Indicator-Based Selection in Multiobjective Search

  • Eckart Zitzler
  • Simon Künzli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3242)


This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection process. To this end, we propose a general indicator-based evolutionary algorithm (IBEA) that can be combined with arbitrary indicators. In contrast to existing algorithms, IBEA can be adapted to the preferences of the user and moreover does not require any additional diversity preservation mechanism such as fitness sharing to be used. It is shown on several continuous and discrete benchmark problems that IBEA can substantially improve on the results generated by two popular algorithms, namely NSGA-II and SPEA2, with respect to different performance measures.


Knapsack Problem Decision Vector Population Member Optimization Goal Multiobjective Evolutionary Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bosman, P.A.N., Thierens, D.: The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Transactions on Evolutionary Computation 7(2), 174–188 (2003)CrossRefGoogle Scholar
  2. 2.
    Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, New York (2002)zbMATHGoogle Scholar
  3. 3.
    Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)zbMATHGoogle Scholar
  4. 4.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9, 115–148 (1995)zbMATHMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: CEC 2002, pp. 825–830. IEEE Press, Los Alamitos (2002)Google Scholar
  7. 7.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. In: Abraham, A., et al. (eds.) Evolutionary Computation Based Multi-Criteria Optimization: Theoretical Advances and Applications, Springer, Heidelberg (2004) (to appear)Google Scholar
  8. 8.
    Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms – part ii: Application example. IEEE Transactions on Systems, Man, and Cybernetics 28(1), 38–47 (1998)CrossRefGoogle Scholar
  9. 9.
    Hansen, M.P., Jaszkiewicz, A.: Evaluating the quality of approximations of the non-dominated set. Technical report, Institute of Mathematical Modeling, Technical University of Denmark, IMM Technical Report IMM-REP-1998-7 (1998)Google Scholar
  10. 10.
    Knowles, J., Corne, D.: On metrics for comparing non-dominated sets. In: CEC 2002, Piscataway, NJ, pp. 711–716. IEEE Press, Los Alamitos (2002)Google Scholar
  11. 11.
    Knowles, J.D.: Local-Search and Hybrid Evolutionary Algorithms for Pareto Optimization. PhD thesis, University of Reading (2002)Google Scholar
  12. 12.
    Kursawe, F.: A variant of evolution strategies for vector optimization. In: Schwefel, H.-P., Männer, R. (eds.) PPSN I, pp. 193–197. Springer, Heidelberg (1991)Google Scholar
  13. 13.
    Laumanns, M., Zitzler, E., Thiele, L.: On the effects of archiving, elitism, and density based selection in evolutionary multi-objective optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 181–196. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Thiele, L., Chakraborty, S., Gries, M., Künzli, S.: Design space exploration of network processor architectures. In: Franklin, M., et al. (eds.) Network Processor Design Issues and Practices, October 2002, vol. 1, ch. 4, Morgan Kaufmann, San Francisco (2002)Google Scholar
  15. 15.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (2000)CrossRefGoogle Scholar
  16. 16.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Giannakoglou, K., et al. (eds.) EUROGEN 2001. International Center for Numerical Methods in Engineering (CIMNE), pp. 95–100 (2001)Google Scholar
  17. 17.
    Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Eckart Zitzler
    • 1
  • Simon Künzli
    • 1
  1. 1.Computer Engineering and Networks Laboratory (TIK)Swiss Federal Institute of Technology ZurichZürichSwitzerland

Personalised recommendations