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Graph-structured data is ubiquitous throughout natural and social sciences, and Graph Neural Networks (GNNs) have recently been shown to be effective at solving prediction and inference problems on graph data. In this paper, we propose and…

Machine Learning · Computer Science 2024-01-12 Victoria M. Dax , Jiachen Li , Kevin Leahy , Mykel J. Kochenderfer

Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for…

Neural and Evolutionary Computing · Computer Science 2024-02-14 Dobrik Georgiev , Danilo Numeroso , Davide Bacciu , Pietro Liò

In recent years, graph neural networks (GNNs) have become increasingly popular for solving NP-hard combinatorial optimization (CO) problems, such as maximum cut and maximum independent set. The core idea behind these methods is to represent…

Machine Learning · Computer Science 2024-06-11 Yang Liu , Peng Zhang , Yang Gao , Chuan Zhou , Zhao Li , Hongyang Chen

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…

Artificial Intelligence · Computer Science 2017-01-16 Irwan Bello , Hieu Pham , Quoc V. Le , Mohammad Norouzi , Samy Bengio

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

Combinatorial Optimization (CO) problems over graphs appear routinely in many applications such as in optimizing traffic, viral marketing in social networks, and matching for job allocation. Due to their combinatorial nature, these problems…

Machine Learning · Computer Science 2024-01-02 Hao Tian , Sourav Medya , Wei Ye

Recent advances in graph neural network architectures and increased computation power have revolutionized the field of combinatorial optimization (CO). Among the proposed models for CO problems, Neural Improvement (NI) models have been…

Artificial Intelligence · Computer Science 2023-10-10 Andoni I. Garmendia , Josu Ceberio , Alexander Mendiburu

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

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

Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…

Artificial Intelligence · Computer Science 2019-10-01 Antoine François , Quentin Cappart , Louis-Martin Rousseau

Deep neural networks based on reinforcement learning (RL) for solving combinatorial optimization (CO) problems are developing rapidly and have shown a tendency to approach or even outperform traditional solvers. However, existing methods…

Machine Learning · Computer Science 2024-05-24 Chaoyang Wang , Pengzhi Cheng , Jingze Li , Weiwei Sun

Machine Learning (ML) can help solve combinatorial optimization (CO) problems better. A popular approach is to use a neural net to compute on the parameters of a given CO problem and extract useful information that guides the search for…

Machine Learning · Computer Science 2021-10-27 Yeong-Dae Kwon , Jinho Choo , Iljoo Yoon , Minah Park , Duwon Park , Youngjune Gwon

Graph neural networks (GNNs) have achieved great success for a variety of tasks such as node classification, graph classification, and link prediction. However, the use of GNNs (and machine learning more generally) to solve combinatorial…

Machine Learning · Computer Science 2024-11-26 Frederik Wenkel , Semih Cantürk , Stefan Horoi , Michael Perlmutter , Guy Wolf

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Machine Learning · Computer Science 2022-04-26 Martin J. A. Schuetz , J. Kyle Brubaker , Helmut G. Katzgraber

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…

Machine Learning · Computer Science 2021-10-26 Runzhong Wang , Zhigang Hua , Gan Liu , Jiayi Zhang , Junchi Yan , Feng Qi , Shuang Yang , Jun Zhou , Xiaokang Yang

In recent years, there has been notable interest in investigating combinatorial optimization (CO) problems by neural-based framework. An emerging strategy to tackle these challenging problems involves the adoption of graph neural networks…

Machine Learning · Computer Science 2024-06-11 Yang Liu , Chuan Zhou , Peng Zhang , Shirui Pan , Zhao Li , Hongyang Chen

Combinatorial optimization (CO) problems are crucial in various scientific and industrial applications. Recently, researchers have proposed using unsupervised Graph Neural Networks (GNNs) to address NP-hard combinatorial optimization…

Machine Learning · Computer Science 2024-07-24 Daria Pugacheva , Andrei Ermakov , Igor Lyskov , Ilya Makarov , Yuriy Zotov

Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…

Machine Learning · Computer Science 2020-07-21 Wenpeng Wei , Toshiko Aizono

Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL…

Machine Learning · Computer Science 2025-05-14 Mingjun Pan , Guanquan Lin , You-Wei Luo , Bin Zhu , Zhien Dai , Lijun Sun , Chun Yuan

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…

Machine Learning · Computer Science 2023-11-08 Constantine Caramanis , Dimitris Fotakis , Alkis Kalavasis , Vasilis Kontonis , Christos Tzamos
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