Deep Reinforcement Learning for Solving the Fleet Size and Mix Vehicle Routing Problem
On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods. Builds on 10 of its 47 references that are in the map. First posted on arXiv 30 Dec 2025.
Builds on
10 of 47 references.
References · 10
- 2018Attention, Learn to Solve Routing Problems!cited by 656
- 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
- 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 608
- 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 348
- 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 333
- 2019Learning Improvement Heuristics for Solving Routing Problemscited by 164
- 2019Exploratory Combinatorial Optimization with Reinforcement Learningcited by 82
- 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 71
- 2021Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problemcited by 31
- 2020Deep Reinforcement Learning for Electric Vehicle Routing Problem with Time Windowscited by 25
Built on by
Not cited yet.
Similar, not cited
Close in wording, no citation either way
- 2026Vehicle-as-Prompt: A Unified Deep Reinforcement Learning Framework for Heterogeneous Fleet Vehicle Routing Problem
- 2026A Deep Reinforcement Learning Algorithm for the Vehicle Routing Problem with Stochastic Demands and Outsourcing
- 2026Vehicle routing problem using deep reinforcement learning - A case study about truck planning in the industry
- 2025SED2AM: Solving Multi-Trip Time-Dependent Vehicle Routing Problem using Deep Reinforcement Learning
- 2024Reinforcement Learning for Solving Stochastic Vehicle Routing Problem with Time Windows
- 2024Deep Reinforcement Learning for Multi-Truck Vehicle Routing Problems with Multi-Leg Demand Routes
- 2026A Curriculum-Based Deep Reinforcement Learning Framework for the Electric Vehicle Routing Problem
- 2026Vehicle Routing with Finite Time Horizon using Deep Reinforcement Learning with Improved Network Embedding