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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

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem with broad applications in logistics and transportation. Real-world CVRPs often involve diverse objectives and complex constraints, such as time windows or…

Artificial Intelligence · Computer Science 2026-05-15 Wen Wang , Xiangchen Wu , Liang Wang , Hao Hu , Xianping Tao

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

Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the…

Machine Learning · Computer Science 2020-12-25 Nina Mazyavkina , Sergey Sviridov , Sergei Ivanov , Evgeny Burnaev

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

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

Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for…

Machine Learning · Computer Science 2020-10-26 Arthur Delarue , Ross Anderson , Christian Tjandraatmadja

This paper addresses the Capacitated Vehicle Routing Problem (CVRP) by comparing classical and quantum Reinforcement Learning (RL) approaches. An Advantage Actor-Critic (A2C) agent is implemented in classical, full quantum, and hybrid…

Artificial Intelligence · Computer Science 2026-02-06 Eva Andrés

Complex real-life routing challenges can be modeled as variations of well-known combinatorial optimization problems. These routing problems have long been studied and are difficult to solve at scale. The particular setting may also make…

Neural and Evolutionary Computing · Computer Science 2020-09-23 Marijn van Knippenberg , Mike Holenderski , Vlado Menkovski

Existing deep reinforcement learning (DRL) based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence,…

Machine Learning · Computer Science 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem in logistics. Augmented Lagrangian Methods (ALM) for solving CVRP performance depends heavily on well-tuned penalty parameters. In this paper, we propose a…

Physics and Society · Physics 2025-09-22 Monit Sharma , Hoong Chuin Lau

Learning to solve combinatorial optimization problems, such as the vehicle routing problem, offers great computational advantages over classical operations research solvers and heuristics. The recently developed deep reinforcement learning…

Machine Learning · Computer Science 2022-01-06 Daniela Thyssens , Jonas Falkner , Lars Schmidt-Thieme

In recent years, reinforcement learning (RL) methods have emerged as a promising approach for solving combinatorial problems. Among RL-based models, POMO has demonstrated strong performance on a variety of tasks, including variants of the…

Artificial Intelligence · Computer Science 2025-08-13 Szymon Jakubicz , Karol Kuźniak , Jan Wawszczak , Paweł Gora

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Yaoxin Wu , Zhi Zheng , Zhenkun Wang

This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to…

Machine Learning · Computer Science 2022-05-06 Aigerim Bogyrbayeva , Meraryslan Meraliyev , Taukekhan Mustakhov , Bissenbay Dauletbayev

This paper gives a detailed review of reinforcement learning (RL) in combinatorial optimization, introduces the history of combinatorial optimization starting in the 1950s, and compares it with the RL algorithms of recent years. This paper…

Machine Learning · Computer Science 2023-10-04 Yunhao Yang , Andrew Whinston

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

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…

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
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