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Multi-objective combinatorial optimization problems (MOCOPs), one type of complex optimization problems, widely exist in various real applications. Although meta-heuristics have been successfully applied to address MOCOPs, the calculation…

Machine Learning · Computer Science 2022-04-27 Le-yang Gao , Rui Wang , Chuang Liu , Zhao-hong Jia

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

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

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

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to…

Data Structures and Algorithms · Computer Science 2012-07-10 Daniel Karapetyan

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

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC)…

Machine Learning · Computer Science 2026-03-25 Yiding Shi , Jianan Zhou , Wen Song , Jieyi Bi , Yaoxin Wu , Zhiguang Cao , Jie Zhang

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

Transportation is an essential area in the nowadays society, both for business sector and citizenry. There are different kinds of transportation systems, each one with its own characteristics. In the same way, various areas of knowledge can…

Artificial Intelligence · Computer Science 2020-03-26 Eneko Osaba

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to…

Artificial Intelligence · Computer Science 2022-02-15 Zizhen Zhang , Zhiyuan Wu , Hang Zhang , Jiahai Wang

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

Machine Learning algorithms have been extensively researched throughout the last decade, leading to unprecedented advances in a broad range of applications, such as image classification and reconstruction, object recognition, and text…

Artificial Intelligence · Computer Science 2022-12-20 Gustavo H. de Rosa , Mateus Roder , João Paulo Papa , Claudio F. G. dos Santos

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

This study investigates the potential of hybrid metaheuristic algorithms to enhance the training of Probabilistic Neural Networks (PNNs) by leveraging the complementary strengths of multiple optimisation strategies. Traditional learning…

Neural and Evolutionary Computing · Computer Science 2025-04-16 Piotr A. Kowalski , Szymon Kucharczyk , Jacek Mańdziuk

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

Heuristics are commonly used to tackle various search and optimization problems. Design heuristics usually require tedious manual crafting with domain knowledge. Recent works have incorporated Large Language Models (LLMs) into automatic…

Artificial Intelligence · Computer Science 2025-02-05 Shunyu Yao , Fei Liu , Xi Lin , Zhichao Lu , Zhenkun Wang , Qingfu Zhang

Multi-robot path finding in dynamic environments is a highly challenging classic problem. In the movement process, robots need to avoid collisions with other moving robots while minimizing their travel distance. Previous methods for this…

Artificial Intelligence · Computer Science 2025-12-12 Shaoming Peng

Learning-based heuristics for solving combinatorial optimization problems has recently attracted much academic attention. While most of the existing works only consider the single objective problem with simple constraints, many real-world…

Neural and Evolutionary Computing · Computer Science 2021-07-19 Yongxin Zhang , Jiahai Wang , Zizhen Zhang , Yalan Zhou

The resource constrained project scheduling problem (RCPSP) is an NP-Hard combinatorial optimization problem. The objective of RCPSP is to schedule a set of activities without violating any activity precedence or resource constraints. In…

Neural and Evolutionary Computing · Computer Science 2022-04-26 Shelvin Chand , Kousik Rajesh , Rohitash Chandra

Real-life problems are often characterized by conflicting optimization objectives. Consequently, there has been a growing interest not only in multi-objective models, but also in specialized multi-objective metaheuristics for solving those…

Optimization and Control · Mathematics 2017-05-30 Piotr Matl , Richard F. Hartl , Thibaut Vidal
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