Deep Reinforcement Learning for Solving the Fleet Size and Mix Vehicle Routing Problem

TL;DR

This paper introduces a deep reinforcement learning approach, using a novel policy network, to efficiently solve the complex Fleet Size and Mix Vehicle Routing Problem, achieving near-optimal solutions quickly in large-scale scenarios.

Contribution

It develops a DRL-based method with a specialized policy network for joint fleet and routing decisions, advancing solution speed and scalability for FSMVRP.

Findings

Demonstrates high computational efficiency and scalability in large instances.

Achieves near-optimal solutions within seconds.

Outperforms traditional methods in time-constrained environments.

Abstract

The Fleet Size and Mix Vehicle Routing Problem (FSMVRP) is a prominent variant of the Vehicle Routing Problem (VRP), extensively studied in operations research and computational science. FSMVRP requires simultaneous decisions on fleet composition and routing, making it highly applicable to real-world scenarios such as short-term vehicle rental and on-demand logistics. However, these requirements also increase the complexity of FSMVRP, posing significant challenges, particularly in large-scale and time-constrained environments. In this paper, we propose a deep reinforcement learning (DRL)-based approach for solving FSMVRP, capable of generating near-optimal solutions within a few seconds. Specifically, we formulate the problem as a Markov Decision Process (MDP) and develop a novel policy network, termed FRIPN, that seamlessly integrates fleet composition and routing decisions. Our method incorporates specialized input embeddings designed for distinctdecision objectives, including a remaining graph embedding to facilitate effective vehicle employment decisions. Comprehensive experiments are conducted on both randomly generated instances and benchmark datasets. The experimental results demonstrate that our method exhibits notable advantages in terms of computational efficiency and scalability, particularly in large-scale and time-constrained scenarios. These strengths highlight the potential of our approach for practical applications and provide valuable inspiration for extending DRL-based techniques to other variants of VRP.