A Neural Column Generation Approach to the Vehicle Routing Problem with Two-Dimensional Loading and Last-In-First-Out Constraints

TL;DR

This paper introduces a novel exact algorithm combining machine learning techniques to efficiently solve the vehicle routing problem with two-dimensional loading and LIFO constraints, outperforming existing methods and solving previously open instances.

Contribution

It presents an innovative integration of attention and recurrence mechanisms into an exact algorithm for 2L-CVRP, significantly improving solution speed and capability.

Findings

Median of 29.79% speed-up over state-of-the-art algorithms

Successfully solves an open instance in the standard test-bed

Demonstrates the effectiveness of machine learning integration in exact algorithms

Abstract

The vehicle routing problem with two-dimensional loading constraints (2L-CVRP) and the last-in-first-out (LIFO) rule presents significant practical and algorithmic challenges. While numerous heuristic approaches have been proposed to address its complexity, stemming from two NP-hard problems: the vehicle routing problem (VRP) and the two-dimensional bin packing problem (2D-BPP), less attention has been paid to developing exact algorithms. Bridging this gap, this article presents an exact algorithm that integrates advanced machine learning techniques, specifically a novel combination of attention and recurrence mechanisms. This integration accelerates the state-of-the-art exact algorithm by a median of 29.79% across various problem instances. Moreover, the proposed algorithm successfully resolves an open instance in the standard test-bed, demonstrating significant improvements brought about by the incorporation of machine learning models. Code is available at https://github.com/xyfffff/NCG-for-2L-CVRP.