Learning to Delegate for Large-scale Vehicle Routing
This work addresses the scalability issue in VRP solvers for practical applications, representing an incremental improvement through a novel hybrid approach.
The paper tackles the challenge of solving large-scale vehicle routing problems (VRPs) by introducing a learning-augmented local search framework that delegates subproblems to a black box solver, achieving 10x to 100x speedup over state-of-the-art solvers while maintaining competitive solution quality for problems with 500 to 3000 cities.
Vehicle routing problems (VRPs) form a class of combinatorial problems with wide practical applications. While previous heuristic or learning-based works achieve decent solutions on small problem instances of up to 100 cities, 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 $\textit{delegating}$ 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.