Skip to main content

Enhancing Policy Gradient for Traveling Salesman Problem with Data Augmented Behavior Cloning

  • Conference paper
  • First Online:
Advances in Knowledge Discovery and Data Mining (PAKDD 2024)

Abstract

The use of deep reinforcement learning (DRL) techniques to solve classical combinatorial optimization problems like the Traveling Salesman Problem (TSP) has garnered considerable attention due to its advantage of flexible and fast model-based inference. However, DRL training often suffers low efficiency and scalability, which hinders model generalization. This paper proposes a simple yet effective pre-training method that utilizes behavior cloning to initialize neural network parameters for policy gradient DRL. To alleviate the need for large amounts of demonstrations in behavior cloning, we exploit the symmetry of TSP solutions for augmentation. Our method is demonstrated by enhancing the state-of-the-art policy gradient models Attention and POMO for the TSP. Experimental results show that the optimality gap of the solution is significantly reduced while the DRL training time is greatly shortened. This also enables effective and efficient solving of larger TSP instances.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aarts, E.H., Lenstra, J.K.: Local search in combinatorial optimization. Princeton University Press (2003)

    Google Scholar 

  2. Bellman, R.: Dynamic programming treatment of the travelling salesman problem. J. ACM (JACM) 9(1), 61–63 (1962)

    Article  MathSciNet  Google Scholar 

  3. Bello, I., Pham, H., Le, Q.V., Norouzi, M., Bengio, S.: Neural combinatorial optimization with reinforcement learning. In: Proceedings of International Conference on Learning Representations (ICLR) (2017)

    Google Scholar 

  4. Bengio, Y., Lodi, A., Prouvost, A.: Machine learning for combinatorial optimization: a methodological tour d’horizon. Eur. J. Oper. Res. 290(2), 405–421 (2021)

    Article  MathSciNet  Google Scholar 

  5. Dai, H., Dai, B., Song, L.: Discriminative embeddings of latent variable models for structured data. In: International Conference on Machine Learning, pp. 2702–2711. PMLR (2016)

    Google Scholar 

  6. Applegate, D., Robert Bixby, V.C., Cook, W.: Concorde TSP Solver (2006). https://www.math.uwaterloo.ca/tsp/concorde/index.html

  7. Halim, A.H., Ismail, I.: Combinatorial optimization: comparison of heuristic algorithms in travelling salesman problem. Arch. Comput. Methods Eng. 26, 367–380 (2019)

    Article  MathSciNet  Google Scholar 

  8. Helsgaun, K.: An extension of the lin-kernighan-helsgaun TSP solver for constrained traveling salesman and vehicle routing problems: Technical report (2017)

    Google Scholar 

  9. Hussein, A., Gaber, M.M., Elyan, E., Jayne, C.: Imitation learning: a survey of learning methods. ACM Comput. Surv. (CSUR) 50(2), 1–35 (2017)

    Article  Google Scholar 

  10. Khalil, E., Dai, H., Zhang, Y., Dilkina, B., Song, L.: Learning combinatorial optimization algorithms over graphs. Adv. Neural. Inf. Process. Syst. 30 (2017)

    Google Scholar 

  11. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: Proceedings of International Conference on Learning Representations (ICLR) (2015)

    Google Scholar 

  12. Kool, W., van Hoof, H., Welling, M.: Attention, learn to solve routing problems! In: International Conference on Learning Representations (2019)

    Google Scholar 

  13. Kwon, Y.D., Choo, J., Kim, B., Yoon, I., Gwon, Y., Min, S.: Pomo: Policy optimization with multiple optima for reinforcement learning. Adv. Neural. Inf. Process. Syst. 33, 21188–21198 (2020)

    Google Scholar 

  14. Lawler, E.L., Wood, D.E.: Branch-and-bound methods: a survey. Oper. Res. 14(4), 699–719 (1966)

    Article  MathSciNet  Google Scholar 

  15. Ma, Q., Ge, S., He, D., Thaker, D., Drori, I.: Combinatorial optimization by graph pointer networks and hierarchical reinforcement learning. In: AAAI Workshop on Deep Learning on Graphs: Methodologies and Applications (2020)

    Google Scholar 

  16. Matai, R., Singh, S.P., Mittal, M.L.: Traveling salesman problem: an overview of applications, formulations, and solution approaches. Traveling Salesman Problem, Theory and Applications 1 (2010)

    Google Scholar 

  17. d O Costa, P.R., Rhuggenaath, J., Zhang, Y., Akcay, A.: Learning 2-opt heuristics for the traveling salesman problem via deep reinforcement learning. In: Asian Conference on Machine Learning, pp. 465–480. PMLR (2020)

    Google Scholar 

  18. Papadimitriou, C.H.: The euclidean travelling salesman problem is np-complete. Theoret. Comput. Sci. 4(3), 237–244 (1977)

    Article  MathSciNet  Google Scholar 

  19. Perron, L., Furnon, V.: Or-tools (2022). https://developers.google.com/optimization/

  20. Pomerleau, D.A.: Alvinn: an autonomous land vehicle in a neural network. Adv. Neural. Inf. Process. Syst. 1 (1988)

    Google Scholar 

  21. Rajeswaran, A., et al.: Learning complex dexterous manipulation with deep reinforcement learning and demonstrations. In: Proceedings of Robotics: Science and Systems. Pittsburgh, Pennsylvania (June 2018)

    Google Scholar 

  22. Riedmiller, M.: Neural fitted Q iteration – first experiences with a data efficient neural reinforcement learning method. In: Gama, J., Camacho, R., Brazdil, P.B., Jorge, A.M., Torgo, L. (eds.) ECML 2005. LNCS (LNAI), vol. 3720, pp. 317–328. Springer, Heidelberg (2005). https://doi.org/10.1007/11564096_32

    Chapter  Google Scholar 

  23. Ross, S., Gordon, G., Bagnell, D.: A reduction of imitation learning and structured prediction to no-regret online learning. In: Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, pp. 627–635. JMLR Workshop and Conference Proceedings (2011)

    Google Scholar 

  24. Silver, D., et al.: Mastering the game of go with deep neural networks and tree search. Nature 529(7587), 484–489 (2016)

    Article  Google Scholar 

  25. Sutskever, I., Vinyals, O., Le, Q.V.: Sequence to sequence learning with neural networks. Adv. Neural. Inf. Process. Syst. 27 (2014)

    Google Scholar 

  26. Thrun, S., Littman, M.L.: Reinforcement learning: an introduction. AI Mag. 21(1), 103–103 (2000)

    Google Scholar 

  27. Torabi, F., Warnell, G., Stone, P.: Recent advances in imitation learning from observation. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, pp. 6324–6331 (2019)

    Google Scholar 

  28. Vinyals, O., Fortunato, M., Jaitly, N.: Pointer networks. Adv. Neural. Inf. Process. Syst. 28 (2015)

    Google Scholar 

  29. Williams, R.J.: Simple statistical gradient-following algorithms for connectionist reinforcement learning. Reinforc. Learn., 5–32 (1992)

    Google Scholar 

  30. Williamson, D.P., Shmoys, D.B.: The design of approximation algorithms. Cambridge University Press (2011)

    Google Scholar 

  31. Xin, L., Song, W., Cao, Z., Zhang, J.: Multi-decoder attention model with embedding glimpse for solving vehicle routing problems. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 12042–12049 (2021)

    Google Scholar 

  32. Xin, L., Song, W., Cao, Z., Zhang, J.: Step-wise deep learning models for solving routing problems. IEEE Trans. Industr. Inf. 17(7), 4861–4871 (2021)

    Article  Google Scholar 

  33. Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? In: International Conference on Learning Representations (2019)

    Google Scholar 

  34. Yang, H., Gu, M.: A new baseline of policy gradient for traveling salesman problem. In: 2022 IEEE 9th International Conference on Data Science and Advanced Analytics (DSAA), pp. 1–7. IEEE (2022)

    Google Scholar 

  35. Zaheer, M., et al.: Big bird: transformers for longer sequences. Adv. Neural. Inf. Process. Syst. 33 (2020)

    Google Scholar 

Download references

Acknowledgments

This work is supported by the Taishan Scholars Young Expert Project of Shandong Province (No. tsqn202211215) and the National Science Foundation of China (Nos. 12271098 and 61772005). The corresponding author is Longkun Guo (lkguo@fzu.edu.cn).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Longkun Guo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhang, Y., Liao, K., Liao, Z., Guo, L. (2024). Enhancing Policy Gradient for Traveling Salesman Problem with Data Augmented Behavior Cloning. In: Yang, DN., Xie, X., Tseng, V.S., Pei, J., Huang, JW., Lin, J.CW. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2024. Lecture Notes in Computer Science(), vol 14646. Springer, Singapore. https://doi.org/10.1007/978-981-97-2253-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-981-97-2253-2_26

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-2252-5

  • Online ISBN: 978-981-97-2253-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics