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In the past decades, we have witnessed significant progress in the domain of autonomous driving. Advanced techniques based on optimization and reinforcement learning (RL) become increasingly powerful at solving the forward problem: given…

Robotics · Computer Science 2020-06-25 Zheng Wu , Liting Sun , Wei Zhan , Chenyu Yang , Masayoshi Tomizuka

Reinforcement Learning (RL) offers a promising solution to enable evolutionary automated driving. However, the conventional RL method is always concerned with risk performance. The updated policy may not obtain a performance enhancement,…

Systems and Control · Electrical Eng. & Systems 2024-12-17 Jia Hu , Xuerun Yan , Tian Xu , Haoran Wang

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

In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to visit a set of customers while minimising the operations' costs. We study a rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and…

Artificial Intelligence · Computer Science 2016-12-07 Arthur Mahéo , Tommaso Urli , Philip Kilby

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

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity…

Unlike traditional homogeneous routing problems, the Heterogeneous Fleet Vehicle Routing Problem (HFVRP) involves heterogeneous fixed costs, variable travel costs, and capacity constraints, rendering solution quality highly sensitive to…

Machine Learning · Computer Science 2026-04-08 Shihong Huang , Shengjie Wang , Lei Gao , Hong Ma , Zhanluo Zhang , Feng Zhang , Weihua Zhou

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

Despite the extensive research efforts and the remarkable results obtained on Vehicle Routing Problems (VRP) by using algorithms proposed by the Machine Learning community that are partially or entirely based on data-driven analysis, most…

Machine Learning · Computer Science 2021-09-30 Luca Accorsi , Andrea Lodi , Daniele Vigo

Local search plays a central role in many effective heuristic algorithms for the vehicle routing problem (VRP) and its variants. However, neighborhood exploration is known to be computationally expensive and time consuming, especially for…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-30 Zhenyu Lei , Jin-Kao Hao , Qinghua Wu

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of…

Machine Learning · Statistics 2019-02-08 Wouter Kool , Herke van Hoof , Max Welling

The Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity in…

Machine Learning · Computer Science 2025-10-10 Daisuke Kikuta , Hiroki Ikeuchi , Kengo Tajiri , Yuusuke Nakano

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

Optimizing delivery routes for last-mile logistics service is challenging and has attracted the attention of many researchers. These problems are usually modeled and solved as variants of vehicle routing problems (VRPs) with challenging…

Artificial Intelligence · Computer Science 2023-03-09 Qian Shao , Shih-Fen Cheng

The Vehicle Routing Problem is about optimizing the routes of vehicles to meet the needs of customers at specific locations. The route graph consists of depots on several levels and customer positions. Several optimization methods have been…

Artificial Intelligence · Computer Science 2024-09-18 László Kovács , Ali Jlidi

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

Deep Reinforcement Learning (DRL) algorithms have been successfully applied to a range of challenging control tasks. However, these methods typically suffer from three core difficulties: temporal credit assignment with sparse rewards, lack…

Machine Learning · Computer Science 2018-10-30 Shauharda Khadka , Kagan Tumer

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

The electric vehicle routing problem with time windows (EVRPTW) is a complex optimization problem in sustainable logistics, where routing decisions must minimize total travel distance, fleet size, and battery usage while satisfying strict…

Machine Learning · Computer Science 2026-01-22 Mertcan Daysalilar , Fuat Uyguroglu , Gabriel Nicolosi , Adam Meyers

The Vehicle Routing Problem with Route Balancing (VRPRB) is a biobjective version of the original Vehicle Routing Problem (VRP) in which, besides minimizing the total distance traveled by the vehicles involved, the balance among route loads…

Optimization and Control · Mathematics 2017-02-21 Jairo Lozano , Luis C. González-Gurrola , Eduardo Rodríguez-Tello , Philippe Lacomme
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