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A Pointer Network Based Deep Learning Algorithm for the Max-Cut Problem

  • Shenshen GuEmail author
  • Yue Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11301)

Abstract

The max-cut problem is one of the classic NP-hard combinatorial optimization problems. In order to solve this problem efficiently, the paper mainly studies the topic of using the pointer network to build a training model to solve the max-cut problem. Then, the network model is trained with supervised learning. The experimental results show that the network trained by this algorithm can obtain the approximate solution to the max-cut problem.

Keywords

Max-cut problem Pointer network Supervised learning 

Notes

Acknowledgments

The work described in the paper was supported by the National Science Foundation of China under Grant 61876105.

References

  1. 1.
    Mehlhorn, K.: NP-completeness. Eatcs Monogr. Theor. Comput. Sci. 5(3), 359–376 (1984)Google Scholar
  2. 2.
    Bie, T.D., Cristianini, N.: Fast SDP relaxations of graph cut clustering, transduction, and other combinatorial problem. J. Mach. Learn. Res. 7(3), 1409–1436 (2006)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Croce, F.D., Kaminski, M.J., Paschos, V.T.: An exact algorithm for MAX-CUT in sparse graphs. Oper. Res. Lett. 35(3), 403–408 (2007)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Krishnan, K., Mitchell, J.E.: A semidefinite programming based polyhedral cut and price approach for the maxcut problem. Comput. Optim. Appl. 33(1), 51–71 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Funabiki, N., Kitamichi, J., Nishikawa, S.: An evolutionary neural network algorithm for max cut problems. In: International Conference on Neural Networks, vol. 2, pp. 1260–1265. IEEE (1997)Google Scholar
  6. 6.
    Krizhevsky, A., Sutskever, I., Hinton, G.E.: ImageNet classification with deep convolutional neural networks. In: International Conference on Neural Information Processing Systems, vol. 60, pp. 1097–1105. Curran Associates Inc. (2012)Google Scholar
  7. 7.
    Deng, L., Li, J., Huang, J.T., Yao, K., Yu, D., Seide, F., et al.: Recent advances in deep learning for speech research at Microsoft. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 8604–8608. IEEE (2013)Google Scholar
  8. 8.
    Vinyals, O., Fortunato, M., Jaitly, N.: Pointer networks. In: International Conference on Neural Information Processing Systems. MIT Press (2015)Google Scholar
  9. 9.
    Milan, A., Rezatofighi, S.H., Garg, R., Dick, A., Reid, I.: Data-driven approximations to NP-hard problems (2017)Google Scholar
  10. 10.
    Sutskever, I., Vinyals, O., Le, Q.V.: Sequence to sequence learning with neural networks, vol. 4, pp. 3104–3112 (2014)Google Scholar
  11. 11.
    Bahdanau, D., Cho, K., Bengio, Y.: Neural machine translation by jointly learning to align and translate. Comput. Sci. (2014)Google Scholar
  12. 12.
    Sak, H., Senior, A., Beaufays, F.: Long short-term memory recurrent neural network architectures for large vocabulary speech recognition. Comput. Sci. 338–342 (2014)Google Scholar
  13. 13.
    Acuna-Agost, R., Acuna-Agost, R.: Deep choice model using pointer networks for airline itinerary prediction. In: ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1575–1583. ACM (2017)Google Scholar
  14. 14.
    Zhou, M.X.: A benchmark generator for Boolean quadratic programming. Comput. Sci. (2015)Google Scholar
  15. 15.
    Barahona, F., Junger, M., Reinelt, G.: Experiments in quadratic 0–1 programming. Math. Program. 44(1–3), 127–137 (1989)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Gu, S., Hao, T.: A pointer network based deep learning algorithm for 0–1 Knapsack Problem. In: International Conference on Advanced Computational Intelligence (ICACI 2018), pp. 357–361 (2018)Google Scholar
  17. 17.
    Gu, S., Hao, T., Yang, S.: The implementation of a pointer network model for traveling salesman problem on a Xilinx PYNQ board. In: Huang, T., Lv, J., Sun, C., Tuzikov, A.V. (eds.) ISNN 2018. LNCS, vol. 10878, pp. 130–138. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-92537-0_16CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mechatronic Engineering and AutomationShanghai UniversityShanghaiChina

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