A scalable learning approach for the capacitated vehicle routing problem

Designing efficient heuristics for the different variants of vehicle routing problems and customising the heuristics to various input distributions is a time-consuming and expensive task. In recent years, end-to-end machine learning techniques have been developed because they are easy to modify for different problem variants, thereby saving on the design time to develop new efficient heuristics. These learning techniques, such as the transformer-based constructive methods, struggle to provide high quality solutions on problem instances with hundreds to thousands of customers in a reasonable time. Furthermore, many of the end-to-end heuristics also do not guarantee that solutions obey fleet-size constraints. We propose a heuristic for solving large capacitated vehicle routing problem (CVRP) that carefully integrates a machine learning heuristic with Integer Linear Programming techniques. To address the issue of solutions with poor objective function values generated by end-to-end machine learning approaches on larger instances, we dynamically partition the CVRP problem instance into smaller sub-problems and apply a machine heuristic on the smaller sub-problems. This allows the machine learning heuristic to always operate on smaller problems similar in size to those for which it was trained. The machine learning heuristic generates many solutions for each sub-problem which are then combined using a set partitioning approach based on a ILP formulation. The set partitioning ILP also guarantees that solutions obey fleet-size constraints. We evaluate the performance of our heuristic on a difficult set of benchmark instances with hundreds to thousands of nodes, achieving small gaps (less than 3% on average) with respect to best known solutions, significantly improving upon the solution quality of the existing learning heuristics. Furthermore, we demonstrate that our results generalise well to other vehicle routing problems, such as green vehicle routing problem.