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Neural Combinatorial Optimization approaches have recently leveraged the expressiveness and flexibility of deep neural networks to learn efficient heuristics for hard Combinatorial Optimization (CO) problems. However, most of the current…

Machine Learning · Computer Science 2022-10-04 Sahil Manchanda , Sofia Michel , Darko Drakulic , Jean-Marc Andreoli

Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…

Artificial Intelligence · Computer Science 2022-05-04 Andoni I. Garmendia , Josu Ceberio , Alexander Mendiburu

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

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

A general framework of unsupervised learning for combinatorial optimization (CO) is to train a neural network (NN) whose output gives a problem solution by directly optimizing the CO objective. Albeit with some advantages over traditional…

Machine Learning · Computer Science 2023-01-24 Haoyu Wang , Pan Li

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

Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based…

Machine Learning · Computer Science 2024-10-02 Runzhong Wang , Yang Li , Junchi Yan , Xiaokang Yang

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…

Machine Learning · Computer Science 2018-10-26 Zhuwen Li , Qifeng Chen , Vladlen Koltun

Since the 1990s, considerable empirical work has been carried out to train statistical models, such as neural networks (NNs), as learned heuristics for combinatorial optimization (CO) problems. When successful, such an approach eliminates…

Machine Learning · Statistics 2026-01-21 Orit Davidovich , Shimrit Shtern , Segev Wasserkrug , Nimrod Megiddo

Neural combinatorial optimization (NCO) aims at designing problem-independent and efficient neural network-based strategies for solving combinatorial problems. The field recently experienced growth by successfully adapting architectures…

Machine Learning · Computer Science 2020-11-13 Michal Lisicki , Arash Afkanpour , Graham W. Taylor

Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn…

Machine Learning · Computer Science 2025-09-05 Tim Dernedde , Daniela Thyssens , Sören Dittrich , Maximilian Stubbemann , Lars Schmidt-Thieme

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

Neural models have shown promise in solving NP-hard graph combinatorial optimization (CO) problems. Once trained, they offer fast inference and reasonably high-quality solutions for in-distribution testing instances, but they generally fall…

Machine Learning · Computer Science 2025-11-26 Jialiang Li , Weitong Chen , Mingyu Guo

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

Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the…

Machine Learning · Computer Science 2020-12-25 Nina Mazyavkina , Sergey Sviridov , Sergei Ivanov , Evgeny Burnaev

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 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

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) 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

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

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