OR Spectrum

, Volume 33, Issue 1, pp 27–48 | Cite as

Global formulation for interactive multiobjective optimization

Regular Article


Interactive methods are useful and realistic multiobjective optimization techniques and, thus, many such methods exist. However, they have two important drawbacks when using them in real applications. Firstly, the question of which method should be chosen is not trivial. Secondly, there are rather few practical implementations of the methods. We introduce a general formulation that can accommodate several interactive methods. This provides a comfortable implementation framework for a general interactive system. Besides, this implementation allows the decision maker to choose how to give preference information to the system, and enables changing it anytime during the solution process. This change-of-method option provides a very flexible framework for the decision maker.


Multiple criteria decision making Multiple objectives Interactive methods Preference information 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Benayoun R, de Montgolfier J, Tergny J, Laritchev O (1971) Programming with multiple objective functions: step method (STEM). Math Program 1(3): 366–375CrossRefGoogle Scholar
  2. Buchanan JT (1997) A naïve approach for solving MCDM problems: the GUESS method. J Oper Res Soc 48(2): 202–206Google Scholar
  3. Caballero R, Luque M, Molina J, Ruiz F (2002) PROMOIN: an interactive system for multiobjective programming. Int J Inform Technol Decis Making 1: 635–656CrossRefGoogle Scholar
  4. Chankong V, Haimes YY (1983) Multiobjective decision making: theory and methodology. North-Holland, New YorkGoogle Scholar
  5. Eschenauer HA, Osyczka A, Schäfer E (1990) Interactive multicriteria optimization in design process. In: Eschenauer H, Koski J, Osyczka A (eds) Multicriteria design optimization procedures and applications. Springer, Berlin, pp 71–114Google Scholar
  6. Gardiner L, Steuer RE (1994a) Unified interactive multiple objective programming. Eur J Oper Res 74(3): 391–406CrossRefGoogle Scholar
  7. Gardiner L, Steuer RE (1994b) Unified interactive multiple objective programming: an open architecture for accommodating new procedures. J Oper Res Soc 45(12): 1456–1466Google Scholar
  8. Hwang CL, Masud ASM (1979) Multiple objective decision making—methods and applications: a state-of-the-art survey. Springer, BerlinGoogle Scholar
  9. Jaszkiewicz A, Slowiński R (1999) The ‘light beam search’ approach—an overview of methodology and applications. Eur J Oper Res 113: 300–314CrossRefGoogle Scholar
  10. Kaliszewski I (2004) Out of the mist—towards decision-maker-friendly multiple criteria decision making support. Eur J Oper Res 158: 293–307CrossRefGoogle Scholar
  11. Klamroth K, Miettinen K (2008) Integrating approximation and interactive decision making in multicriteria optimization. Oper Res 56(1): 222–234CrossRefGoogle Scholar
  12. Luque M, Caballero R, Molina J, Ruiz F (2007) Equivalent information for multiobjective interactive procedures. Manage Sci 53(1): 125–134CrossRefGoogle Scholar
  13. Luque M, Yang JB, Wong BYH (2008) PROJECT method for multiobjective optimisation based on gradient projection and reference point. IEEE Trans Syst Man Cybern—Part A (to appear)Google Scholar
  14. Luque M, Miettinen K, Eskelinen P, Ruiz F (2009) Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega 37(2): 450–462CrossRefGoogle Scholar
  15. Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonGoogle Scholar
  16. Miettinen K (2006) IND-NIMBUS for demanding interactive multiobjective optimization. In: Trzaskalik T (eds) Multiple Criteria Decision Making ’05. The Karol Adamiecki University of Economics in Katowice, Katowice, pp 137–150Google Scholar
  17. Miettinen K, Mäkelä MM (1995) Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. Optimization 34(3): 231–246CrossRefGoogle Scholar
  18. Miettinen K, Mäkelä MM (1997) Interactive method NIMBUS for nondifferentiable multiobjective optimization problems. In: Climaco J (eds) Multicriteria analysis. Springer, Berlin, pp 310–319Google Scholar
  19. Miettinen K, Mäkelä MM (1999) Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation. J Oper Res Soc 50(9): 949–959Google Scholar
  20. Miettinen K, Mäkelä MM (2000) Interactive multiobjective optimization system WWW-NIMBUS on the Internet. Comput Oper Res 27(7–8): 709–723CrossRefGoogle Scholar
  21. Miettinen K, Mäkelä MM (2002) On scalarizing functions in multiobjective optimization. OR Spectr 24(2): 193–213CrossRefGoogle Scholar
  22. Miettinen K, Mäkelä MM (2006) Synchronous approach in interactive multiobjective optimization. Eur J Oper Res 170(3): 909–922CrossRefGoogle Scholar
  23. Miettinen K, Mäkelä MM, Kaario K (2006) Experiments with classification-based scalarizing functions in interactive multiobjective optimization. Eur J Oper Res 175(2): 931–947CrossRefGoogle Scholar
  24. 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
  25. Narula SC, Weistroffer HR (1989) A flexible method for nonlinear multicriteria decisionmaking problems. IEEE Trans Syst Man Cybern 19(4): 883–887CrossRefGoogle Scholar
  26. Romero C (2001) Extended lexicographic goal programming: a unified approach. Omega 29: 63–71CrossRefGoogle Scholar
  27. Sakawa M (1982) Interactive multiobjective decision making by the sequential proxy optimization technique: SPOT. Eur J Oper Res 9(4): 386–396CrossRefGoogle Scholar
  28. Sawaragi Y, Nakayama H, Tanino T (1985) Theory of multiobjective optimization. Academic Press, OrlandoGoogle Scholar
  29. Steuer RE (1986) Multiple criteria optimization: theory, computation and applicationGoogle Scholar
  30. Steuer RE, Choo EU (1983) An interactive weighted Tchebycheff procedure for multiple objective programming. Math Program 26: 326–344CrossRefGoogle Scholar
  31. Vassileva M, Miettinen K, Vassilev V (2005) Generalized scalarizing problem for multicriteria optimization. IIT Working Papers IIT/WP-205, Institute of Information Technologies, BulgariaGoogle Scholar
  32. Wierzbicki AP (1980) The use of reference objectives in multiobjective optimization. In: Fandel G, Gal T (eds) Multiple criteria decision making, theory and applications. Springer, Berlin, pp 468–486Google Scholar
  33. Wierzbicki AP (1986) On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectr 8(2): 73–87Google Scholar
  34. Yang JB (1999) Gradient projection and local region search for multiobjective optimization. Eur J Oper Res 112: 432–459CrossRefGoogle Scholar
  35. Yang JB, Li D (2002) Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimisation. IEEE Trans Syst Man Cybern A Syst Humans 32(3): 305–319CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Mariano Luque
    • 1
  • Francisco Ruiz
    • 1
  • Kaisa Miettinen
    • 2
  1. 1.University of MálagaMálagaSpain
  2. 2.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland

Personalised recommendations