Edge-Selector Model Applied for Local Search Neighborhood for Solving Vehicle Routing Problems

TL;DR

This paper introduces a hybrid machine learning approach using an edge selector model to improve local search in vehicle routing problems, demonstrating scalability and generalizability across various problem sizes and types.

Contribution

It presents a novel edge solution selector model combining machine learning and metaheuristics to enhance local search efficiency in VRPs, including GNN-based and tabular classifiers.

Findings

Performance improvements across multiple metaheuristics

Effective handling of large-scale VRPs up to 30,000 nodes

Demonstrated scalability and generalizability

Abstract

This research proposes a hybrid Machine Learning and metaheuristic mechanism that is designed to solve Vehicle Routing Problems (VRPs). The main of our method is an edge solution selector model, which classifies solution edges to identify prohibited moves during the local search, hence guiding the search process within metaheuristic baselines. Two learning-based mechanisms are used to develop the edge selector: a simple tabular binary classifier and a Graph Neural Network (GNN). The tabular classifier employs Gradient Boosting Trees and Feedforward Neural Network as the baseline algorithms. Adjustments to the decision threshold are also applied to handle the class imbalance in the problem instance. An alternative mechanism employs the GNN to utilize graph structure for direct solution edge prediction, with the objective of guiding local search by predicting prohibited moves. These hybrid mechanisms are then applied in state-fo-the-art metaheuristic baselines. Our method demonstrates both scalability and generalizability, achieving performance improvements across different baseline metaheuristics, various problem sizes and variants, including the Capacitated Vehicle Routing Problem (CVRP) and CVRP with Time Windows (CVRPTW). Experimental evaluations on benchmark datasets up to 30,000 customer nodes, supported by pair-wise statistical analysis, verify the observed improvements.