Learning to Deliver: a Foundation Model for the Montreal Capacitated Vehicle Routing Problem

TL;DR

This paper introduces FM-MCVRP, a deep learning model based on a Transformer architecture, that effectively approximates solutions to the Montreal Capacitated Vehicle Routing Problem, outperforming traditional heuristics and generalizing well to larger instances.

Contribution

We propose a novel Transformer-based foundation model for MCVRP that leverages NLP techniques, trained on sub-optimal solutions, and demonstrates superior performance and generalization capabilities.

Findings

FM-MCVRP outperforms training data solutions.

Model solutions are within 2% of benchmarks for 400-customer problems.

The model generalizes to larger problem instances and various parameters.

Abstract

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.