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Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when…

机器学习 · 计算机科学 2024-11-08 Elija Deineko , Carina Kehrt

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a…

机器学习 · 计算机科学 2024-04-15 Fei Liu , Xi Lin , Zhenkun Wang , Qingfu Zhang , Xialiang Tong , Mingxuan Yuan

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…

机器学习 · 计算机科学 2025-10-31 Fu Luo , Yaoxin Wu , Zhi Zheng , Zhenkun Wang

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

机器学习 · 计算机科学 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

Neural Combinatorial Optimization (NCO) has emerged as a powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance…

Vehicle Routing Problems (VRPs) are significant Combinatorial Optimization (CO) problems holding substantial practical importance. Recently, Neural Combinatorial Optimization (NCO), which involves training deep learning models on extensive…

人工智能 · 计算机科学 2024-12-03 Han Li , Fei Liu , Zhi Zheng , Yu Zhang , Zhenkun Wang

Although several surveys on Neural Combinatorial Optimization (NCO) solvers specifically designed to solve Vehicle Routing Problems (VRPs) have been conducted, they did not cover the state-of-the-art (SOTA) NCO solvers emerged recently.…

人工智能 · 计算机科学 2025-04-28 Xuan Wu , Di Wang , Lijie Wen , Yubin Xiao , Chunguo Wu , Yuesong Wu , Chaoyu Yu , Douglas L. Maskell , You Zhou

Deep reinforcement learning (DRL)-based combinatorial optimization (CO) methods (i.e., DRL-NCO) have shown significant merit over the conventional CO solvers as DRL-NCO is capable of learning CO solvers less relying on problem-specific…

机器学习 · 计算机科学 2023-01-06 Minsu Kim , Junyoung Park , Jinkyoo Park

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm…

机器学习 · 计算机科学 2025-10-31 Fu Luo , Xi Lin , Mengyuan Zhong , Fei Liu , Zhenkun Wang , Jianyong Sun , Qingfu Zhang

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…

人工智能 · 计算机科学 2026-04-14 Xiangchi Meng , Jianan Zhou , Jie Gao , Yifan Lu , Yaoxin Wu , Gonglin Yuan , Yaqing Hou

Numerous Neural Combinatorial Optimization (NCO) solvers have been proposed to address Vehicle Routing Problems (VRPs). However, most of these solvers focus exclusively on single-vehicle VRP variants, overlooking the more realistic min-max…

机器学习 · 计算机科学 2026-03-17 Xuan Wu , Di Wang , Chunguo Wu , Kaifang Qi , Chunyan Miao , Yubin Xiao , Jian Zhang , You Zhou

We propose a novel visual localization and navigation framework for real-world environments directly integrating observed visual information into the bird-eye-view map. While the renderable neural radiance map (RNR-Map) shows considerable…

图像与视频处理 · 电气工程与系统科学 2024-10-10 Minsoo Kim , Obin Kwon , Howoong Jun , Songhwai Oh

Vehicle routing problems (VRPs) are central to combinatorial optimization with significant practical implications. Recent advancements in neural combinatorial optimization (NCO) have demonstrated promising results by leveraging neural…

机器学习 · 计算机科学 2025-07-08 Han Li , Fei Liu , Zhenkun Wang , Qingfu Zhang

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

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

The Vehicle Routing Problem (VRP) is a fundamental challenge in logistics management research, given its substantial influence on transportation efficiency, cost minimization, and service quality. As a combinatorial optimization problem,…

计算工程、金融与科学 · 计算机科学 2025-07-01 Souad Abdoune , Menouar Boulif

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most…

量子物理 · 物理学 2024-04-23 Ningyi Xie , Xinwei Lee , Dongsheng Cai , Yoshiyuki Saito , Nobuyoshi Asai , Hoong Chuin Lau

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…

数据结构与算法 · 计算机科学 2026-04-07 Yongyu Chen

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 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
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