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The field of neural combinatorial optimization (NCO) trains neural policies to solve NP-hard problems such as the traveling salesperson problem (TSP). We ask whether, beyond producing good tours, a trained TSP solver learns internal…

Machine Learning · Computer Science 2026-02-10 Reuben Narad , Léonard Boussioux , Michael Wagner

Leveraging planning during learning and decision-making is central to the long-term development of intelligent agents. Recent works have successfully combined tree-based search methods and self-play learning mechanisms to this end. However,…

Artificial Intelligence · Computer Science 2024-11-01 Matthew V Macfarlane , Edan Toledo , Donal Byrne , Paul Duckworth , Alexandre Laterre

This paper gives a detailed review of reinforcement learning (RL) in combinatorial optimization, introduces the history of combinatorial optimization starting in the 1950s, and compares it with the RL algorithms of recent years. This paper…

Machine Learning · Computer Science 2023-10-04 Yunhao Yang , Andrew Whinston

Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function is fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for…

Machine Learning · Computer Science 2019-11-25 Jaynta Mandi , Emir Demirović , Peter. J Stuckey , Tias Guns

Recently, Supervised Contrastive Learning (SCL) has been shown to achieve excellent performance in most classification tasks. In SCL, a neural network is trained to optimize two objectives: pull an anchor and positive samples together in…

Computation and Language · Computer Science 2022-09-29 Youness Moukafih , Mounir Ghogho , Kamel Smaili

Combinatorial optimization problems, such as scheduling and route planning, are crucial in various industries but are computationally intractable due to their NP-hard nature. Neural Combinatorial Optimization methods leverage machine…

Machine Learning · Computer Science 2025-02-14 Imanol Echeverria , Maialen Murua , Roberto Santana

Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic…

Machine Learning · Computer Science 2022-05-10 Xi Lin , Zhiyuan Yang , Qingfu Zhang

The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…

Machine Learning · Computer Science 2025-01-09 Yong Liang Goh , Wee Sun Lee , Xavier Bresson , Thomas Laurent , Nicholas Lim

Recent studies have revealed that neural combinatorial optimization (NCO) has advantages over conventional algorithms in many combinatorial optimization problems such as routing, but it is less efficient for more complicated optimization…

Artificial Intelligence · Computer Science 2021-11-15 Dongda Li , Zhaoquan Gu , Yuexuan Wang , Changwei Ren , Francis C. M. Lau

Multi-Task Learning (MTL) in Neural Combinatorial Optimization (NCO) is a promising approach to train a unified model capable of solving multiple Vehicle Routing Problem (VRP) variants. However, existing Reinforcement Learning (RL)-based…

Machine Learning · Computer Science 2025-11-05 Yuepeng Zheng , Fu Luo , Zhenkun Wang , Yaoxin Wu , Yu Zhou

Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…

Computational Physics · Physics 2026-05-18 Wen You , Shaoqian Zhou , Xuhui Meng

To train machine learning models that are robust to distribution shifts in the data, distributionally robust optimization (DRO) has been proven very effective. However, the existing approaches to learning a distributionally robust model…

Machine Learning · Computer Science 2022-03-21 Farzin Haddadpour , Mohammad Mahdi Kamani , Mehrdad Mahdavi , Amin Karbasi

Efficiently training a multi-task neural solver for various combinatorial optimization problems (COPs) has been less studied so far. Naive application of conventional multi-task learning approaches often falls short in delivering a…

Machine Learning · Computer Science 2025-05-27 Chenguang Wang , Zhang-Hua Fu , Pinyan Lu , Tianshu Yu

Recent successes in self-supervised learning (SSL) model spatial co-occurrences of visual features either by masking portions of an image or by aggressively cropping it. Here, we propose a new way to model spatial co-occurrences by aligning…

Machine Learning · Computer Science 2025-01-07 Arthur Aubret , Céline Teulière , Jochen Triesch

Lifelong or continual learning remains to be a challenge for artificial neural network, as it is required to be both stable for preservation of old knowledge and plastic for acquisition of new knowledge. It is common to see previous…

Machine Learning · Computer Science 2020-10-08 Song Zhang , Gehui Shen , Jinsong Huang , Zhi-Hong Deng

Deep models, e.g., CNNs and Vision Transformers, have achieved impressive achievements in many vision tasks in the closed world. However, novel classes emerge from time to time in our ever-changing world, requiring a learning system to…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Da-Wei Zhou , Qi-Wei Wang , Zhi-Hong Qi , Han-Jia Ye , De-Chuan Zhan , Ziwei Liu

The problem of path planning has been studied for years. Classic planning pipelines, including perception, mapping, and path searching, can result in latency and compounding errors between modules. While recent studies have demonstrated the…

Robotics · Computer Science 2025-10-31 Fan Yang , Chen Wang , Cesar Cadena , Marco Hutter

Exploiting unlabeled data through semi-supervised learning (SSL) or leveraging pre-trained models via fine-tuning are two prevailing paradigms for addressing label-scarce scenarios. Recently, growing attention has been given to combining…

Machine Learning · Computer Science 2026-05-26 Rui Zhu , Song-Lin Lv , Zi-Kang Wang , Lan-Zhe Guo

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…

Optimization and Control · Mathematics 2025-12-04 James Kotary , Himanshu Sharma , Ethan King , Draguna Vrabie , Ferdinando Fioretto , Jan Drgona

Neural combinatorial optimization (NCO) has achieved remarkable performance, yet its learned model representations and decision rationale remain a black box. This impedes both academic research and practical deployment, since researchers…

Machine Learning · Computer Science 2025-10-28 Zhiqin Zhang , Yining Ma , Zhiguang Cao , Hoong Chuin Lau