Advertisement

Journal of Global Optimization

, Volume 63, Issue 4, pp 633–652 | Cite as

A new preference handling technique for interactive multiobjective optimization without trading-off

  • Kaisa Miettinen
  • Dmitry Podkopaev
  • Francisco Ruiz
  • Mariano Luque
Article

Abstract

Because the purpose of multiobjective optimization methods is to optimize conflicting objectives simultaneously, they mainly focus on Pareto optimal solutions, where improvement with respect to some objective is only possible by allowing some other objective(s) to impair. Bringing this idea into practice requires the decision maker to think in terms of trading-off, which may limit the ability of effective problem solving. We outline some drawbacks of this and exploit another idea emphasizing the possibility of simultaneous improvement of all objectives. Based on this idea, we propose a technique for handling decision maker’s preferences, which eliminates the necessity to think in terms of trade-offs. We incorporate this technique into an interactive trade-off-free method for multiobjective optimization. We call the resulting method NAUTILUS 2, which is also suitable for negotiation support. We demonstrate the applicability of the new method with an example problem.

Keywords

Multiple objectives Interactive methods Preference information  NAUTILUS method Negotiation support 

Notes

Acknowledgments

This research has been partially supported by the Regional Government of Andalucia (research groups SEJ-445 and SEJ-532), and by the Spanish Ministry of Education and Science (projects ECO2013-47129-C4-2 and MTM2010-14992).

Supplementary material

10898_2015_301_MOESM1_ESM.zip (2 kb)
Supplementary material 1 (zip 3 KB)

References

  1. 1.
    Aloysius, J.A., Davis, F.D., Wilson, D.D., Taylor, A.R., Kottemann, J.E.: User acceptance of multi-criteria decision support systems: the impact of preference elicitation techniques. Eur. J. Oper. Res. 169, 273–285 (2006)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Arbel, A., Korhonen, P.: Using aspiration levels in an interior primal-dual multiobjective linear programming algorithm. J. Multi Crit. Decis. Anal. 5, 61–71 (1996)MATHCrossRefGoogle Scholar
  3. 3.
    Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.): Multiobjective optimization: interactive and evolutionary approaches. Springer, Berlin, Heidelberg (2008)Google Scholar
  4. 4.
    Buchanan, J.T., Corner, J.: The effects of anchoring in interactive MCDM solution methods. Comput. Oper. Res. 24(10), 907–918 (1997)MATHCrossRefGoogle Scholar
  5. 5.
    Cabello, J., Luque, M., Miguel, F., Ruiz, A., Ruiz, F.: A multiobjective interactive approach to determine the optimal electricity mix in Andalucía (Spain). TOP 22(1), 109–127 (2014)MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Cormen, T.: Introduction to algorithms. Mit Press, Cambridge (2009)MATHGoogle Scholar
  7. 7.
    Deb, K., Miettinen, K., Chaudhuri, S.: Towards an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Trans. Evol. Comput. 14(6), 821–841 (2010)CrossRefGoogle Scholar
  8. 8.
    Ehtamo, H., Kettunen, E., Hamalainen, R.P.: Searching for joint gains in multi-party negotiations. Eur. J. Oper. Res. 130(1), 54–69 (2001)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Gardiner, L., Vanderpooten, D.: Interactive multiple criteria procedures: some reflections. In: Climaco, J. (ed.) Multicriteria analysis, pp. 290–301. Springer, Berlin, Heidelberg (1997)CrossRefGoogle Scholar
  10. 10.
    Guerraggio, A., Molho, E.: The origins of quasi-concavity: a development between mathematics and economics. Hist. Math. 31(1), 62–75 (2004)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Janis, I.L., Mann, L.: Decision making: a psychological analysis of conflict, choice and commitment. The Free Press, New York (1977)Google Scholar
  12. 12.
    Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–291 (1979)MATHCrossRefGoogle Scholar
  13. 13.
    Kaliszewski, I.: Out of the mist-towards decision-maker-friendly multiple criteria decision making support. Eur. J. Oper. Res. 158(2), 293–307 (2004)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Keeney, R.: Value-focused thinking. A path to creative decisionmaking. Harvard University Press, Cambridge (1996)Google Scholar
  15. 15.
    Korhonen, P., Wallenius, J.: Behavioural issues in MCDM: neglected research questions. J. Multi Crit. Decis. Anal. 5, 178–182 (1996)CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    Luque, M., Ruiz, F., Miettinen, K.: Global formulation for interactive multiobjective optimization. OR Spectr. 33, 27–48 (2011)MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Miettinen, K.: Nonlinear multiobjective optimization. Kluwer Academic Publishers, Boston (1999)MATHGoogle Scholar
  19. 19.
    Miettinen, K.: Interactive nonlinear multiobjective procedures. In: Ehrgott, M., Gandibleux, X. (eds.) Multiple criteria optimization: state of the art annotated bibliographic surveys, pp. 227–276. Springer, Berlin (2002)Google Scholar
  20. 20.
    Miettinen, K., Hakanen, J.: Why use interactive multi-objective optimization in chemical process design? In: Rangaiah, G.P. (ed.) Multi-objective optimization: techniques and applications in chemical engineering. World Scientific, Singapore (2009)Google Scholar
  21. 21.
    Miettinen, K., Ruiz, F., Wierzbicki, A.: Introduction to multiobjective optimization: interactive approaches. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective optimization: interactive and evolutionary approaches, pp. 27–57. Springer, Berlin, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Miettinen, K., Eskelinen, P., Ruiz, F., Luque, M.: NAUTILUS method: an interactive technique in multiobjective optimization based on the nadir point. Eur. J. Oper. Res. 206(2), 426–434 (2010)MATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Narula, S.C., Weistroffer, H.R.: A flexible method for nonlinear multicriteria decisionmaking problems. IEEE Trans. Syst. Man Cybern. 19(4), 883–887 (1989)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Podkopaev, D.: An approach to finding trade-off solutions by a linear transformation of objective functions. Control Cybern. 36(2), 347–356 (2007)MATHMathSciNetGoogle Scholar
  25. 25.
    Podkopaev, D., Miettinen, K.: Handling preferences in the “pre-conflicting” phase of decision making processes under multiple criteria. In: Brafman R., Roberts F., Tsoukias A. (eds.) Proceedings of Algorithmic decision theory: second international conference, ADT 2011, pp. 234–246. Springer, Berlin, Heidelberg (2011)Google Scholar
  26. 26.
    Ruiz, F., Luque, M., Miettinen, K.: Improving the computational efficiency of a global formulation (GLIDE) for interactive multiobjective optimization. Ann. Oper. Res. 197(1), 47–70 (2012)MATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    Simon, H.A.: Rational choice and the structure of the environment. Psychol. Rev. 63(2), 129–138 (1956)CrossRefGoogle Scholar
  28. 28.
    Szczepanski, M., Wierzbicki, A.P.: Application of multiple criterion evolutionary algorithm to vector optimization, decision support and reference point approaches. J. Telecommun. Inf. Technol. 3, 16–33 (2003)Google Scholar
  29. 29.
    Tsay, C.-J., Bazerman, M.H.: A decision-making perspective to negotiation: a review of the past and a look to the future. Negot. J. 25(4), 467–480 (2009)CrossRefGoogle Scholar
  30. 30.
    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, Berlin, Heidelberg (1980)CrossRefGoogle Scholar
  31. 31.
    Wierzbicki, A.P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectr. 8, 73–87 (1986)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Kaisa Miettinen
    • 1
  • Dmitry Podkopaev
    • 2
    • 3
  • Francisco Ruiz
    • 4
  • Mariano Luque
    • 4
  1. 1.University of Jyvaskyla, Department of Mathematical Information TechnologyUniversity of JyvaskylaFinland
  2. 2.University of Jyvaskyla, Department of Biology and Environmental ScienceUniversity of JyvaskylaFinland
  3. 3.Department of Intelligent SystemsSystem Research Institute of the Polish Academy of ScienceWarsawPoland
  4. 4.Department of Applied Economics (Mathematics)Universidad de MálagaMálagaSpain

Personalised recommendations