Exact Approaches for the Travelling Thief Problem

  • Junhua Wu
  • Markus Wagner
  • Sergey Polyakovskiy
  • Frank Neumann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10593)


Many evolutionary and constructive heuristic approaches have been introduced in order to solve the Travelling Thief Problem (TTP). However, the accuracy of such approaches is unknown due to their inability to find global optima. In this paper, we propose three exact algorithms and a hybrid approach to the TTP. We compare these with state-of-the-art approaches to gather a comprehensive overview on the accuracy of heuristic methods for solving small TTP instances.



This work was supported by the Australian Research councils through grants DP130104395 and DE160100850, and by the supercomputing resources provided by the Phoenix HPC service at the University of Adelaide.


  1. 1.
    Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Concorde TSP solver (2006).
  2. 2.
    Benchimol, P., Van Hoeve, W.-J., Régin, J.-C., Rousseau, L.-M., Rueher, M.: Improved filtering for weighted circuit constraints. Constraints 17(3), 205–233 (2012). doi: 10.1007/s10601-012-9119-x. ISSN 1572-9354MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bonyadi, M., Michalewicz, Z., Barone, L.: The travelling thief problem: the first step in the transition from theoretical problems to realistic problems. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 1037–1044 (2013)Google Scholar
  4. 4.
    Bonyadi, M.R., Michalewicz, Z., Przybylek, M.R., Wierzbicki, A.: Socially inspired algorithms for the travelling thief problem. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, GECCO 2014, pp. 421–428. ACM (2014)Google Scholar
  5. 5.
    El Yafrani, M., Ahiod, B.: Cosolver2B: an efficient local search heuristic for the travelling thief problem. In: 2015 IEEE/ACS 12th International Conference of Computer Systems and Applications (AICCSA), pp. 1–5. IEEE (2015)Google Scholar
  6. 6.
    El Yafrani, M., Ahiod, B.: Population-based vs. single-solution heuristics for the travelling thief problem. In: Proceedings of the Genetic and Evolutionary Computation Conference 2016, GECCO 2016, pp. 317–324. ACM (2016)Google Scholar
  7. 7.
    Faulkner, H., Polyakovskiy, S., Schultz, T., Wagner, M.: Approximate approaches to the traveling thief problem. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, GECCO 2015, pp. 385–392. ACM (2015)Google Scholar
  8. 8.
    Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. In: Proceedings of the 1961 16th ACM National Meeting, ACM 1961, pp. 71.201-71.204. ACM (1961)Google Scholar
  9. 9.
    Hooker, J.N.: Logic, optimization, and constraint programming. INFORMS J. Comput. 14(4), 295–321 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Mei, Y., Li, X., Yao, X.: Improving efficiency of heuristics for the large scale traveling thief problem. In: Dick, G., et al. (eds.) SEAL 2014. LNCS, vol. 8886, pp. 631–643. Springer, Cham (2014). doi: 10.1007/978-3-319-13563-2_53. ISBN 978-3-319-13563-2Google Scholar
  12. 12.
    Mei, Y., Li, X., Salim, F., Yao, X.: Heuristic evolution with genetic programming for traveling thief problem. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 2753–2760, May 2015. doi: 10.1109/CEC.2015.7257230
  13. 13.
    Mei, Y., Li, X., Yao, X.: On investigation of interdependence between sub-problems of the travelling thief problem. Soft Comput. 20(1), 157–172 (2016)CrossRefGoogle Scholar
  14. 14.
    Neumann, F., Polyakovskiy, S., Skutella, M., Stougie, L., Wu, J.: A Fully Polynomial Time Approximation Scheme for Packing While Traveling. ArXiv e-prints (2017)Google Scholar
  15. 15.
    Pisinger, D.: Advanced Generator for 0–1 Knapsack Problem.
  16. 16.
    Pisinger, D.: Where are the hard knapsack problems? Comput. Oper. Res. 32(9), 2271–2284 (2005). doi: 10.1016/j.cor.2004.03.002. ISSN 0305-0548MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Polyakovskiy, S., Neumann, F.: The packing while traveling problem. Eur. J. Oper. Res. 258(2), 424–439 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Polyakovskiy, S., Bonyadi, M.R., Wagner, M., Michalewicz, Z., Neumann, F.: A comprehensive benchmark set and heuristics for the traveling thief problem. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, GECCO 2014, pp. 477–484. ACM (2014)Google Scholar
  19. 19.
    Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30201-8_41 CrossRefGoogle Scholar
  20. 20.
    Reinelt, G.: TSPLIB—a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)CrossRefzbMATHGoogle Scholar
  21. 21.
    Stützle, T., Hoos, H.H.: MAX MIN ant system. Future Gener. Comput. Syst. 16(8), 889–914 (2000)CrossRefzbMATHGoogle Scholar
  22. 22.
    Wagner, M.: Stealing items more efficiently with ants: a swarm intelligence approach to the travelling thief problem. In: Dorigo, M., Birattari, M., Li, X., López-Ibáñez, M., Ohkura, K., Pinciroli, C., Stützle, T. (eds.) ANTS 2016. LNCS, vol. 9882, pp. 273–281. Springer, Cham (2016). doi: 10.1007/978-3-319-44427-7_25 CrossRefGoogle Scholar
  23. 23.
    Wagner, M., Lindauer, M., Mısır, M., Nallaperuma, S., Hutter, F.: A case study of algorithm selection for the traveling thief problem. J. Heuristics pp. 1–26 (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Junhua Wu
    • 1
  • Markus Wagner
    • 1
  • Sergey Polyakovskiy
    • 1
  • Frank Neumann
    • 1
  1. 1.Optimisation and Logistics, School of Computer ScienceThe University of AdelaideAdelaideAustralia

Personalised recommendations