Neuro CROSS exchange: Learning to CROSS exchange to solve realistic vehicle routing problems

TL;DR

This paper introduces Neuro CE, a graph neural network-based operator that learns to efficiently guide vehicle routing problem solutions, significantly reducing search complexity and outperforming traditional and neural methods across various VRP variants.

Contribution

The paper presents Neuro CE, a learned meta-heuristic operator that reduces search complexity from O(n^4) to O(n^2) and generalizes well across multiple VRP types without extra training.

Findings

Neuro CE outperforms traditional meta-heuristics on VRPs.

Neuro CE surpasses neural baselines on special VRP cases.

Training is simple and supervised, using easily prepared samples.

Abstract

CROSS exchange (CE), a meta-heuristic that solves various vehicle routing problems (VRPs), improves the solutions of VRPs by swapping the sub-tours of the vehicles. Inspired by CE, we propose Neuro CE (NCE), a fundamental operator of learned meta-heuristic, to solve various VRPs while overcoming the limitations of CE (i.e., the expensive $\mathcal{O}(n^4)$ search cost). NCE employs a graph neural network to predict the cost-decrements (i.e., results of CE searches) and utilizes the predicted cost-decrements as guidance for search to decrease the search cost to $\mathcal{O}(n^2)$. As the learning objective of NCE is to predict the cost-decrement, the training can be simply done in a supervised fashion, whose training samples can be prepared effortlessly. Despite the simplicity of NCE, numerical results show that the NCE trained with flexible multi-depot VRP (FMDVRP) outperforms the meta-heuristic baselines. More importantly, it significantly outperforms the neural baselines when solving distinctive special cases of FMDVRP (e.g., MDVRP, mTSP, CVRP) without additional training.