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An Investigation of Hybrid Tabu Search for the Traveling Salesman Problem

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Book cover Bio-Inspired Computing -- Theories and Applications (BIC-TA 2015)

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Abstract

The Traveling Salesman Problem (TSP) is one of the most well-known problems in combinatorial optimization. Due to its \({\mathcal {NP}}\)-hardness, research has focused on approximate methods like metaheuristics. Tabu Search (TS) is a very efficient metaheuristic for combinatorial problems. We investigate four different versions of TS with different tabu objects and compare them to the Lin-Kernighan (LK) heuristic as well as the recently developed Multi-Neighborhood Search (MNS). LK is currently considered to be the best approach for solving the TSP, while MNS has shown to be highly competitive. We then propose new hybrid algorithms by hybridizing TS with Evolutionary Algorithms and Ant Colony Optimization. These hybrids are compared to similar hybrids based on LK and MNS. This paper presents the first statistically sound and comprehensive comparison taking the entire optimization processes of (hybrid) TS, LK, and MNS into consideration based on a large-scale experimental study. We show that our new hybrid TS algorithms are highly efficient and comparable to the state-of-the-art algorithms along this line of research.

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References

  1. Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2007)

    MATH  Google Scholar 

  2. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley Interscience, Chichester (1985)

    MATH  Google Scholar 

  3. Gutin, G.Z., Punnen, A.P. (eds.): The Traveling Salesman Problem and its Variations. Kluwer Academic Publishers, Norwell (2002)

    MATH  Google Scholar 

  4. Jiang, H., Sun, W., Ren, Z., Lai, X., Piao, Y.: Evolving hard and easy traveling salesman problem instances: a multi-objective approach. In: Dick, G., Browne, W.N., Whigham, P., Zhang, M., Bui, L.T., Ishibuchi, H., Jin, Y., Li, X., Shi, Y., Singh, P., Tan, K.C., Tang, K. (eds.) SEAL 2014. LNCS, vol. 8886, pp. 216–227. Springer, Heidelberg (2014)

    Google Scholar 

  5. Woeginger, G.J.: Exact algorithms for np-hard problems: a survey. In: Revised Papers of the 5th International Works on Combinatorial Optimization, pp. 185–207. Springer, Aussois (2001)

    Google Scholar 

  6. Weise, T.: Global Optimization Algorithms - Theory and Application. Self-Published, Germany (it-weise.de) (2009)

    Google Scholar 

  7. Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation. Oxford University Press, New York (1997)

    MATH  Google Scholar 

  8. De Jong, K.A.: Evolutionary Computation: A Unified Approach. MIT Press, Cambridge (2006)

    MATH  Google Scholar 

  9. Dorigo, M.: Optimization, Learning and Natural Algorithms, Ph.D. thesis. Dipartimento di Elettronica, Politecnico di Milano, Milano (1992)

    Google Scholar 

  10. Dorigo, M., Birattari, M., Stützle, T.: Ant colony optimization - artificial ants as a computational intelligence technique. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)

    Article  Google Scholar 

  11. Gambardella, L.M., Dorigo, M.: Solving symmetric and asymmetric tsps by ant colonies. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp. 622–627. Nagoya, 20–22 May 1996

    Google Scholar 

  12. Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  13. Weise, T., Chiong, R., Tang, K., Lässig, J., Tsutsui, S., Chen, W., Michalewicz, Z., Yao, X.: Benchmarking optimization algorithms: an open source framework for the traveling salesman problem. IEEE Comput. Intell. Mag. 9(3), 40–52 (2014)

    Article  Google Scholar 

  14. Hansen, P., Mladenović, N., Moreno Pérez, J.A.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175(1), 367–407 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guntsch, M., Middendorf, M.: Applying population based aco to dynamic optimization problems. In: Proceedings of the 3rd International Works on Ant Colony Optimization, pp. 111–122. Brussels (2002)

    Google Scholar 

  16. Glover, F.W., Taillard, É.D., de Werra, D.: A user’s guide to tabu search. Ann. Oper. Res. 41(1), 3–28 (1993)

    Article  MATH  Google Scholar 

  17. Misevičius, A.: Using iterated tabu search for the traveling salesman problem. Inf. Technol. Control 32(3), 29–40 (2015)

    Google Scholar 

  18. Osaba, E., Diaz, F.: Comparison of a memetic algorithm and a tabu search algorithm for the traveling salesman problem. In: 2012 Federated Conference on Computer Science and Information Systems, pp. 131–136 (2012)

    Google Scholar 

  19. Reinelt, G.: Tsplib 95. Technical report. Universität Heidelberg, Institut für Mathematik, Heidelberg (1995)

    Google Scholar 

  20. Basu, S.: Tabu search implementation on traveling salesman problem and its variations: a literature survey. Am. J. Oper. Res. 2(2), 163–173 (2012)

    Article  Google Scholar 

  21. Boddy, M.S., Dean, T.L.: Solving time-dependent planning problems. Technical report CS-89-03. Brown University, Providence (1989)

    Google Scholar 

  22. Jiang, Y., Weise, T., Lässig, J., Chiong, R., Athauda, R.: Comparing a hybrid branch and bound algorithm with evolutionary computation methods, local search and their hybrids on the TSP. In: Proceedings of the IEEE Symposium Series on Computational Intelligence. Orlando, 9–12 Dec 2014

    Google Scholar 

  23. Hansen, N., Auger, A., Finck, S., Ros, R.: Real-parameter black-box optimization benchmarking: experimental setup. Technical report, Université Paris Sud, INRIA, Équipe TAO, Orsay (2012)

    Google Scholar 

  24. Tompkins, D.A.D., Hoos, H.H.: UBCSAT: an implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT. In: 7th International Conference on Theory and Applications of Satisfiability Testing, pp. 306–320. Springer, Berlin (2004)

    Google Scholar 

  25. Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (2005)

    MATH  Google Scholar 

  26. Hoos, H.H., Stützle, T.: Evaluating Las Vegas algorithms - pitfalls and remedies. In: Proceedings of the 14th Conference on Uncertainty in AI, pp. 238–245. Morgan Kaufmann, Madison, 24–26 July 1998

    Google Scholar 

  27. Johnson, D.S., McGeoch, L.A.: Experimental analysis of heuristics for the STSP. The Traveling Salesman Problem and its Variations, pp. 369–443. Springer, New York (2002)

    Google Scholar 

  28. Johnson, D.S., Gutin, G.Z., McGeoch, L.A., Yeo, A., Zhang, W., Zverovitch, A.: Experimental analysis of heuristics for the ATSP. The Traveling Salesman Problem and its Variations, pp. 445–487. Kluwer, Dordrecht (2002)

    Google Scholar 

  29. Wu, Y., Weise, T., Chiong, R.: Local search for the traveling salesman problem: a comparative study. In: Proceedings of 14th IEEE Conference on Cognitive Informatics and Cognitive Computing, pp. 213–220, 6–8 July 2015

    Google Scholar 

  30. Larranaga, P., Kuijpers, C.M.H., Murga, R.H., Inza, I., Dizdarevic, S.: Genetic algorithms for the travelling salesman problem: a review of representations and operators. J. Artif. Intell. Res. 13(2), 129–170 (1999)

    Article  Google Scholar 

  31. Michalewicz, Z.: Genetic Algorithms \(+\) Data Structures \(=\) Evolution Programs. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  32. Fogel, D.B.: An evolutionary approach to the traveling salesman problem. Biol. Cybern. 60(2), 139–144 (1988)

    Article  MathSciNet  Google Scholar 

  33. Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Ann Arbor (1975)

    MATH  Google Scholar 

  34. Glover, F.W.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13(5), 533–549 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  35. Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Sci. Mag. 220(4598), 671–680 (1983)

    Google Scholar 

  36. Wang, D., Wang, J., Wang, H., Zhang, R., Guo, Z.: Intelligent Optimization Methods. Higher Education Press, China (2007)

    Google Scholar 

  37. Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. Technical report, Roskilde University, Denmark (1998)

    Google Scholar 

  38. Applegate, D.L., Cook, W.J., Rohe, A.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS J. Comput. 15(1), 82–92 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  39. Helsgaun, K.: General k-opt submoves for the Lin-Kernighan TSP heuristic. Math. Program. Comput. 1(2–3), 119–163 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  40. Whitley, L.D., Starkweather, T., Fuquay, D.: Scheduling problems and traveling salesman: the genetic edge recombination operator. In: Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 133–140 (1989)

    Google Scholar 

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Acknowledgments

We acknowledge support from the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China under Grant 6115 0110488, Special Financial Grant 201104329 from the China Postdoctoral Science Foundation, the Chinese Academy of Sciences (CAS) Fellowship for Young International Scientists 2011Y1GB01, and the European Union 7th Framework Program under Grant 247619. The experiments reported in this paper were executed on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

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Authors and Affiliations

  1. Joint USTC-Birmingham Research Institute in Intelligent Computation and Its Applications (UBRI), School of Computer Science and Technology, University of Science and Technology of China, Hefei, 230027, Anhui, China

    Dan Xu, Thomas Weise & Yuezhong Wu

  2. Department of Computer Science, Enterprise Application Development Group, University of Applied Sciences Zittau/Görlitz, 02826, Görlitz, Germany

    Jörg Lässig

  3. School of Design, Communication and IT, Faculty of Science and IT, The University of Newcastle, Callaghan, NSW, 2308, Australia

    Raymond Chiong

Authors
  1. Dan Xu
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  2. Thomas Weise
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  3. Yuezhong Wu
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  4. Jörg Lässig
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  5. Raymond Chiong
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Corresponding author

Correspondence to Thomas Weise .

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Editors and Affiliations

  1. Xidian University, Xi'an, China

    Maoguo Gong

  2. Huazhong Univ. of Science and Technology, Wuhan, China

    Pan Linqiang

  3. University of Petroleum, Qingdao, China

    Song Tao

  4. University of Science and Technology of China, Hefei, China

    Ke Tang

  5. Anhui University, Hefei, China

    Xingyi Zhang

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Xu, D., Weise, T., Wu, Y., Lässig, J., Chiong, R. (2015). An Investigation of Hybrid Tabu Search for the Traveling Salesman Problem. In: Gong, M., Linqiang, P., Tao, S., Tang, K., Zhang, X. (eds) Bio-Inspired Computing -- Theories and Applications. BIC-TA 2015. Communications in Computer and Information Science, vol 562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49014-3_47

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  • DOI: https://doi.org/10.1007/978-3-662-49014-3_47

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