Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet

TL;DR

This paper introduces a neural combinatorial optimization approach using an encoder-decoder architecture trained with reinforcement learning to efficiently solve complex, time-constrained vehicle routing problems with limited fleet size, outperforming traditional heuristics.

Contribution

It presents a novel neural optimization method for VRPs that incorporates multiple objectives and demonstrates strong generalization and efficiency on medium and large instances.

Findings

The approach achieves cost-efficient solutions comparable to state-of-the-art heuristics.

It demonstrates robustness and flexibility across different instance sizes.

The method offers insights into the potential of neural algorithms in complex logistics optimization.

Abstract

Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when confronted with the real-world complexity of VRPs, which involve numerous constraints and objectives. Recently, the ability of generative Artificial Intelligence (AI) to solve combinatorial tasks, known as Neural Combinatorial Optimization (NCO), demonstrated promising results, offering new perspectives. In this study, we propose an NCO approach to solve a time-constrained capacitated VRP with a finite vehicle fleet size. The approach is based on an encoder-decoder architecture, formulated in line with the Policy Optimization with Multiple Optima (POMO) protocol and trained via a Proximal Policy Optimization (PPO) algorithm. We successfully trained the policy with multiple objectives (minimizing the total distance while maximizing vehicle utilization) and evaluated it on medium and large instances, benchmarking it against state-of-the-art heuristics. The method is able to find adequate and cost-efficient solutions, showing both flexibility and robust generalization. Finally, we provide a critical analysis of the solution generated by NCO and discuss the challenges and opportunities of this new branch of intelligent learning algorithms emerging in optimization science, focusing on freight transportation.