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

2025-08-12

AI Summary

This work addresses the challenge of effectively identifying critical edge structures during local search for the Vehicle Routing Problem (VRP). We propose a machine learning–driven hybrid optimization framework. Its core innovation is a multi-model edge selector—integrating gradient-boosted trees, feedforward neural networks, and graph neural networks—that dynamically predicts and prunes low-quality edges to guide metaheuristic search toward high-quality solution regions. To mitigate class imbalance inherent in edge quality prediction, we introduce an adaptive decision threshold mechanism. The framework is rigorously evaluated on standard VRP benchmarks spanning multiple variants and scales, including instances with up to 30,000 nodes. Results demonstrate statistically significant improvements over state-of-the-art metaheuristic baselines, confirming superior scalability and generalization capability across diverse problem settings.

Technology Category

• Machine Learning: Learning on the Edge & Model Compression
• Search and Optimization: Metareasoning and Metaheuristics
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Proposes hybrid ML-metaheuristic for Vehicle Routing Problems
• Develops edge selector model to classify prohibited moves
• Enhances local search scalability across problem variants

Innovation

• Edge selector model classifies solution edges
• Uses tabular classifier and Graph Neural Network
• Guides local search in metaheuristic baselines