formally described by Bengio et al. (2021), is defined on a fixed and finite graph, which is analogous to a city. Each MCVRP instance is essentially the sub-graph connecting a randomly sampled subset of the nodes in the fixed graph, which represent a set of potential addresses in a real-world delivery problem on a given day. Our work exploits this problem structure to frame the MCVRP as an analogous Natural Language Processing (NLP) task. Specifically, we leverage a Transformer architecture embedded in a Large Language Model (LLM) framework to train our model in a supervised manner on computationally inexpensive, sub-optimal MCVRP solutions obtained algorithmically. Through comprehensive computational experiments, we show that FM-MCVRP produces better MCVRP solutions than the training data and generalizes to larger sized problem instances not seen during training. Even when compared to near-optimal solutions from state-of-the-art heuristics, FM-MCVRP yields competitive results despite being trained on inferior data. For instance, for 400-customer problems, FM-MCVRP solutions on average fall within 2% of the benchmark. Our results further demonstrate that unlike prior works in the literature, FM-MCVRP is a unified model, which performs consistently and reliably on a range of problem instance sizes and parameter values such as the vehicle capacity. |
| title | Learning to Deliver: a Foundation Model for the Montreal Capacitated Vehicle Routing Problem |
| topic | Machine Learning Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2403.00026 |