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We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment…

Optimization and Control · Mathematics 2018-03-19 Túlio A. M. Toffolo , Thibaut Vidal , Tony Wauters

The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…

Data Structures and Algorithms · Computer Science 2026-04-07 Yongyu Chen

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing…

Artificial Intelligence · Computer Science 2025-10-09 Fangting Zhou , Attila Lischka , Balazs Kulcsar , Jiaming Wu , Morteza Haghir Chehreghani , Gilbert Laporte

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

The traveling purchaser problem (TPP) is an important combinatorial optimization problem with broad applications. Due to the coupling between routing and purchasing, existing works on TPPs commonly address route construction and purchase…

Optimization and Control · Mathematics 2025-07-03 Haofeng Yuan , Rongping Zhu , Wanlu Yang , Shiji Song , Keyou You , Wei Fan , C. L. Philip Chen

Developing and testing automated driving models in the real world might be challenging and even dangerous, while simulation can help with this, especially for challenging maneuvers. Deep reinforcement learning (DRL) has the potential to…

A major challenge in todays power grid is to manage the increasing load from electric vehicle (EV) charging. Demand response (DR) solutions aim to exploit flexibility therein, i.e., the ability to shift EV charging in time and thus avoid…

Artificial Intelligence · Computer Science 2022-03-29 Manu Lahariya , Nasrin Sadeghianpourhamami , Chris Develder

Vehicle routing problems (VRPs) constitute a core optimization challenge in modern logistics and supply chain management. The recent neural combinatorial optimization (NCO) has demonstrated superior efficiency over some traditional…

Artificial Intelligence · Computer Science 2026-04-14 Xiangchi Meng , Jianan Zhou , Jie Gao , Yifan Lu , Yaoxin Wu , Gonglin Yuan , Yaqing Hou

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

The problem of constrained reinforcement learning (CRL) holds significant importance as it provides a framework for addressing critical safety satisfaction concerns in the field of reinforcement learning (RL). However, with the introduction…

Machine Learning · Computer Science 2023-05-24 Chengbin Xuan , Feng Zhang , Faliang Yin , Hak-Keung Lam

Autonomous driving in urban crowds at unregulated intersections is challenging, where dynamic occlusions and uncertain behaviors of other vehicles should be carefully considered. Traditional methods are heuristic and based on…

Robotics · Computer Science 2021-09-20 Peide Cai , Sukai Wang , Hengli Wang , Ming Liu

Recent deep reinforcement learning (DRL) successes rely on end-to-end learning from fixed-size observational inputs (e.g. image, state-variables). However, many challenging and interesting problems in decision making involve observations or…

Machine Learning · Computer Science 2022-06-08 Vince Jankovics , Michael Garcia Ortiz , Eduardo Alonso

The vehicle routing problem with two-dimensional loading constraints (2L-CVRP) and the last-in-first-out (LIFO) rule presents significant practical and algorithmic challenges. While numerous heuristic approaches have been proposed to…

Artificial Intelligence · Computer Science 2024-06-19 Yifan Xia , Xiangyi Zhang

The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive…

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or…

Artificial Intelligence · Computer Science 2023-06-12 Pierre Tassel , Martin Gebser , Konstantin Schekotihin

Electric vehicles (EVs) have been adopted in urban areas to reduce environmental pollution and global warming as a result of the increasing number of freight vehicles. However, there are still deficiencies in routing the trajectories of…

Artificial Intelligence · Computer Science 2022-06-08 Erick Rodríguez-Esparza , Antonio D Masegosa , Diego Oliva , Enrique Onieva

Deep learning has been extensively explored to solve vehicle routing problems (VRPs), which yields a range of data-driven neural solvers with promising outcomes. However, most neural solvers are trained to tackle VRP instances in a…

Machine Learning · Computer Science 2025-08-19 Shaodi Feng , Zhuoyi Lin , Jianan Zhou , Cong Zhang , Jingwen Li , Kuan-Wen Chen , Senthilnath Jayavelu , Yew-Soon Ong

Deep learning approaches have shown promising results in solving routing problems. However, there is still a substantial gap in solution quality between machine learning and operations research algorithms. Recently, another line of research…

Artificial Intelligence · Computer Science 2021-09-20 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , Babak Abbasi , A. K. Qin

In this paper, we study the vehicle routing problem with a finite time horizon. In this routing problem, the objective is to maximize the number of customer requests served within a finite time horizon. We present a novel routing network…

Artificial Intelligence · Computer Science 2026-01-22 Ayan Maity , Sudeshna Sarkar

Multi-robot navigation is a challenging task in which multiple robots must be coordinated simultaneously within dynamic environments. We apply deep reinforcement learning (DRL) to learn a decentralized end-to-end policy which maps raw…

Robotics · Computer Science 2022-09-08 Christian Jestel , Hartmut Surmann , Jonas Stenzel , Oliver Urbann , Marius Brehler