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

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Evolutionary Multi-Criterion Optimization (EMO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10173))

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Abstract

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.

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References

  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. 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)

    MATH  Google Scholar 

  3. Lagoudakis, M.G.: The 0–1 Knapsack Problem - An Introductory Survey (1996)

    Google Scholar 

  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. 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). http://doi.acm.org/10.1145/2576768.2598249

  6. Reinelt, G.: TSPLIB - A t.s.p. library. Universität Augsburg, Institut für Mathematik, Augsburg. Technical report 250 (1990)

    Google Scholar 

  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). http://doi.acm.org/10.1145/2739480.2754716

  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). http://doi.acm.org/10.1145/2576768.2598367

  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, compute@compute.dtu.dk (2015). http://www.compute.dtu.dk/English.aspx

  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). http://dx.doi.org/10.1109/CEC.2015.7257230

  11. Mei, Y., Li, X., Yao, X.: On investigation of interdependence between sub-problems of the travelling thief problem. Soft Comput., 1–16 (2014). http://dx.doi.org/10.1007/s00500-014-1487-2

  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). http://dx.doi.org/10.1007/978-3-319-13563-2_53

  13. Wachter, C.: Solving the travelling thief problem with an evolutionary algorithm. Diplomarbeit, Technischen Universitt Wien (2015)

    Google Scholar 

  14. Applegate, D., Cook, W., Rohe, A.: Chained lin-kernighan for large traveling salesman problems. INFORMS J. Comput. 15(1), 82–92 (2003). http://dx.doi.org/10.1287/ijoc.15.1.82.15157

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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). http://dx.doi.org/10.1007/978-3-642-02538-9_5

  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)

    Article  MATH  Google Scholar 

  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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Acknowledgment

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

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Authors and Affiliations

  1. Otto-von-Guericke University, 39106, Magdeburg, Germany

    Julian Blank & Sanaz Mostaghim

  2. Michigan State University, East Lansing, Michigan, 48824, USA

    Kalyanmoy Deb

Authors
  1. Julian Blank
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  2. Kalyanmoy Deb
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  3. Sanaz Mostaghim
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Corresponding author

Correspondence to Julian Blank .

Editor information

Editors and Affiliations

  1. University of Münster, Münster, Germany

    Heike Trautmann

  2. TU Dortmund University, Dortmund, Germany

    Günter Rudolph

  3. University of Wuppertal, Wuppertal, Germany

    Kathrin Klamroth

  4. CINVESTAV-IPN, Mexico City, Mexico

    Oliver Schütze

  5. Clemson University, Clemson, South Carolina, USA

    Margaret Wiecek

  6. University of Surrey, Guildford, United Kingdom

    Yaochu Jin

  7. University of Münster, Münster, Germany

    Christian Grimme

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Blank, J., Deb, K., Mostaghim, S. (2017). Solving the Bi-objective Traveling Thief Problem with Multi-objective Evolutionary Algorithms. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-54157-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54156-3

  • Online ISBN: 978-3-319-54157-0

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