Advertisement

Local Search Based on a Local Utopia Point for the Multiobjective Travelling Salesman Problem

  • Krzysztof MichalakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9375)

Abstract

Performing a local search around solutions found by an evolutionary algorithm is a common practice. Local search is well known to significantly improve the solutions, in particular in the case of combinatorial problems. In this paper a new local search procedure is proposed that uses a locally established utopia point. In the tests in which several instances of the Travelling Salesman Problem (TSP) were solved using an evolutionary algorithm the proposed local search procedure outperformed a local search procedure based on Pareto dominance. Because the local search is focused on improving individual solutions and the multiobjective evolutionary algorithm can improve diversity, various strategies of sharing computational resources between the evolutionary algorithm and the local search are used in this paper. The results attained by the tested methods are compared with respect to computation time, which allows a fair comparison between strategies that distribute computational resources between the evolutionary optimization and the local search in various proportions.

Keywords

Multiobjective optimization Combinatorial optimization Travelling salesman problem Local search 

References

  1. 1.
    Chiang, C.W., Lee, W.P., Heh, J.S.: A 2-opt based differential evolution for global optimization. Appl. Soft Comput. 10(4), 1200–1207 (2010)CrossRefGoogle Scholar
  2. 2.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002)CrossRefGoogle Scholar
  3. 3.
    Derrac, J., Garca, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011)CrossRefGoogle Scholar
  4. 4.
    Dubois-Lacoste, J., et al.: A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems. Comput. Oper. Res. 38(8), 1219–1236 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Goldberg, D.E., Voessner, S.: Optimizing global-local search hybrids. In: Banzhaf, W., Daida, J., Eiben, A.E., Garzon, M.H., Honavar, V., Jakiela, M., Smith, R.E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, vol. 1, pp. 220–228. Morgan Kaufmann, Orlando (1999)Google Scholar
  6. 6.
    Ishibuchi, H.: Memetic algorithms for evolutionary multiobjective combinatorial optimization. In: 2010 40th International Conference on Computers and Industrial Engineering (CIE), pp. 1–2 (2010)Google Scholar
  7. 7.
    Li, M., Zheng, J.: Spread assessment for evolutionary multi-objective optimization. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 216–230. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  8. 8.
    Lust, T., Teghem, J.: Two-phase pareto local search for the biobjective traveling salesman problem. J. Heuristics 16(3), 475–510 (2010)CrossRefzbMATHGoogle Scholar
  9. 9.
    Ott, L., Longnecker, M.: An Introduction to Statistical Methods and Data Analysis. Brooks/Cole Cengage Learning, Boston (2010) Google Scholar
  10. 10.
    Sinha, A., Goldberg, D.E.: Verification and extension of the theory of global-local hybrids. In: Proceedings of GECCO (2001)Google Scholar
  11. 11.
    Tao, G., Michalewicz, Z.: Inver-over operator for the TSP. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 803–812. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  12. 12.
    Thibaut Lust: Multiobjective TSP (2015). https://sites.google.com/site/thibautlust/research/multiobjective-tsp. Accessed 29 January 2015
  13. 13.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7, 117–132 (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Information Technologies, Institute of Business InformaticsWroclaw University of EconomicsWroclawPoland

Personalised recommendations