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On the Performance of Local Search for the Biobjective Traveling Salesman Problem

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Advances in Multi-Objective Nature Inspired Computing

Part of the book series: Studies in Computational Intelligence ((SCI,volume 272))

Summary

In this chapter we investigate experimentally the performance of multiobjective local search approaches that are based on the component-wise acceptance criterion search model. This model gives a framework for many well-known evolutionary and local search algorithms. Using the biobjective traveling salesman problem as an example application, we analyse the impact of three important algorithmic components on the performance of a simple local search algorithm that follows this search model: initialization strategy, neighborhood structure and archive bounding. By following principles of experimental design, we study the effects of each component, both in terms of solution quality and computation time. The experimental analysis indicates the existence of several complex trade-offs between solution quality and run-time for many of the choices available for each component.

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References

  1. Angel, E., Bampis, E., Gourvés, L.: Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem. Theoretical Computer Science 310, 135–146 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Angel, E., Bampis, E., Gourvés, L.: A dynasearch neighborhood for the bicriteria traveling salesman problem. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’kindt, V. (eds.) Metaheuristics for Multiobjective Optimisation. LNCS, vol. 535, pp. 153–176. Springer, Berlin (2004)

    Google Scholar 

  3. Armetano, V.A., Arroyo, J.E.: An application of multi-objective tabu search algorithm to a bicriteria flowshop problem. Journal of Heuristics 10(5), 463–481 (2004)

    Article  Google Scholar 

  4. Baykasoglu, A., Owen, S., Gindy, N.: A taboo search based approach to find the Pareto optimal set in multiobjective optimization. Journal of Engineering Optimization 31, 731–748 (1999)

    Article  Google Scholar 

  5. Borges, P.: CHESS – Changing Horizon Efficient Set Search: A simple principle for multiobjective optimization. Journal of Heuristics 6(3), 405–418 (2000)

    Article  MATH  Google Scholar 

  6. Conover, J.: Practical Nonparametric Statistics. John Wiley & Sons, New York (1980)

    Google Scholar 

  7. Emelichev, V.A., Perepelitsa, V.A.: On the cardinality of the set of alternatives in discrete many-criterion problems. Discrete Mathematics and Applications 2(5), 461–471 (1992)

    Article  MathSciNet  Google Scholar 

  8. Fonseca, C.M., Fleming, P.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  9. Fonseca, C.M., Grunert da Fonseca, V., Paquete, L.: Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 250–264. Springer, Heidelberg (2005)

    Google Scholar 

  10. Good, P.I.: Permutation Tests: A practical guide to resampling methods for testing hypothesis, 2nd edn. Springer Series in Statistics. Springer, New York (2000)

    Google Scholar 

  11. Grunert da Fonseca, V., Fonseca, C.M., Hall, A.: Inferential performance assessment of stochastic optimizers and the attainment function. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 213–225. Springer, Heidelberg (2001)

    Google Scholar 

  12. Hansen, M.P.: Use of substitute scalarizing functions to guide a local search base heuristics: The case of moTSP. Journal of Heuristics 6, 419–431 (2000)

    Article  MATH  Google Scholar 

  13. Hansen, M.P., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark (1998)

    Google Scholar 

  14. Hsu, J.: Multiple Comparisons - Theory and Methods. Chapman & Hall/CRC, Boca Raton (1996)

    MATH  Google Scholar 

  15. Jaszkiewicz, A.: Genetic local search for multiple objective combinatorial optimization. European Journal of Operational Research 1(137), 50–71 (2002)

    Article  MathSciNet  Google Scholar 

  16. Jozefowiez, N., Semet, F., Talbi, E.-G.: Parallel and hybrid models for multi-objective optimization: Application to the vehicle routing problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 271–280. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Knowles, J., Corne, D.: The Pareto archived evolution strategy: A new base line algorithm for multiobjective optimisation. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC 1999), pp. 98–105. IEEE Press, Piscataway (1999)

    Google Scholar 

  18. Knowles, J., Corne, D.: M-PAES: A memetic algorithm for multiobjective optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation (CEC 2000), vol. 1, pp. 325–332. IEEE Press, Piscataway (2000)

    Chapter  Google Scholar 

  19. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: On the convergence and diversity-preservation properties of multi-objective evolutionary algorithms. TIK-Report 108, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich (May 2001)

    Google Scholar 

  20. Laumanns, M., Thiele, L., Zitzler, E., Welzl, E., Deb, K.: Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem. In: Guervos, J.M., Adamis, P., Beyer, H.-G., Fernández-Villacañas, J., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 44–53. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. López-Ibáñez, M., Paquete, L., Stützle, T.: Hybrid population-based algorithms for the bi-objective quadratic assignment problem. Journal of Mathematical Modelling and Algorithms 5(1), 111–137 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lust, T., Teghem, J.: Two phase stochastic local search algorithms for the biobjective traveling salesman problem. In: Ridge, E., Stützle, T., Birattari, M., Hoos, H.H. (eds.) Proceedings of SLS-DS 2007, Doctoral Symposium on Engineering Stochastic Local Search Algorithms, Brussels, Belgium, pp. 21–25 (2007)

    Google Scholar 

  23. Morita, H., Gandibleux, X., Katoh, N.: Experimental feedback on biobjective permutation scheduling problems solved with a population heuristic. Foundations of Computing and Decision Sciences 26(1), 23–50 (2001)

    Google Scholar 

  24. Paquete, L., Chiarandini, M., Stützle, T.: Pareto local optimum sets in the biobjective traveling salesman problem: An experimental study. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’kindt, V. (eds.) Metaheuristics for Multiobjective Optimisation. LNEMS, vol. 535, pp. 177–200. Springer, Berlin (2004)

    Google Scholar 

  25. Paquete, L., Fonseca, C.M.: A study of examination timetabling with multiobjective evolutionary algorithms. In: Proceedings of the Fourth Metaheuristics International Conference, Porto, pp. 149–154 (2001)

    Google Scholar 

  26. Paquete, L., Schiavinotto, T., Stützle, T.: On local optima in multiobjective combinatorial optimization problems. Annals of Operations Research 156(1), 83–98 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  27. Paquete, L., Stützle, T.: Stochastic local search algorithms for multiobjective combinatorial optimization: A review. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics. Computer and Information Science Series, pp. 29–1—29–15. Chapman & Hall/CRC, Boca Raton (2007)

    Google Scholar 

  28. Paquete, L., Stützle, T.: Clusters of non-dominated solutions in multiobjective combinatorial optimization. In: Barichard, V., Ehrgott, M., Gandibleux, X., T’Kindt, V. (eds.) Multiobjective Programming and Goal Programming: Theoretical Results and Practical Applications. LNEMS, vol. 618, pp. 69–77. Springer, Berlin (2009)

    Google Scholar 

  29. Paquete, L., Stützle, T.: Design and analysis of stochastic local search algorithms for the multiobjective traveling salesman problem. Computers & Operations Research 36(9), 2610–2631 (2009)

    Article  Google Scholar 

  30. Paquete, L., Stützle, T., López-Ibáñez, M.: Using experimental design to analyze stochastic local search algorithms for multiobjective problems. In: Doerner, K.F., Gendreau, M., Greistörfer, P., Gutjahr, W.J., Hartl, R.F., Reimann, M. (eds.) Metaheuristics — Progress in Complex Systems Optimization. Operations Research/Computer Science Interface Series, vol. 39, pp. 325–344. Springer, New York (2007)

    Google Scholar 

  31. Serafini, P.: Some considerations about computational complexity for multiobjective combinatorial problems. In: Jahn, J., Krabs, W. (eds.) Recent Advances and Historical Development of Vector Optimization. LNEMS, vol. 294, pp. 222–231. Springer, Berlin (1986)

    Google Scholar 

  32. Stützle, T., Hoos, H.: Analyzing the run-time behaviour of iterated local search for the TSP. In: Hansen, P., Ribeiro, C. (eds.) Essays and Surveys on Metaheuristics, pp. 589–612. Kluwer Academic Publishers, Boston (2002)

    Google Scholar 

  33. Talbi, E.G.: A hybrid evolutionary approach for multicriteria optimization problems: Application to the flow shop. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 416–428. Springer, Heidelberg (2001)

    Google Scholar 

  34. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)

    Article  Google Scholar 

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Paquete, L., Stützle, T. (2010). On the Performance of Local Search for the Biobjective Traveling Salesman Problem. In: Coello Coello, C.A., Dhaenens, C., Jourdan, L. (eds) Advances in Multi-Objective Nature Inspired Computing. Studies in Computational Intelligence, vol 272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11218-8_7

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  • DOI: https://doi.org/10.1007/978-3-642-11218-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11217-1

  • Online ISBN: 978-3-642-11218-8

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