Solving the Bi-objective Traveling Thief Problem with Multi-objective Evolutionary Algorithms

  • Julian Blank
  • Kalyanmoy Deb
  • Sanaz Mostaghim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10173)


This publication investigates characteristics of and algorithms for the quite new and complex Bi-Objective Traveling Thief Problem, where the well-known Traveling Salesman Problem and Binary Knapsack Problem interact. The interdependence of these two components builds an interwoven system where solving one subproblem separately does not solve the overall problem. The objective space of the Bi-Objective Traveling Thief Problem has through the interaction of two discrete subproblems some interesting properties which are investigated. We propose different kind of algorithms to solve the Bi-Objective Traveling Thief Problem. The first proposed deterministic algorithm picks items on tours calculated by a Traveling Salesman Problem Solver greedily. As an extension, the greedy strategy is substituted by a Knapsack Problem Solver and the resulting Pareto front is locally optimized. These methods serve as a references for the performance of multi-objective evolutionary algorithms. Additional experiments on evolutionary factory and recombination operators are presented. The obtained results provide insights into principles of an exemplary bi-objective interwoven system and new starting points for ongoing research.


Traveling Thief Problem Traveling Salesman Problem Knapsack problem Interwoven systems Multi-objective optimization Discrete optimization Combinatoric problems 



This work was supported by a fellowship within the FITweltweit programme of the German Academic Exchange Service (DAAD).


  1. 1.
    Ishibushi, H., Klamroth, K., Mostaghim, S., Naujoks, B., Poles, S., Purshouse, R., Rudolph, G., Ruzika, S., Sayin, S., Wiecek, M.M., Yao, X.: Multiobjective Optimization for Interwoven Systems. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2015)Google Scholar
  2. 2.
    Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2007)zbMATHGoogle Scholar
  3. 3.
    Lagoudakis, M.G.: The 0–1 Knapsack Problem - An Introductory Survey (1996)Google Scholar
  4. 4.
    Bonyadi, M.R., Michalewicz, Z., Barone, L.: The travelling thief problem: the first step in the transition from theoretical problems to realistic problems. In: IEEE Congress on Evolutionary Computation, pp. 1037–1044. IEEE (2013)Google Scholar
  5. 5.
    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, ser. GECCO 2014, pp. 477–484. ACM, New York (2014).
  6. 6.
    Reinelt, G.: TSPLIB - A t.s.p. library. Universität Augsburg, Institut für Mathematik, Augsburg. Technical report 250 (1990)Google Scholar
  7. 7.
    Faulkner, H., Polyakovskiy, S., Schultz, T., Wagner, M.: Approximate approaches to the traveling thief problem. In: Proceedings of the 2015 on Genetic and Evolutionary Computation Conference, ser. GECCO 2015, pp. 385–392. ACM, New York (2015).
  8. 8.
    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, ser. GECCO 2014, pp. 421–428. ACM, New York (2014).
  9. 9.
    Birkedal, R.: Design, implementation, comparison of randomized search heuristics for the traveling thief problem, Master’s thesis. Technical University of Denmark, Department of Applied Mathematics, Computer Science, Richard Petersens Plads, Building 324, DK-2800 Kgs. Lyngby, Denmark, (2015).
  10. 10.
    Mei, Y., Li, X., Salim, F., Yao, X.: Heuristic evolution with genetic programming for traveling thief problem. In: IEEE Congress on Evolutionary Computation, CEC 2015, Sendai, Japan, 25–28 May 2015, pp. 2753–2760 (2015).
  11. 11.
    Mei, Y., Li, X., Yao, X.: On investigation of interdependence between sub-problems of the travelling thief problem. Soft Comput., 1–16 (2014).
  12. 12.
    Mei, Y., Li, X., Yao, X.: Improving efficiency of heuristics for the large scale traveling thief problem. In: Proceedings of the Simulated Evolution, Learning - 10th International Conference, SEAL 2014, Dunedin, New Zealand, 15–18 December 2014, pp. 631–643 (2014).
  13. 13.
    Wachter, C.: Solving the travelling thief problem with an evolutionary algorithm. Diplomarbeit, Technischen Universitt Wien (2015)Google Scholar
  14. 14.
    Applegate, D., Cook, W., Rohe, A.: Chained lin-kernighan for large traveling salesman problems. INFORMS J. Comput. 15(1), 82–92 (2003). MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2000)CrossRefGoogle Scholar
  16. 16.
    Fonseca, V.G., Fonseca, C.M.: The attainment-function approach to stochastic multiobjective optimizer assessment and comparison. In: Experimental Methods for the Analysis of Optimization Algorithms, pp. 103–130. Springer, Heidelberg (2010).
  17. 17.
    Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0–1 knapsack problem. Manage. Sci. 45(3), 414–424 (1999)CrossRefzbMATHGoogle Scholar
  18. 18.
    Oliver, I.M., Smith, D.J., Holland, J.R.C.: A study of permutation crossover operators on the traveling salesman problem. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and their Application, pp. 224–230. L.E. Associates Inc., Mahwah (1987)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Otto-von-Guericke UniversityMagdeburgGermany
  2. 2.Michigan State UniversityEast LansingUSA

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