Neural Networks for Local Search and Crossover in Vehicle Routing: A Possible Overkill?

TL;DR

This study explores using graph neural network predictions to enhance a vehicle routing heuristic, finding that simpler measures like distance can match the performance of complex GNN-based heatmaps, highlighting potential overkill.

Contribution

The paper evaluates the effectiveness of GNN-derived heatmaps in improving a vehicle routing algorithm and shows that simpler measures can achieve similar results, questioning the necessity of complex models.

Findings

GNN heatmaps can improve heuristic performance.

Simpler distance measures perform comparably to GNN heatmaps.

Overkill in using complex models when simpler alternatives suffice.

Abstract

Extensive research has been conducted, over recent years, on various ways of enhancing heuristic search for combinatorial optimization problems with machine learning algorithms. In this study, we investigate the use of predictions from graph neural networks (GNNs) in the form of heatmaps to improve the Hybrid Genetic Search (HGS), a state-of-the-art algorithm for the Capacitated Vehicle Routing Problem (CVRP). The crossover and local-search components of HGS are instrumental in finding improved solutions, yet these components essentially rely on simple greedy or random choices. It seems intuitive to attempt to incorporate additional knowledge at these levels. Throughout a vast experimental campaign on more than 10,000 problem instances, we show that exploiting more sophisticated strategies using measures of node relatedness (heatmaps, or simply distance) within these algorithmic components can significantly enhance performance. However, contrary to initial expectations, we also observed that heatmaps did not present significant advantages over simpler distance measures for these purposes. Therefore, we faced a common -- though rarely documented -- situation of overkill: GNNs can indeed improve performance on an important optimization task, but an ablation analysis demonstrated that simpler alternatives perform equally well.