Dominance Based Crossover Operator for Evolutionary Multi-objective Algorithms

  • Olga Rudenko
  • Marc Schoenauer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3242)


In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates – but contradictory conclusions have been reported. This paper introduces a particular mating restriction for Evolutionary Multi-objective Algorithms, based on the Pareto dominance relation: the partner of a non-dominated individual will be preferably chosen among the individuals of the population that it dominates. Coupled with the BLX crossover operator, two different ways of generating offspring are proposed. This recombination scheme is validated within the well-known NSGA-II framework on three bi-objective benchmark problems and one real-world bi-objective constrained optimization problem. An acceleration of the progress of the population toward the Pareto set is observed on all problems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Corne, D.W., Knowles, J.D., Oates, M.L.: The Pareto Envelope-based Selection Algorithm for Multiobjective Optimization. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 839–848. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley, Chichester (2001)MATHGoogle Scholar
  3. 3.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Deb, K., Jain, S.: Running performance metrics for evolutionary multi-objective optimization. Technical Report 2002004, Indian Institute of Technology, Kanpur (May 2002)Google Scholar
  5. 5.
    Eshelman, L., Schaffer, J.D.: Real-coded genetic algorithms and intervalschemata. In: Whitley, L.D. (ed.) Foundations of Genetic Algorithms, vol. 2, pp. 187–202. Morgan Kaufmann, San Francisco (1993)Google Scholar
  6. 6.
    Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: ICGA 1993, pp. 416–423. Morgan Kaufmann, San Francisco (1993)Google Scholar
  7. 7.
    Goldberg, D.E.: Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading (1989)MATHGoogle Scholar
  8. 8.
    Hajela, P., Lin, C.Y.: Genetic search strategies in multicriterion optimal design. Structural Optimization 4, 99–107 (1992)CrossRefGoogle Scholar
  9. 9.
    Horn, J., Nafpliotis, S.N., Goldberg, D.E.: A niched pareto genetic algorithm for multiobjective optimization. In: Michalewicz, Z., et al. (eds.) Proc. of ICEC 1994, pp. 82–87. IEEE Press, Los Alamitos (1994)Google Scholar
  10. 10.
    Rudenko, O.: Application des algorithmes évolutionnaires aux problèmes d’optimisation multi-objectif avec contraintes. PhD thesis, +cole Polytechnique (2004)Google Scholar
  11. 11.
    Rudenko, O., Schoenauer, M.: A steady performance stopping criterion for pareto-based evolutionary algorithms. In: Proc. 6th Intl Conf. on Multi Objective Programming and Goal Programming (2004)Google Scholar
  12. 12.
    Rudenko, O., Schoenauer, M., Bosio, T., Fontana, R.: A multiobjective evolutionary algorithm for car front end design. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, pp. 205–216. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Wildman, A., Parks, G.: A comparative study of selective breeding strategies in a multiobjective genetic algorithm. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 418–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Wright, J., Loosemore, H.: An infeasibility objective for use in constrained pareto optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 256–268. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 125–148 (2000)CrossRefGoogle Scholar
  16. 16.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory, ETH, Zurich, Switzerland (2001)Google Scholar
  17. 17.
    Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms – a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Olga Rudenko
    • 1
  • Marc Schoenauer
    • 1
  1. 1.TAO Team, INRIA Futurs, LRI, bat. 490Université Paris-SudOrsay CedexFrance

Personalised recommendations