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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…

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

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 powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance…

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

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

Learning to solve vehicle routing problems (VRPs) has garnered much attention. However, most neural solvers are only structured and trained independently on a specific problem, making them less generic and practical. In this paper, we aim…

Artificial Intelligence · Computer Science 2024-05-07 Jianan Zhou , Zhiguang Cao , Yaoxin Wu , Wen Song , Yining Ma , Jie Zhang , Chi Xu

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

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

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

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

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

In this research, we propose an iterative learning hybrid optimization solver developed to strengthen the performance of metaheuristic algorithms in solving the Capacitated Vehicle Routing Problem (CVRP). The iterative hybrid mechanism…

Artificial Intelligence · Computer Science 2025-08-13 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux , Daniele Vigo

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…

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

Traditional solvers for tackling combinatorial optimization (CO) problems are usually designed by human experts. Recently, there has been a surge of interest in utilizing deep learning, especially deep reinforcement learning, to…

Neural and Evolutionary Computing · Computer Science 2023-04-13 Shengcai Liu , Yu Zhang , Ke Tang , Xin Yao

The electric vehicle routing problem (EVRP) has garnered great interest from researchers and industrialists in an attempt to move from fuel-based vehicles to healthier and more efficient electric vehicles (EVs). While it seems that the EVRP…

Neural and Evolutionary Computing · Computer Science 2022-08-29 Kousik Rajesh , Eklavya Jain , Prakash Kotecha

Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MOCOPs). However, they are still struggling to achieve high learning efficiency and…

Machine Learning · Computer Science 2023-10-25 Jinbiao Chen , Jiahai Wang , Zizhen Zhang , Zhiguang Cao , Te Ye , Siyuan Chen

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed…

Optimization and Control · Mathematics 2014-04-25 Sepideh Pourazarm , Christos G. Cassandras

Existing neural solvers for Multi-Objective Combinatorial Optimization Problems (MOCOPs) commonly adopt decomposition-based strategies that scalarize an MOCOP into multiple subproblems associated with distinct weight vectors. However, they…

Machine Learning · Computer Science 2026-05-25 Xuan Wu , Jinbiao Chen , Yang Li , Lijie Wen , Chunguo Wu , Yuanshu Li , Yubin Xiao , Chunyan Miao , You Zhou , Di Wang
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