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We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given…

Artificial Intelligence · Computer Science 2018-05-23 Mohammadreza Nazari , Afshin Oroojlooy , Lawrence V. Snyder , Martin Takáč

Deep reinforcement learning (DRL) has been used to learn effective heuristics for solving complex combinatorial optimisation problem via policy networks and have demonstrated promising performance. Existing works have focused on solving…

Machine Learning · Computer Science 2020-12-25 Nasrin Sultana , Jeffrey Chan , A. K. Qin , Tabinda Sarwar

Recently, the applications of the methodologies of Reinforcement Learning (RL) to NP-Hard Combinatorial optimization problems have become a popular topic. This is essentially due to the nature of the traditional combinatorial algorithms,…

Optimization and Control · Mathematics 2022-08-02 Simone Foa , Corrado Coppola , Giorgio Grani , Laura Palagi

Combinatorial optimization (CO) problems are traditionally addressed using Operations Research (OR) methods, including metaheuristics. In this study, we introduce a demand selection problem for the Vehicle Routing Problem (VRP) with an…

Data Structures and Algorithms · Computer Science 2025-05-27 Farid Najar , Dominique Barth , Yann Strozecki

In this paper we present a new approach to tackle complex routing problems with an improved state representation that utilizes the model complexity better than previous methods. We enable this by training from temporal differences.…

Machine Learning · Computer Science 2021-04-27 Ahmad Bdeir , Simon Boeder , Tim Dernedde , Kirill Tkachuk , Jonas K. Falkner , Lars Schmidt-Thieme

This study addresses a gap in the utilization of Reinforcement Learning (RL) and Machine Learning (ML) techniques in solving the Stochastic Vehicle Routing Problem (SVRP) that involves the challenging task of optimizing vehicle routes under…

Artificial Intelligence · Computer Science 2023-11-15 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

There has been a paradigm-shift in urban logistic services in the last years; demand for real-time, instant mobility and delivery services grows. This poses new challenges to logistic service providers as the underlying stochastic dynamic…

Artificial Intelligence · Computer Science 2021-03-02 Florentin D Hildebrandt , Barrett Thomas , Marlin W Ulmer

Heavy goods vehicles are vital backbones of the supply chain delivery system but also contribute significantly to carbon emissions with only 60% loading efficiency in the United Kingdom. Collaborative vehicle routing has been proposed as a…

Machine Learning · Computer Science 2024-06-12 Stefan Schoepf , Stephen Mak , Julian Senoner , Liming Xu , Netland Torbjörn , Alexandra Brintrup

This paper develops an inherently parallelised, fast, approximate learning-based solution to the generic class of Capacitated Vehicle Routing Problems with Time Windows and Dynamic Routing (CVRP-TWDR). Considering vehicles in a fleet as…

Artificial Intelligence · Computer Science 2021-04-15 Nazneen N Sultana , Vinita Baniwal , Ansuma Basumatary , Piyush Mittal , Supratim Ghosh , Harshad Khadilkar

This paper introduces a reinforcement learning approach to optimize the Stochastic Vehicle Routing Problem with Time Windows (SVRP), focusing on reducing travel costs in goods delivery. We develop a novel SVRP formulation that accounts for…

Artificial Intelligence · Computer Science 2024-02-16 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

The Entrance Dependent Vehicle Routing Problem (EDVRP) is a variant of the Vehicle Routing Problem (VRP) where the scale of cities influences routing outcomes, necessitating consideration of their entrances. This paper addresses EDVRP in…

Robotics · Computer Science 2025-03-05 Yixuan Fan , Haotian Xu , Mengqiao Liu , Qing Zhuo , Tao Zhang

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…

Artificial Intelligence · Computer Science 2026-01-01 Pengfu Wan , Jiawei Chen , Gangyan Xu

In this paper, we evaluate the use of Reinforcement Learning (RL) to solve a classic combinatorial optimization problem: the Capacitated Vehicle Routing Problem (CVRP). We formalize this problem in the RL framework and compare two of the…

Artificial Intelligence · Computer Science 2022-01-17 Leo Ardon

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-19 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Takaho Saito , Alan Arai

Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed…

Optimization and Control · Mathematics 2022-08-16 Jian Zhang , Kelin Luo , Alexandre M. Florio , Tom Van Woensel

Motivated by the promising advances of deep-reinforcement learning (DRL) applied to cooperative multi-agent systems we propose a model and learning procedure to solve the Capacitated Multi-Vehicle Routing Problem (CMVRP) with fixed fleet…

Neural and Evolutionary Computing · Computer Science 2019-12-10 Jose Manuel Vera , Andres G. Abad

Route planning is essential to mobile robot navigation problems. In recent years, deep reinforcement learning (DRL) has been applied to learning optimal planning policies in stochastic environments without prior knowledge. However, existing…

Robotics · Computer Science 2023-04-21 Xi Lin , Paul Szenher , John D. Martin , Brendan Englot

The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-31 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Saito Takaho , Alan Arai

Model-free deep-reinforcement-based learning algorithms have been applied to a range of COPs~\cite{bello2016neural}~\cite{kool2018attention}~\cite{nazari2018reinforcement}. However, these approaches suffer from two key challenges when…

Machine Learning · Computer Science 2022-06-01 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , A. K. Qin
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