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Predicting Parallel TSP Performance: a Computational Approach [chapter]

Dolores Rexachs, Emilio Luque, Paula Cecilia
2010 Traveling Salesman Problem, Theory and Applications  
Traveling Salesman Problem The Traveling Salesman Problem (TSP) is one of the most famous problems (and the best one perhaps studied) in the field of combinatorial optimization.  ...  input data beyond the number of cities.  ...  In particular, the Traveling Salesman Problem (TSP) is one of the most famous problems (and the best one perhaps studied) in the field of the combinatorial optimization.  ... 
doi:10.5772/13206 fatcat:zim2o4kboraexjbrbwbfwjajny

Combinatorial optimization and reasoning with graph neural networks [article]

Quentin Cappart, Didier Chételat, Elias Khalil, Andrea Lodi, Christopher Morris, Petar Veličković
2021 arXiv   pre-print
However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by  ...  Combinatorial optimization is a well-established area in operations research and computer science.  ...  Graph Neural Networks Intuitively, GNNs compute a vectorial representation, i.e., a d-dimensional real vector, representing each node in a graph by aggregating information from neighboring nodes; see  ... 
arXiv:2102.09544v2 fatcat:eweej3mq2bbohaifazeghswcpi

On Learning Paradigms for the Travelling Salesman Problem [article]

Chaitanya K. Joshi, Thomas Laurent, Xavier Bresson
2019 arXiv   pre-print
We explore the impact of learning paradigms on training deep neural networks for the Travelling Salesman Problem.  ...  scale-invariant solvers for novel combinatorial problems.  ...  We contribute to existing literature on neural combinatorial optimization by empirically exploring the impact of learning paradigms for TSP, and believe that RL will be a key component towards building  ... 
arXiv:1910.07210v2 fatcat:gvjveiqp4fbgtlsu2khwj2b2sy

Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking [article]

Natalia Vesselinova, Rebecca Steinert, Daniel F. Perez-Ramirez, Magnus Boman
2020 arXiv   pre-print
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances.  ...  We organize and compare the structures involved with learning to solve combinatorial optimization problems, with a special eye on the telecommunications domain and its continuous development of live and  ...  In addition and by contrast to existing surveys, we illustrate how the machine learning structures used for solving combinatorial optimization problems on graphs can be leveraged to combinatorial problems  ... 
arXiv:2005.11081v1 fatcat:ajqghcevqvdrvdlcrknxlzlqdi

Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking

Natalia Vesselinova, Rebecca Steinert, Daniel F. Perez-Ramirez, Magnus Boman
2020 IEEE Access  
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances.  ...  We organize and compare the structures involved with learning to solve combinatorial optimization problems, with a special eye on the telecommunications domain and its continuous development of live and  ...  Junaid Shuja, who coordinated the review process, and to the anonymous reviewers for their expeditious and helpful review comments received in preparation of the final version of the manuscript.  ... 
doi:10.1109/access.2020.3004964 fatcat:v7i7x6p77zfi7dntipxoiolily

Differentiation of Blackbox Combinatorial Solvers [article]

Marin Vlastelica and Anselm Paulus and Vít Musil and Georg Martius and Michal Rolínek
2020 arXiv   pre-print
One possible approach is to introduce combinatorial building blocks into neural networks.  ...  Such end-to-end architectures have the potential to tackle combinatorial problems on raw input data such as ensuring global consistency in multi-object tracking or route planning on maps in robotics.  ...  We acknowledge the support from the German Federal Ministry of Education and Research (BMBF) through the Tbingen AI Center (FKZ: 01IS18039B).  ... 
arXiv:1912.02175v2 fatcat:uasyrwlozzehleotno3omrkdh4

Novelty and imitation within the brain: a Darwinian neurodynamic approach to combinatorial problems

Dániel Czégel, Hamza Giaffar, Márton Csillag, Bálint Futó, Eörs Szathmáry
2021 Scientific Reports  
We also demonstrate the existence of a sharp error threshold, a neural noise level beyond which information accumulated by an evolutionary process cannot be maintained.  ...  We demonstrate that the emerging Darwinian population of readout activity patterns is capable of maintaining and continually improving upon existing solutions over rugged combinatorial reward landscapes  ...  Here, we select the TSP as a classic example of a difficult combinatorial optimization problem to demonstrate the behaviour of this recurrent DN architecture.  ... 
doi:10.1038/s41598-021-91489-5 pmid:34131159 fatcat:hwugkfhghvgelbljb5uecmjuea

Equivariant quantum circuits for learning on weighted graphs [article]

Andrea Skolik, Michele Cattelan, Sheir Yarkoni, Thomas Bäck, Vedran Dunjko
2022 arXiv   pre-print
We evaluate the performance of this ansatz on a complex learning task on weighted graphs, where a ML model is used to implement a heuristic for a combinatorial optimization problem.  ...  In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations.  ...  AS, MC and SY are funded by the German Ministry for Education and Research (BMB+F) in the project QAI2-Q-KIS under grant 13N15587.  ... 
arXiv:2205.06109v1 fatcat:ymfyie2q6fglth4irppevappi4

Darwinian dynamics over recurrent neural computations for combinatorial problem solving [article]

Dániel Czégel, Hamza Giaffar, Márton Csillag, Bálint Futó, Eörs Szathmáry
2020 bioRxiv   pre-print
We demonstrate the existence of a sharp error threshold, a neural noise level beyond which information accumulated by an evolutionary process cannot be maintained.  ...  We point at the importance of neural representation, akin to genotype-phenotype maps, in determining the efficiency of any evolutionary search in the brain.  ...  Here, we select the TSP as a classic example of a difficult combinatorial optimization problem to demonstrate the behaviour of this recurrent DN architecture.  ... 
doi:10.1101/2020.11.06.372284 fatcat:wwfnrwpvqvdkxoy2ii4hcmiaxq

A Review: Machine Learning for Combinatorial Optimization Problems in Energy Areas

Xinyi Yang, Ziyi Wang, Hengxi Zhang, Nan Ma, Ning Yang, Hualin Liu, Haifeng Zhang, Lei Yang
2022 Algorithms  
Combinatorial optimization problems (COPs) are a class of NP-hard problems with great practical significance.  ...  timeline of the improvements for some fundamental COPs is the layout.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a15060205 fatcat:tea63hytzrau7jitrwwapl3bfi

Challenges and Opportunities in Deep Reinforcement Learning with Graph Neural Networks: A Comprehensive review of Algorithms and Applications [article]

Sai Munikoti, Deepesh Agarwal, Laya Das, Mahantesh Halappanavar, Balasubramaniam Natarajan
2022 arXiv   pre-print
Similarly, graph neural networks (GNN) have also demonstrated their superior performance in supervised learning for graph-structured data.  ...  In recent times, the fusion of GNN with DRL for graph-structured environments has attracted a lot of attention. This paper provides a comprehensive review of these hybrid works.  ...  Another important problem of cooperative combinatorial optimization in TSP is related to optimization of the multiple TSPs (MTSP). [67] developed an architecture consisting of a shared GNN and distributed  ... 
arXiv:2206.07922v1 fatcat:cajusof5cjegvbvvctsrguz7nu

Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research

Kate A. Smith
1999 INFORMS journal on computing  
This article briefly summarizes the work that has been done and presents the current standing of neural networks for combinatorial optimization by considering each of the major classes of combinatorial  ...  It has been over a decade since neural networks were first applied to solve combinatorial optimization problems.  ...  Acknowledgements The author is grateful to three anonymous referees, an associate editor, Dr. M. Gendreau, and Dr. B. Golden for their helpful comments and suggestions.  ... 
doi:10.1287/ijoc.11.1.15 fatcat:jy5jur2pyjhndpi45argti2f54

Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon [article]

Yoshua Bengio and Andrea Lodi and Antoine Prouvost
2020 arXiv   pre-print
We advocate for pushing further the integration of machine learning and combinatorial optimization and detail a methodology to do so.  ...  This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems.  ...  , Martina Fischetti, Elias Khalil, Bistra Dilkina, Sebastian Pokutta, Marco Lübbecke, Andrea Tramontani, Dimitris Bertsimas and the entire CERC team for endless discussions on the subject and for reading  ... 
arXiv:1811.06128v2 fatcat:sslxegsjszfl7dvohv3253fyru

Neural Combinatorial Optimization: a New Player in the Field [article]

Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu
2022 arXiv   pre-print
Recently, its good performance has encouraged many practitioners to develop neural architectures for a wide variety of combinatorial problems.  ...  To that end, we select the Linear Ordering Problem as a case of study, an NP-hard problem, and develop a Neural Combinatorial Optimization model to optimize it.  ...  CONCLUSION In this paper we conducted a critical analysis of Neural Combinatorial Optimization algorithms and their incorporation in the conventional optimization framework.  ... 
arXiv:2205.01356v1 fatcat:l53bar7bfrf6xdfr45yi57plcm

POMO: Policy Optimization with Multiple Optima for Reinforcement Learning [article]

Yeong-Dae Kwon, Jinho Choo, Byoungjip Kim, Iljoo Yoon, Youngjune Gwon, Seungjai Min
2021 arXiv   pre-print
In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems.  ...  It is designed to exploit the symmetries in the representation of a CO solution. POMO uses a modified REINFORCE algorithm that forces diverse rollouts towards all optimal solutions.  ...  But when this solution is represented as a sequence of nodes, multiple representations exist (RIGHT).  ... 
arXiv:2010.16011v3 fatcat:wtya56t7q5agrmhijylszjddqi
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