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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

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…

Machine Learning · Computer Science 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

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…

Machine Learning · Computer Science 2024-11-08 Elija Deineko , Carina Kehrt

Neural combinatorial optimization (NCO) is a promising learning-based approach for solving challenging combinatorial optimization problems without specialized algorithm design by experts. However, most constructive NCO methods cannot solve…

Machine Learning · Computer Science 2024-01-17 Fu Luo , Xi Lin , Fei Liu , Qingfu Zhang , Zhenkun Wang

Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant…

Artificial Intelligence · Computer Science 2025-05-20 Changliang Zhou , Xi Lin , Zhenkun Wang , Qingfu Zhang

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.…

Artificial Intelligence · Computer Science 2025-04-28 Xuan Wu , Di Wang , Lijie Wen , Yubin Xiao , Chunguo Wu , Yuesong Wu , Chaoyu Yu , Douglas L. Maskell , You Zhou

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…

Artificial Intelligence · Computer Science 2024-12-03 Han Li , Fei Liu , Zhi Zheng , Yu Zhang , Zhenkun Wang

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…

Machine Learning · Computer Science 2026-03-17 Xuan Wu , Di Wang , Chunguo Wu , Kaifang Qi , Chunyan Miao , Yubin Xiao , Jian Zhang , You Zhou

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…

Quantum Physics · Physics 2024-04-23 Ningyi Xie , Xinwei Lee , Dongsheng Cai , Yoshiyuki Saito , Nobuyoshi Asai , Hoong Chuin Lau

This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…

Machine Learning · Computer Science 2020-06-23 Ruben Solozabal , Josu Ceberio , Martin Takáč

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

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…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Xi Lin , Mengyuan Zhong , Fei Liu , Zhenkun Wang , Jianyong Sun , Qingfu Zhang

The practical deployment of Neural Combinatorial Optimization (NCO) for Vehicle Routing Problems (VRPs) is hindered by a critical sim-to-real gap. This gap stems not only from training on oversimplified Euclidean data but also from…

Machine Learning · Computer Science 2026-03-17 Jiwoo Son , Zhikai Zhao , Federico Berto , Chuanbo Hua , Zhiguang Cao , Changhyun Kwon , Jinkyoo Park

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…

In this paper, we evaluate the use of Reinforcement Learning (RL) to solve a classic combinatorial optimization problem: the Capacitated Vehicle Routing Problem (CVRP). We formalize this problem in the RL framework and compare two of the…

Artificial Intelligence · Computer Science 2022-01-17 Leo Ardon

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…

Machine Learning · Computer Science 2024-04-15 Fei Liu , Xi Lin , Zhenkun Wang , Qingfu Zhang , Xialiang Tong , Mingxuan Yuan

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…

Machine Learning · Computer Science 2022-02-22 Bingjie Li , Guohua Wu , Yongming He , Mingfeng Fan , Witold Pedrycz

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…

Machine Learning · Computer Science 2023-01-06 Minsu Kim , Junyoung Park , Jinkyoo Park

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

Machine Learning · Computer Science 2026-05-12 Samuel J. K. Chin , Maximilian Schiffer
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