While previous heuristic or learning-based works achieve decent solutions on small problem instances, their performance deteriorates in large problems. This article presents a novel learning-augmented local search framework to solve large-scale VRP. The method iteratively improves the solution by identifying appropriate subproblems and $delegating$ their improvement to a black box subsolver. At each step, we leverage spatial locality to consider only a linear number of subproblems, rather than exponential. We frame subproblem selection as regression and train a Transformer on a generated training set of problem instances. Our method accelerates state-of-the-art VRP solvers by 10x to 100x while achieving competitive solution qualities for VRPs with sizes ranging from 500 to 3000. Learned subproblem selection offers a 1.5x to 2x speedup over heuristic or random selection. Our results generalize to a variety of VRP distributions, variants, and solvers.

Manually designing (meta-)heuristics for the Vehicle Routing Problem (VRP) is a challenging task that requires significant domain expertise. Recently, data-driven approaches have emerged as a promising solution, automatically learning heuristics that perform well on training instances and generalize to unseen test cases. Such an approach learns (meta-)heuristics that can perform well on the training instances, expecting it to generalize well on the unseen test instances. A recent method, named GPGLS, uses Genetic Programming (GP) to learn the utility function in Guided Local Search (GLS) and solved large scale VRP effectively. However, the selection of appropriate training instances during the learning process remains an open question, with most existing studies including GPGLS relying on random instance selection. To address this, we propose a novel method, CL-GPGLS, which integrates Curriculum Learning (CL) into GPGLS. Our approach leverages a predefined curriculum to introduce training instances progressively, starting with simpler tasks and gradually increasing complexity, enabling the model to better adapt and optimize for large-scale VRP (LSVRP). Extensive experiments verify the effectiveness of CL-GPGLS, demonstrating significant performance improvements over three baseline methods.

While previous heuristic or learning-based works achieve decent solutions on small problem instances, their performance deteriorates in large problems. This article presents a novel learning-augmented local search framework to solve large-scale VRP. The method iteratively improves the solution by identifying appropriate subproblems and delegating their improvement to a black box subsolver. At each step, we leverage spatial locality to consider only a linear number of subproblems, rather than exponential. We frame subproblem selection as regression and train a Transformer on a generated training set of problem instances.

Waiting for a holiday package to be delivered? There's a tricky math problem that needs to be solved before the delivery truck pulls up to your door, and MIT researchers have a strategy that could speed up the solution. The approach applies to vehicle routing problems such as last-mile delivery, where the goal is to deliver goods from a central depot to multiple cities while keeping travel costs down. While there are algorithms designed to solve this problem for a few hundred cities, these solutions become too slow when applied to a larger set of cities. To remedy this, Cathy Wu, the Gilbert W. Winslow Career Development Assistant Professor in Civil and Environmental Engineering and the Institute for Data, Systems, and Society, and her students have come up with a machine-learning strategy that accelerates some of the strongest algorithmic solvers by 10 to 100 times.

Waiting for a holiday package to be delivered? There's a tricky math problem that needs to be solved before the delivery truck pulls up to your door, and MIT researchers have a strategy that could speed up the solution. The approach applies to vehicle routing problems such as last-mile delivery, where the goal is to deliver goods from a central depot to multiple cities while keeping travel costs down. While there are algorithms designed to solve this problem for a few hundred cities, these solutions become too slow when applied to a larger set of cities. To remedy this, Cathy Wu, the Gilbert W. Winslow Career Development Assistant Professor in Civil and Environmental Engineering and the Institute for Data, Systems, and Society, and her students have come up with a machine-learning strategy that accelerates some of the strongest algorithmic solvers by 10 to 100 times.