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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

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

Unsupervised neural combinatorial optimization (NCO) enables learning powerful solvers without access to ground-truth solutions. Existing approaches fall into two disjoint paradigms: models trained for generalization across instances, and…

Machine Learning · Computer Science 2026-04-28 Yiqiao Liao , Farinaz Koushanfar , Parinaz Naghizadeh

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving various vehicle routing problems without much manual algorithm design. However, the current NCO methods mainly focus on the in-distribution…

Machine Learning · Computer Science 2024-05-22 Fei Liu , Xi Lin , Weiduo Liao , Zhenkun Wang , Qingfu Zhang , Xialiang Tong , Mingxuan Yuan

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) 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

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 aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far…

Machine Learning · Computer Science 2025-08-05 Daniela Thyssens , Tim Dernedde , Wilson Sentanoe , Lars Schmidt-Thieme

The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale…

Machine Learning · Computer Science 2024-05-03 Fu Luo , Xi Lin , Zhenkun Wang , Xialiang Tong , Mingxuan Yuan , Qingfu Zhang

Robotic systems often require a team of robots to collectively visit multiple targets while optimizing competing objectives, such as total travel cost and makespan. This setting can be formulated as the Multi-Objective Multiple Traveling…

Robotics · Computer Science 2026-03-20 Fengxiaoxiao Li , Xiao Mao , Mingfeng Fan , Yifeng Zhang , Yi Li , Tanishq Duhan , Guillaume Sartoretti

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

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

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

Current methods for end-to-end constructive neural combinatorial optimization usually train a policy using behavior cloning from expert solutions or policy gradient methods from reinforcement learning. While behavior cloning is…

Machine Learning · Computer Science 2024-11-05 Jonathan Pirnay , Dominik G. Grimm

While transformer models have been highly successful, they are computationally inefficient. We observe that for each layer, the full width of the layer may be needed only for a small subset of tokens inside a batch and that the "effective"…

Machine Learning · Computer Science 2024-12-19 Bartosz Wójcik , Alessio Devoto , Karol Pustelnik , Pasquale Minervini , Simone Scardapane

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

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

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with…

Artificial Intelligence · Computer Science 2024-12-19 Igor G. Smit , Yaoxin Wu , Pavel Troubil , Yingqian Zhang , Wim P. M. Nuijten

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…

Machine Learning · Computer Science 2025-05-27 Arman Mielke , Uwe Bauknecht , Thilo Strauss , Mathias Niepert

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…

Optimization and Control · Mathematics 2025-05-27 Chengrui Gao , Haopu Shang , Ke Xue , Chao Qian
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