Introduction to Multiobjective Optimization: Interactive Approaches

  • Kaisa Miettinen
  • Francisco Ruiz
  • Andrzej P. Wierzbicki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5252)


We give an overview of interactive methods developed for solving nonlinear multiobjective optimization problems. In interactive methods, a decision maker plays an important part and the idea is to support her/him in the search for the most preferred solution. In interactive methods, steps of an iterative solution algorithm are repeated and the decision maker progressively provides preference information so that the most preferred solution can be found. We identify three types of specifying preference information in interactive methods and give some examples of methods representing each type. The types are methods based on trade-off information, reference points and classification of objective functions.


Decision Maker Pareto Optimal Solution Interactive Method Aspiration Level Multiobjective Optimization Problem 
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. Benayoun, R., de Montgolfier, J., Tergny, J., Laritchev, O.: Programming with multiple objective functions: Step method (STEM). Mathematical Programming 1, 366–375 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Buchanan, J.T.: Multiple objective mathematical programming: A review. New Zealand Operational Research 14, 1–27 (1986)MathSciNetGoogle Scholar
  3. Buchanan, J.T.: A naïve approach for solving MCDM problems: The GUESS method. Journal of the Operational Research Society 48, 202–206 (1997)CrossRefzbMATHGoogle Scholar
  4. Chankong, V., Haimes, Y.Y.: The interactive surrogate worth trade-off (ISWT) method for multiobjective decision making. In: Zionts, S. (ed.) Multiple Criteria Problem Solving, pp. 42–67. Springer, Berlin (1978)CrossRefGoogle Scholar
  5. Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making. Theory and Methodology. North-Holland, New York (1983)zbMATHGoogle Scholar
  6. Ehrgott, M., Tenfelde-Podehl, D.: Nadir values: Computation and use in compromise programming. Technical report, Universität Kaiserslautern Fachbereich Mathematik (2000)Google Scholar
  7. Eschenauer, H.A., Osyczka, A., Schäfer, E.: Interactive multicriteria optimization in design process. In: Eschenauer, H., Koski, J., Osyczka, A. (eds.) Multicriteria Design Optimization Procedures and Applications, pp. 71–114. Springer, Berlin (1990)CrossRefGoogle Scholar
  8. Gardiner, L., Steuer, R.E.: Unified interactive multiobjective programming. European Journal of Operational Research 74, 391–406 (1994)CrossRefzbMATHGoogle Scholar
  9. Geoffrion, A.M., Dyer, J.S., Feinberg, A.: An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Management Science 19, 357–368 (1972)CrossRefzbMATHGoogle Scholar
  10. Haimes, Y.Y., Hall, W.A.: Multiobjectives in water resources systems analysis: the surrogate worth trade off method. Water Resources Research 10, 615–624 (1974)CrossRefGoogle Scholar
  11. Haimes, Y.Y., Tarvainen, K., Shima, T., Thadathil, J.: Hierarchical Multiobjective Analysis of Large-Scale Systems. Hemisphere Publishing Corporation, New York (1990)Google Scholar
  12. Hakanen, J., Miettinen, K., Mäkelä, M., Manninen, J.: On interactive multiobjective optimization with NIMBUS in chemical process design. Journal of Multi-Criteria Decision Analysis 13, 125–134 (2005)CrossRefzbMATHGoogle Scholar
  13. Hakanen, J., Kawajiri, Y., Miettinen, K., Biegler, L.: Interactive multi-objective optimization for simulated moving bed processes. Control and Cybernetics 36, 283–302 (2007)MathSciNetzbMATHGoogle Scholar
  14. Hämäläinen, J., Miettinen, K., Tarvainen, P., Toivanen, J.: Interactive solution approach to a multiobjective optimization problem in paper machine headbox design. Journal of Optimization Theory and Applications 116, 265–281 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  15. Heikkola, E., Miettinen, K., Nieminen, P.: Multiobjective optimization of an ultrasonic transducer using NIMBUS. Ultrasonics 44, 368–380 (2006)CrossRefGoogle Scholar
  16. Hwang, C.L., Masud, A.S.M.: Multiple Objective Decision Making – Methods and Applications: A State-of-the-Art Survey. Springer, Berlin (1979)CrossRefzbMATHGoogle Scholar
  17. Jaszkiewicz, A., Słowiński, R.: The ‘light beam search’ approach - an overview of methodology and applications. European Journal of Operational Research 113, 300–314 (1999)CrossRefzbMATHGoogle Scholar
  18. Kaliszewski, I.: Out of the mist–towards decision-maker-friendly multiple criteria decision support. European Journal of Operational Research 158, 293–307 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  19. Kaliszewski, I., Michalowski, W.: Searching for psychologically stable solutions of multiple criteria decision problems. European Journal of Operational Research 118, 549–562 (1999)CrossRefzbMATHGoogle Scholar
  20. Keeney, R.: Value Focused Thinking, a Path to Creative Decision Making. Harvard University Press, Harvard (1992)Google Scholar
  21. Keeney, R., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York (1976)zbMATHGoogle Scholar
  22. Klamroth, K., Miettinen, K.: Integrating approximation and interactive decision making in multicriteria optimization. Operations Research 56, 222–234 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  23. Korhonen, P.: Interactive methods. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis. State of the Art Surveys, pp. 641–665. Springer, New York (2005)CrossRefGoogle Scholar
  24. Korhonen, P., Laakso, J.: A visual interactive method for solving the multiple criteria problem. European Journal of Operational Research 24, 277–287 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  25. Korhonen, P., Wallenius, J.: Behavioural issues in MCDM: Neglected research questions. Journal of Multi-Criteria Decision Analysis 5, 178–182 (1996)CrossRefzbMATHGoogle Scholar
  26. Larichev, O.: Cognitive validity in design of decision aiding techniques. Journal of Multi-Criteria Decision Analysis 1, 127–138 (1992)CrossRefzbMATHGoogle Scholar
  27. Lewandowski, A., Wierzbicki, A.P.: Aspiration Based Decision Support Systems. Theory, Software and Applications. Springer, Berlin (1989)CrossRefzbMATHGoogle Scholar
  28. Lotov, A.V., Bushenkov, V.A., Kamenev, G.K.: Interactive Decision Maps. Approximation and Visualization of Pareto Frontier. Kluwer Academic Publishers, Boston (2004)CrossRefzbMATHGoogle Scholar
  29. Luque, M., Caballero, R., Molina, J., Ruiz, F.: Equivalent information for multiobjective interactive procedures. Management Science 53, 125–134 (2007a)CrossRefzbMATHGoogle Scholar
  30. Luque, M., Ruiz, F., Miettinen, K.: GLIDE – general formulation for interactive multiobjective optimization. Technical Report W-432, Helsinki School of Economics, Helsinki (2007b)Google Scholar
  31. Makowski, M.: Model-based decision making support for problems with conflicting goals. In: Proceedings of the 2nd International Symposium on System and Human Science, Lawrence Livermore National Laboratory, Livermore (2005)Google Scholar
  32. Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston (1999)zbMATHGoogle Scholar
  33. Miettinen, K.: IND-NIMBUS for demanding interactive multiobjective optimization. In: Trzaskalik, T. (ed.) Multiple Criteria Decision Making ’05, pp. 137–150. The Karol Adamiecki University of Economics, Katowice (2006)Google Scholar
  34. Miettinen, K., Kaario, K.: Comparing graphic and symbolic classification in interactive multiobjective optimization. Journal of Multi-Criteria Decision Analysis 12, 321–335 (2003)CrossRefzbMATHGoogle Scholar
  35. Miettinen, K., Kirilov, L.: Interactive reference direction approach using implicit parametrization for nonlinear multiobjective optimization. Journal of Multi-Criteria Decision Analysis 13, 115–123 (2005)CrossRefzbMATHGoogle Scholar
  36. Miettinen, K., Mäkelä, M.M.: Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. Optimization 34, 231–246 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  37. Miettinen, K., Mäkelä, M.M.: Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation. Journal of the Operational Research Society 50, 949–959 (1999)CrossRefzbMATHGoogle Scholar
  38. Miettinen, K., Mäkelä, M.M.: Interactive multiobjective optimization system WWW-NIMBUS on the Internet. Computers & Operations Research 27, 709–723 (2000)CrossRefzbMATHGoogle Scholar
  39. Miettinen, K., Mäkelä, M.M.: On scalarizing functions in multiobjective optimization. OR Spectrum 24, 193–213 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  40. Miettinen, K., Mäkelä, M.M.: Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research 170, 909–922 (2006)CrossRefzbMATHGoogle Scholar
  41. Miettinen, K., Mäkelä, M.M., Männikkö, T.: Optimal control of continuous casting by nondifferentiable multiobjective optimization. Computational Optimization and Applications 11, 177–194 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 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, 63–80 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  43. Miettinen, K., Mäkelä, M.M., Kaario, K.: Experiments with classification-based scalarizing functions in interactive multiobjective optimization. European Journal of Operational Research 175, 931–947 (2006)CrossRefzbMATHGoogle Scholar
  44. Nakayama, H.: Aspiration level approach to interactive multi-objective programming and its applications. In: Pardalos, P.M., Siskos, Y., Zopounidis, C. (eds.) Advances in Multicriteria Analysis, pp. 147–174. Kluwer Academic Publishers, Dordrecht (1995)CrossRefGoogle Scholar
  45. Nakayama, H., Sawaragi, Y.: Satisficing trade-off method for multiobjective programming. In: Grauer, M., Wierzbicki, A.P. (eds.) Interactive Decision Analysis, pp. 113–122. Springer, Heidelberg (1984)CrossRefGoogle Scholar
  46. Narula, S.C., Kirilov, L., Vassilev, V.: Reference direction approach for solving multiple objective nonlinear programming problems. IEEE Transactions on Systems, Man, and Cybernetics 24, 804–806 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  47. Ogryczak, W.: On multicriteria optimization with fair aggregation of individual achievements. In: CSM’06: 20th Workshop on Methodologies and Tools for Complex System Modeling and Integrated Policy Assessment, IIASA, Laxenburg, Austria (2006),
  48. Rawls, J.: A Theory of Justice. Belknap Press, Cambridge (1971)Google Scholar
  49. Saaty, T.: Decision Making for Leaders: the Analytical Hierarchy Process for Decisions in a Complex World. Lifetime Learning Publications, Belmont (1982)Google Scholar
  50. Sakawa, M.: Interactive multiobjective decision making by the sequential proxy optimization technique. European Journal of Operational Research 9, 386–396 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  51. Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Orlando (1985)zbMATHGoogle Scholar
  52. Shin, W.S., Ravindran, A.: Interactive multiple objective optimization: Survey I – continuous case. Computers & Operations Research 18, 97–114 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  53. Statnikov, R.B.: Multicriteria Design: Optimization and Identification. Kluwer Academic Publishers, Dordrecht (1999)CrossRefGoogle Scholar
  54. Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation, and Applications. Wiley, Chichester (1986)zbMATHGoogle Scholar
  55. Steuer, R.E.: The Tchebycheff procedure of interactive multiple objective programming. In: Karpak, B., Zionts, S. (eds.) Multiple Criteria Decision Making and Risk Analysis Using Microcomputers, pp. 235–249. Springer, Berlin (1989)CrossRefGoogle Scholar
  56. Steuer, R.E., Silverman, J., Whisman, A.W.: A combined Tchebycheff/aspiration criterion vector interactive multiobjective programming procedure. Management Science 39, 1255–1260 (1993)CrossRefzbMATHGoogle Scholar
  57. Stewart, T.J.: A critical survey on the status of multiple criteria decision making theory and practice. Omega 20, 569–586 (1992)CrossRefGoogle Scholar
  58. Tabucanon, M.T.: Multiple Criteria Decision Making in Industry. Elsevier Science Publishers, Amsterdam (1988)Google Scholar
  59. Tarvainen, K.: On the implementation of the interactive surrogate worth trade-off (ISWT) method. In: Grauer, M., Wierzbicki, A.P. (eds.) Interactive Decision Analysis, pp. 154–161. Springer, Berlin (1984)CrossRefGoogle Scholar
  60. Vanderpooten, D., Vincke, P.: Description and analysis of some representative interactive multicriteria procedures. Mathematical and Computer Modelling 12, 1221–1238 (1989)CrossRefGoogle Scholar
  61. Vassilev, V.S., Narula, S.C., Gouljashki, V.G.: An interactive reference direction algorithm for solving multi-objective convex nonlinear integer programming problems. International Transactions in Operational Research 8, 367–380 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  62. Vincke, P.: Multicriteria Decision-Aid. Wiley, Chichester (1992)zbMATHGoogle Scholar
  63. Wierzbicki, A.P.: Basic properties of scalarizing functionals for multiobjective optimization. Mathematische Operationsforschung und Statistik – Optimization 8, 55–60 (1977)MathSciNetCrossRefGoogle Scholar
  64. Wierzbicki, A.P.: The use of reference objectives in multiobjective optimization. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making, Theory and Applications, pp. 468–486. Springer, Berlin (1980)CrossRefGoogle Scholar
  65. Wierzbicki, A.P.: A mathematical basis for satisficing decision making. Mathematical Modeling 3, 391–405 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  66. Wierzbicki, A.P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectrum 8, 73–87 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  67. Wierzbicki, A.P.: On the role of intuition in decision making and some ways of multicriteria aid of intuition. Journal of Multi-Criteria Decision Analysis 6, 65–78 (1997)CrossRefzbMATHGoogle Scholar
  68. Wierzbicki, A.P.: Reference point approaches. In: Gal, T., Stewart, T.J., Hanne, T. (eds.) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications, pp. 9-1–9-39, Kluwer, Dordrecht (1999)Google Scholar
  69. Wierzbicki, A.P., Makowski, M., Wessels, J. (eds.): Decision Support Methodology with Environmental Applications. Kluwer Academic Publishers, Dordrecht (2000)zbMATHGoogle Scholar
  70. Yang, J.B.: Gradient projection and local region search for multiobjective optimisation. European Journal of Operational Research 112, 432–459 (1999)CrossRefzbMATHGoogle Scholar
  71. Yang, J.B., Li, D.: Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimisation. IEEE Transactions on Systems, Man and Cybernetics 32, 305–319 (2002)CrossRefGoogle Scholar
  72. Zionts, S., Wallenius, J.: An interactive programming method for solving the multiple criteria problem. Management Science 22, 652–663 (1976)CrossRefzbMATHGoogle Scholar
  73. Zionts, S., Wallenius, J.: An interactive multiple objective linear programming method for a class of underlying utility functions. Management Science 29, 519–529 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Kaisa Miettinen
    • 1
  • Francisco Ruiz
    • 2
  • Andrzej P. Wierzbicki
    • 3
    • 4
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläFinland
  2. 2.Department of Applied Economics (Mathematics)University of MálagaMálagaSpain
  3. 3.21st Century COE Program: Technology Creation Based on Knowledge Science, JAIST (Japan Advanced Institute of Science and Technology)Nomi, IshikawaJapan
  4. 4.National Institute of TelecommunicationsPoland

Personalised recommendations