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Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known…

Artificial Intelligence · Computer Science 2021-11-08 Helge Spieker , Arnaud Gotlieb

Combinatorial optimization (CO) is essential for improving efficiency and performance in engineering applications. As complexity increases with larger problem sizes and more intricate dependencies, identifying the optimal solution become…

Computational Engineering, Finance, and Science · Computer Science 2025-10-30 Shuo Jiang , Min Xie , Jianxi Luo

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

Although LLM-based agents have attracted significant attention in domains such as software engineering and machine learning research, their role in advancing combinatorial optimization (CO) remains relatively underexplored. This gap…

Computation and Language · Computer Science 2025-08-25 Weiwei Sun , Shengyu Feng , Shanda Li , Yiming Yang

As concerns surrounding AI-driven labor displacement intensify in knowledge-intensive sectors, existing benchmarks fail to measure performance on tasks that define practical professional expertise. Finance, in particular, has been…

Federated learning (FL) has found numerous applications in healthcare, finance, and IoT scenarios. Many existing FL frameworks offer a range of benchmarks to evaluate the performance of FL under realistic conditions. However, the process of…

Machine Learning · Computer Science 2023-06-22 Zheng Wang , Xiaoliang Fan , Zhaopeng Peng , Xueheng Li , Ziqi Yang , Mingkuan Feng , Zhicheng Yang , Xiao Liu , Cheng Wang

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard…

Machine Learning · Computer Science 2022-10-25 Haoyu Wang , Nan Wu , Hang Yang , Cong Hao , Pan Li

It is important to guarantee that machine learning algorithms deployed in the real world do not result in unfairness or unintended social consequences. Fair ML has largely focused on the protection of single attributes in the simpler…

Machine Learning · Computer Science 2022-11-14 Tennison Liu , Alex J. Chan , Boris van Breugel , Mihaela van der Schaar

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

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

Machine learning (ML) needs industry-standard performance benchmarks to support design and competitive evaluation of the many emerging software and hardware solutions for ML. But ML training presents three unique benchmarking challenges…

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential…

Machine Learning · Computer Science 2024-09-05 Jayanta Mandi , James Kotary , Senne Berden , Maxime Mulamba , Victor Bucarey , Tias Guns , Ferdinando Fioretto

Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…

Quantum Physics · Physics 2025-03-20 Monit Sharma , Hoong Chuin Lau

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

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

Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is…

Machine Learning · Computer Science 2022-03-29 Guangmo Tong

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

Combinatorial Optimization (CO) addresses many important problems, including the challenging Maximum Independent Set (MIS) problem. Alongside exact and heuristic solvers, differentiable approaches have emerged, often using continuous…

Discrete Mathematics · Computer Science 2025-06-10 Ismail Alkhouri , Cedric Le Denmat , Yingjie Li , Cunxi Yu , Jia Liu , Rongrong Wang , Alvaro Velasquez

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely…

Artificial Intelligence · Computer Science 2026-01-29 Kostis Michailidis , Dimos Tsouros , Tias Guns

Combinatorial optimization (CO) layers in machine learning (ML) pipelines are a powerful tool to tackle data-driven decision tasks, but they come with two main challenges. First, the solution of a CO problem often behaves as a piecewise…

Machine Learning · Statistics 2022-12-06 Guillaume Dalle , Léo Baty , Louis Bouvier , Axel Parmentier