On the Use of Preferential Weights in Interactive Reference Point Based Methods

  • Kaisa Miettinen
  • Petri Eskelinen
  • Mariano Luque
  • Francisco Ruiz
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 618)

Abstract

We introduce a new way of utilizing preference information specified by the decision maker in interactive reference point based methods. A reference point consists of aspiration levels for each objective function. We take the desires of the decision maker into account more closely when projecting the reference point to become nondominated. In this way we can support the decision maker in finding the most satisfactory solutions faster. In practice, we adjust the weights in the achievement scalarizing function that projects the reference point. We demonstrate our idea with an example and we summarize results of computational tests that support the efficiency of the idea proposed.

Keywords

Interactive methods Multiple objectives Multiobjective optimization Multiobjective programming Preferences Reference point methods 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benayoun R, de Montgolfier J, Tergny J, Laritchev O (1971) Linear programming with multiple objective functions: step method (STEM). Math Prog 1:366–375CrossRefGoogle Scholar
  2. 2.
    Buchanan JT (1997) A naïve approach for solving MCDM problems: the GUESS method. J Oper Res Soc 48:202–206CrossRefGoogle Scholar
  3. 3.
    Jaszkiewicz A, Slowiński R (1999) The ‘light beam search’ approach—an overview of methodology and applications. Eur J Oper Res 113:300–314CrossRefGoogle Scholar
  4. 4.
    Korhonen P, Laakso J (1986) A visual interactive method for solving the multiple criteria problem. Eur J Oper Res 24:277–287CrossRefGoogle Scholar
  5. 5.
    Luque M, Miettinen K, Eskelinen P, Ruiz F (2009) Incorporating Preference information in interactive reference point methods for multiobjective optimization. Omega 37: 450–462CrossRefGoogle Scholar
  6. 6.
    Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonGoogle Scholar
  7. 7.
    Miettinen K, Lotov AV, Kamenev GK, Berezkin VE (2003) Integration of two multiobjective optimization methods for nonlinear problems. Optim Meth Soft 18:63–80CrossRefGoogle Scholar
  8. 8.
    Miettinen K, Mäkelä MM (1995) Interactive bundle-based method for nondifferentiable mul-tiobjective optimization: NIMBUS. Optimization 34:231–246CrossRefGoogle Scholar
  9. 9.
    Miettinen K, Mäkelä MM (1999) Comparative evaluation of some interactive reference point based methods for multi-objective optimisation. J Oper Res Soc 50:949–959CrossRefGoogle Scholar
  10. 10.
    Miettinen K, Mäkelä MM (2002) On scalarizing functions in multiobjective optimization. OR Spectrum 24:193–213CrossRefGoogle Scholar
  11. 11.
    Miettinen K, Mäkelä MM (2006) Synchronous approach in interactive multiobjective optimization. Eur J Oper Res 170:909–922CrossRefGoogle Scholar
  12. 12.
    Miettinen K, Mäkelä MM, Kaario K (2006) Experiments with classification-based scalarizing functions in interactive multiobjective optimization. Eur J Oper Res 175:931–947CrossRefGoogle Scholar
  13. 13.
    Nakayama H, Sawaragi Y (1984) Satisficing Trade-off method for multiobjective programming. In: Grauer M, Wierzbicki AP (eds) Interactive decision analysis. Springer, Berlin, pp 113–122Google Scholar
  14. 14.
    Steuer RE (1986) Multiple criteria optimization: theory, computation, and application. Wiley, New YorkGoogle Scholar
  15. 15.
    Wierzbicki AP (1982) A Mathematical basis for satisficing decision making. Math Modell 3:391–405CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kaisa Miettinen
    • 1
  • Petri Eskelinen
    • 2
  • Mariano Luque
    • 3
  • Francisco Ruiz
    • 3
  1. 1.Department of Mathematical Information TechnologyFI-40014 University of JyväskyläFinland
  2. 2.Helsinki School of EconomicsHelsinkiFinland
  3. 3.University of MálagaMálagaSpain

Personalised recommendations