Learning to repeatedly solve routing problems

TL;DR

This paper introduces a machine learning heuristic for efficiently reoptimizing capacitated vehicle routing problems after minor data changes, achieving near-optimal solutions quickly.

Contribution

It presents a novel learned heuristic that predicts stable edges in reoptimization, reducing complexity and improving solution speed for dynamic routing problems.

Findings

Optimality gap of 0% to 1.7% on benchmarks

Significant reduction in reoptimization time

Effective for static client locations with demand changes

Abstract

In the last years, there has been a great interest in machine-learning-based heuristics for solving NP-hard combinatorial optimization problems. The developed methods have shown potential on many optimization problems. In this paper, we present a learned heuristic for the reoptimization of a problem after a minor change in its data. We focus on the case of the capacited vehicle routing problem with static clients (i.e., same client locations) and changed demands. Given the edges of an original solution, the goal is to predict and fix the ones that have a high chance of remaining in an optimal solution after a change of client demands. This partial prediction of the solution reduces the complexity of the problem and speeds up its resolution, while yielding a good quality solution. The proposed approach resulted in solutions with an optimality gap ranging from 0\% to 1.7\% on different benchmark instances within a reasonable computing time.