A Preference Based Interactive Evolutionary Algorithm for Multi-objective Optimization: PIE

  • Karthik Sindhya
  • Ana Belen Ruiz
  • Kaisa Miettinen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6576)


This paper describes a new Preference-based Interactive Evolutionary (PIE) algorithm for multi-objective optimization which exploits the advantages of both evolutionary algorithms and multiple criteria decision making approaches. Our algorithm uses achievement scalarizing functions and the potential of population based evolutionary algorithms to help the decision maker to direct the search towards the desired Pareto optimal solution. Starting from an approximated nadir point, the PIE algorithm improves progressively the objective function values of a solution by finding a better solution at each iteration that improves the previous one. The decision maker decides from which solution, in which direction, and at what distance from the Pareto front to find the next solution. Thus, the PIE algorithm is guided interactively by the decision maker. A flexible approach is obtained with the use of archive sets to store all the solutions generated during an evolutionary algorithm’s run, as it allows the decision maker to freely navigate and inspect previous solutions if needed. The PIE algorithm is demonstrated using a pollution monitoring station problem and shown to be effective in helping the decision maker to find a solution that satisfies her/his preferences.


Decision Maker Evolutionary Algorithm Pareto Front Multiobjective Optimization Preference Information 
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.
    Branke, J., Kaubler, T., Schmeck, H.: Guidence in evolutionary multi-objective optimization. Advances in Engineering Software 32(6), 499–507 (2001)CrossRefzbMATHGoogle Scholar
  2. 2.
    Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. Elsevier Science Publishing Co., Inc., New York (1983)zbMATHGoogle Scholar
  3. 3.
    Coello, C.A.C., Lamont, G.B., Veldhuizen, D.A.V.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007)zbMATHGoogle Scholar
  4. 4.
    Deb, K.: Multi-objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)zbMATHGoogle Scholar
  5. 5.
    Deb, K., Kumar, A.: Light beam search based multi-objective optimization using evolutionary algorithms. In: Proceedings of the Congress on Evolutionary Computation (CEC 2007), pp. 2125–2132. IEEE Press, Los Alamitos (2007)Google Scholar
  6. 6.
    Deb, K., Miettinen, K., Chaudhuri, S.: Towards an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Transactions on Evolutionary Computation 14(6), 821–841 (2010)CrossRefGoogle Scholar
  7. 7.
    Deb, K., Saxena, D.K.: Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In: Proceedings of the Congress on Evolutionary Computation (CEC 2006), pp. 3353–3360. IEEE Press, Los Alamitos (2006)Google Scholar
  8. 8.
    Deb, K., Sinha, A., Korhonen, P.J., Wallenius, J.: An interactive evolutionary multi-objective optimization method based on progressively approximated value functions. Tech. Rep. 2009005, KanGAL (2009)Google Scholar
  9. 9.
    Deb, K., Sundar, J., Rao, U.B., Chaudhuri, S.: Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research 2(3), 273–286 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 825–830. IEEE Press, Los Alamitos (2002)Google Scholar
  11. 11.
    Hakanen, J., Miettinen, K., Mäkelä, M.M.: Using genetic algorithms in multiobjective process optimization. In: Bugeda, G., et al. (eds.) Proceedings of the Congress on Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems (EUROGEN 2003), CD-Proceedings, CIMNE, Barcelona (2003)Google Scholar
  12. 12.
    Imai, A., Sasaki, K., Nishimura, E., Papadimitriou, S.: Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks. European Journal of Operational Research 171(2), 373–389 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    Knowles, J., Corne, D.: Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In: Obayashi, S., et al. (eds.) EMO 2007. LNCS, vol. 4403, pp. 757–771. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Luque, M., Miettinen, K., Eskelinen, P., Ruiz, F.: Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega 37(2), 450–462 (2009)CrossRefGoogle Scholar
  15. 15.
    Luque, M., Ruiz, F., Miettinen, K.: Global formulation for interactive multiobjective optimization. OR Spectrum 33(1), 27–48 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)zbMATHGoogle Scholar
  17. 17.
    Miettinen, K.: Using interactive multiobjective optimization in continuous casting of steel. Materials and Manufacturing Processes 22, 585–593 (2007)CrossRefGoogle Scholar
  18. 18.
    Miettinen, K., Eskelinen, P., Ruiz, F., Luque, M.: NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point. European Journal of Operational Research 206(2), 426–434 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Miettinen, K., Lotov, A.V., Kamenev, G.K., Berezkin, V.E.: Integration of two multiobjective optimization methods for nonlinear problems. Optimization Methods and Software 18(1), 63–80 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Ruiz, F., Luque, M., Cabello, J.M.: A classification of the weighting schemes in reference point procedures for multiobjective programming. Journal of the Operations Research Society 60, 544–553 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    Thiele, L., Miettinen, K., Korhonen, P.J., Molina, J.: A preference-based evolutionary algorithm for multi-objective optimization. Evolutionary Computation 17(3), 411–436 (2009)CrossRefGoogle Scholar
  22. 22.
    Tversky, A., Kahneman, D.: The framing of decisions and the psychology of choice. Science 211, 453–458 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Wierzbicki, A.P.: The use of reference objectives in multiobjective optimization. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making: Theory and Application, pp. 468–486. Springer, Hagen (1980)CrossRefGoogle Scholar
  24. 24.
    Wierzbicki, A.P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spektrum 8, 73–87 (1986)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Karthik Sindhya
    • 1
  • Ana Belen Ruiz
    • 2
  • Kaisa Miettinen
    • 1
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläAgoraFinland
  2. 2.Department of Applied Economics (Mathematics)University of MalagaMalagaSpain

Personalised recommendations