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This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs.
Solution of a large-scale traveling-salesman problem
George Dantzig, Ray Fulkerson, and Selmer Johnson · 1954
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A method for solving traveling-salesman problems
Georges A Croes · 1958
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Speech understanding systems: Report of a steering committee
Mark F. Medress, Franklin S Cooper, Jim W. Forgie, CC Green, Dennis H. Klatt, Michael H. O’Malley, Edward P Neuburg, Allen Newell, DR Reddy, B Ritea, et al · 1977
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The euclidean travelling salesman problem is np-complete
Christos H Papadimitriou · 1977
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“neural” computation of decisions in optimization problems
John J Hopfield and David W Tank · 1985
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Self-organizing feature maps and the travelling salesman problem
Bernard Angeniol, Gael De La Croix Vaubois, and Jean-Yves Le Texier · 1988
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Solving a combinatorial problem via self-organizing process: An application of the kohonen algorithm to the traveling salesman problem
JC Fort · 1988
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A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems
Manfred Padberg and Giovanni Rinaldi · 1991
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Simple statistical gradient-following algorithms for connectionist reinforcement learning
Ronald J Williams · 1992
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Neural networks for combinatorial optimization: a review of more than a decade of research
Kate A Smith · 1999
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Implementing the dantzig-fulkerson-johnson algorithm for large traveling salesman problems
David Applegate, Robert Bixby, Vašek Chvátal, and William Cook · 2003
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The traveling salesman problem: a computational study
David L Applegate, Robert E Bixby, Vasek Chvatal, and William J Cook · 2006
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The graph neural network model
Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini · 2009
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Comparison of neural networks for solving the travelling salesman problem
Bert FJ La Maire and Valeri M Mladenov · 2012
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Spectral networks and locally connected networks on graphs
Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun · 2013
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Playing atari with deep reinforcement learning
Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wierstra, and Martin Riedmiller · 2013
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Neural machine translation by jointly learning to align and translate
Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Sequence to sequence learning with neural networks
Ilya Sutskever, Oriol Vinyals, and Quoc VV Le · 2014
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Sergey Ioffe and Christian Szegedy · 2015
Geometric deep learning: going beyond euclidean data
Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst · 2017
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Learning combinatorial optimization algorithms over graphs
Hanjun Dai, Elias Khalil, Yuyu Zhang, Bistra Dilkina, and Le Song · 2017
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Inductive representation learning on large graphs
Will Hamilton, Zhitao Ying, and Jure Leskovec · 2017
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Encoding sentences with graph convolutional networks for semantic role labeling
Diego Marcheggiani and Ivan Titov · 2017
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A note on learning algorithms for quadratic assignment with graph neural networks
Alex Nowak, Soledad Villar, Afonso S Bandeira, and Joan Bruna · 2017
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Pointer networks
Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly · 2015
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Neural combinatorial optimization with reinforcement learning
Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, and Samy Bengio · 2016
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Discriminative embeddings of latent variable models for structured data
Hanjun Dai, Bo Dai, and Le Song · 2016
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Convolutional neural networks on graphs with fast localized spectral filtering
Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst · 2016
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Semi-supervised classification with graph convolutional networks
Thomas N Kipf and Max Welling · 2016
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Learning multiagent communication with backpropagation
Sainbayar Sukhbaatar, Arthur Szlam, and Rob Fergus · 2016
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Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio · 2017
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Machine learning for combinatorial optimization: a methodological tour d’horizon
Yoshua Bengio, Andrea Lodi, and Antoine Prouvost · 2018
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Learning heuristics for the tsp by policy gradient
Michel Deudon, Pierre Cournut, Alexandre Lacoste, Yossiri Adulyasak, and Louis-Martin Rousseau · 2018
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Learning the multiple traveling salesmen problem with permutation invariant pooling networks
Yoav Kaempfer and Lior Wolf · 2018
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Combinatorial optimization with graph convolutional networks and guided tree search
Zhuwen Li, Qifeng Chen, and Vladlen Koltun · 2018
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Reinforcement learning for solving the vehicle routing problem
Mohammadreza Nazari, Afshin Oroojlooy, Lawrence Snyder, and Martin Takác · 2018
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Graph2seq: Scalable learning dynamics for graphs
Shaileshh Bojja Venkatakrishnan, Mohammad Alizadeh, and Pramod Viswanath · 2018
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Attention, learn to solve routing problems!
Wouter Kool, Herke van Hoof, and Max Welling · 2019
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Learning heuristics over large graphs via deep reinforcement learning
Akash Mittal, Anuj Dhawan, Sourav Medya, Sayan Ranu, and Ambuj Singh · 2019
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