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The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with…

量子物理 · 物理学 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

Vehicle routing problem (VRP) is a typical discrete combinatorial optimization problem, and many models and algorithms have been proposed to solve the VRP and its variants. Although existing approaches have contributed a lot to the…

机器学习 · 计算机科学 2022-02-22 Bingjie Li , Guohua Wu , Yongming He , Mingfeng Fan , Witold Pedrycz

This paper introduces the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys…

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,…

机器学习 · 计算机科学 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

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,…

最优化与控制 · 数学 2022-08-02 Simone Foa , Corrado Coppola , Giorgio Grani , Laura Palagi

Electric Vehicles (EVs) are becoming increasingly prevalent nowadays, with studies highlighting their potential as mobile energy storage systems to provide grid support. Realising this potential requires effective charging coordination,…

系统与控制 · 电气工程与系统科学 2025-07-22 Jun Kang Yap , Vishnu Monn Baskaran , Wen Shan Tan , Ze Yang Ding , Hao Wang , David L. Dowe

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be…

系统与控制 · 电气工程与系统科学 2024-03-22 Mark Pustilnik , Francesco Borrelli

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…

人工智能 · 计算机科学 2018-05-23 Mohammadreza Nazari , Afshin Oroojlooy , Lawrence V. Snyder , Martin Takáč

The Vehicle Routing Problem (VRP) is the combinatorial optimization problem of designing routes for vehicles to visit customers in such a fashion that a cost function, typically the number of vehicles, or the total travelled distance is…

人工智能 · 计算机科学 2021-07-01 Sabino Francesco Roselli , Martin Fabian , Knut Åkesson

The increasing use of electric vehicles (EVs) requires efficient route planning solutions that take into account the limited range of EVs and the associated charging times, as well as the different types of charging stations. In this work,…

系统与控制 · 电气工程与系统科学 2025-12-29 Dominik Köster , Florian Porkert , Klaus Volbert

For NP-hard combinatorial optimization problems, it is usually difficult to find high-quality solutions in polynomial time. The design of either an exact algorithm or an approximate algorithm for these problems often requires significantly…

机器学习 · 计算机科学 2021-05-07 Kun Lei , Peng Guo , Yi Wang , Xiao Wu , Wenchao Zhao

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To…

机器学习 · 计算机科学 2025-06-23 Dian Meng , Zhiguang Cao , Yaoxin Wu , Yaqing Hou , Hongwei Ge , Qiang Zhang

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…

最优化与控制 · 数学 2025-05-27 Chengrui Gao , Haopu Shang , Ke Xue , Chao Qian

In modern logistics management systems, route planning requires high efficiency. The Open Capacitated Vehicle Routing Problem (OCVRP) deals with finding optimal delivery routes for a fleet of vehicles serving geographically distributed…

计算与语言 · 计算机科学 2025-10-01 Assem Omar , Youssef Omar , Marwa Solayman , Hesham Mansour

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…

人工智能 · 计算机科学 2025-08-13 Szymon Jakubicz , Karol Kuźniak , Jan Wawszczak , Paweł Gora

The Capacitated Vehicle Routing Problem (CVRP) underpins modern last-mile logistics. Current Neural Combinatorial Optimization (NCO) methods construct CVRP solutions autoregressively, inheriting sequential decoding bottlenecks, sensitivity…

机器学习 · 计算机科学 2026-05-12 Samuel J. K. Chin , Maximilian Schiffer

There has never been a more exciting time for the future of quantum computing than now. Near-term quantum computing usage is now the next XPRIZE. With that challenge in mind we have explored a new approach as a hybrid quantum-classical…

新兴技术 · 计算机科学 2024-04-23 James Holliday , Braeden Morgan , Hugh Churchill , Khoa Luu

Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose Best-anchored…

机器学习 · 计算机科学 2025-06-03 Zijun Liao , Jinbiao Chen , Debing Wang , Zizhen Zhang , Jiahai Wang

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making…

机器学习 · 计算机科学 2025-03-14 Zhenwei Wang , Ruibin Bai , Tiehua Zhang

Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning…

机器学习 · 计算机科学 2025-01-03 Qi Li , Zhiguang Cao , Yining Ma , Yaoxin Wu , Yue-Jiao Gong