Local Search Guided by Path Relinking and Heuristic Bounds

  • Joseph M. Pasia
  • Xavier Gandibleux
  • Karl F. Doerner
  • Richard F. Hartl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4403)


In this paper we present three path relinking approaches for solving a bi-objective permutation flowshop problem. The path relinking phase is initialized by optimizing the two objectives using Ant Colony System. The initiating and guiding solutions of path relinking are randomly selected and some of the solutions along the path are intensified using local search. The three approaches differ in their strategy of defining the heuristic bounds for the local search, i.e., each approach allows its solutions to undergo local search under different conditions. These conditions are based on local nadir points. Several test instances are used to investigate the performances of the different approaches. Computational results show that the decision which allows solutions to undergo local search has an influence in the performance of path relinking. We also demonstrate that path relinking generates competitive results compared to the best known solutions of the test instances.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lenstra, J.K., Kan, A.H.G.R., Brucker, P.: Complexity of machine scheduling problems. Annals of Discrete Mathematics 1, 343–362 (1977)Google Scholar
  2. 2.
    Du, J., Leung, J.Y.T.: Minimizing total tardiness on one machine is np-hard. Mathematics of operations research 15, 483–495 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Glover, F.: Tabu search and adaptive memory programming advances, applications and challenges. In: Barr, R., Helgason, R., Kennington, J. (eds.) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer Academic Publishers, Dordrecht (1996)Google Scholar
  4. 4.
    Gandibleux, X., Morita, H., Katoh, N.: The supported solutions used as a genetic information in a population heuristic. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 429–442. Springer, Heidelberg (2001)Google Scholar
  5. 5.
    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
  6. 6.
    Haubelt, C., Gamenik, J., Teich, J.: Initial population construction for convergence improvement of moeas. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 191–205. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Gandibleux, X., Morita, H., Katoh, H.: Evolutionary operators based on elite solutions for bi-objective combinatorial optimization. In: Coello Coello, C., Lamont, G. (eds.) Applications of Multi-Objective Evolutionary Algorithms. Advances in Natural Computation, vol. 1, pp. 555–579. World Scientific, New Jersey (2004)Google Scholar
  8. 8.
    Basseur, M., Seynhaeve, F., Talbi, E.: Path relinking in pareto multi-objective genetic algorithms. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 120–134. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Dorigo, M., Di Caro, G: The ant colony optimization meta-heuristic. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 11–32. McGraw-Hill, New York (1999)Google Scholar
  10. 10.
    Pasia, J., Hartl, R., Doerner, K.: Solving bi-objective flowshop problem using pareto-ant colony optimization. In: Dorigo, M., Gambardella, L.M., Birattari, M., Martinoli, A., Poli, R., Stützle, T. (eds.) ANTS 2006. LNCS, vol. 4150, pp. 294–305. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Taillard, E.: Benchmarks for basic scheduling problems. European Journal of Operational Research 64, 278–285 (1993)zbMATHCrossRefGoogle Scholar
  12. 12.
    Talbi, E., Rahoual, M., Mabed, M., Dhaenens, C.: A hybrid evolutionary approach for multicriteria optimization problems: Application to the flowshop. 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
  13. 13.
    Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical Report TIK-Report No. 214, Computer Engineering and Networks Laboratory, ETH Zurich, Gloriastrasse 35, ETH-Zentum, 8092 Zurich, Switzerland (2006)Google Scholar
  14. 14.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar
  15. 15.
    Hansen, M., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Technical Report Technical Report IMM-REP-1998-7, Technical University of Denmark (1998)Google Scholar
  16. 16.
    Basseur, M., Seynhaeve, F., Talbi, E.G.: Adaptive mechanisms for multi-objective evolutionary algorithms (S3-R-00-222). In: IMACS multiconference, Computational Engineering in Systems Applications (CESA’03), Piscataway, IEEE Computer Society Press, Los Alamitos (2003)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Joseph M. Pasia
    • 1
    • 3
  • Xavier Gandibleux
    • 2
  • Karl F. Doerner
    • 3
  • Richard F. Hartl
    • 3
  1. 1.Department of Mathematics, University of the Philippines-Diliman, Quezon CityPhilippines
  2. 2.Laboratoire d’ Informatique de Nantes Atlantique, Université de Nantes, NantesFrance
  3. 3.Department of Management Science, University of Vienna, ViennaAustria

Personalised recommendations