Skip to main content
Springer Nature Link
Log in

Visualization in the Multiple Objective Decision-Making Framework

  • Chapter
Multiobjective Optimization

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5252))

Abstract

In this paper we describe various visualization techniques which have been used or which might be useful in the multiple objective decision making framework. Several of the ideas originate from statistics, especially multivariate statistics. Some techniques are simply for illustrating snapshots of a single solution or a set of solutions. Others are used as an essential part of the human-computer interface.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Andrews, D.: Plots of high dimensional data. Biometrics 28, 125–136 (1972)

    Article  Google Scholar 

  • Belton, V., Stewart, T.J.: Multiple Criteria Decision Analysis: An Integrated Approach. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  • Bowerman, B.L., O’Connell, R.T., Orris, J.B.: Essentials in Business Statistics. McGraw-Hill, New York (2004)

    Google Scholar 

  • Chernoff, H.: Using faces to represent points in k-dimensional space graphically. Journal of American Statistical Association 68, 361–368 (1973)

    Article  Google Scholar 

  • Cohon, J.L.: Multiobjective Programming and Planning. Academic Press, New York (1978)

    MATH  Google Scholar 

  • Everitt, B.: Graphical Techniques for Multivariate Data. Heinemann Educational Books, London (1978)

    Google Scholar 

  • Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annual Eugenics 7, 179–188 (1936)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Grauer, M.: Reference point optimization – the nonlinear case. In: Hansen, P. (ed.) Essays and Surveys on Multiple Criteria Decision Making, vol. 209, pp. 126–135. Springer, Berlin (1983)

    Chapter  Google Scholar 

  • Grauer, M., Lewandowski, A., Wierzbicki, A.: DIDASS – theory, implementation and experiences. In: Grauer, M., Wierzbicki, A. (eds.) Interactive Decision Analysis, vol. 229, pp. 22–30. Springer, Berlin (1984)

    Chapter  Google Scholar 

  • Hämäläinen, R.P.: Reversing the perspective on the applications of decision analysis. Decision Analysis 1, 26–31 (2004)

    Article  Google Scholar 

  • Huff, D.: How to Lie with Statistics. Norton, New York (1954)

    Google Scholar 

  • Jacquet-Lagreze, E., Siskos, J.: Assessing a set of additive utility functions for multicriteria decision making, the uta method. European Journal of Operational Research 10, 151–164 (1982)

    Article  MATH  Google Scholar 

  • Kok, M., Lootsma, F.: Pairwise-comparison methods in multiple objective programming, with applications in a long-term energy-planning model. European Journal of Operational Research 22, 44–55 (1985)

    Article  MATH  Google Scholar 

  • Korhonen, P.: VIG: A Visual Interactive Support System for Multiple Criteria Decision Making. Belgian Journal of Operations Research, Statistics and Computer Science 27, 3–15 (1987)

    Google Scholar 

  • Korhonen, P.: A visual reference direction approach to solving discrete multiple criteria problems. European Journal of Operational Research 34, 152–159 (1988)

    Article  Google Scholar 

  • Korhonen, P.: Using harmonious houses for visual pairwise comparison of multiple criteria alternatives. Decision Support Systems 7, 47–54 (1991)

    Article  Google Scholar 

  • Korhonen, P., Karaivanova, J.: An algorithm for projecting a reference direction onto the nondominated set of given points. IEEE Transactions on Systems, Man, and Cybernetics 29, 429–435 (1999)

    Article  Google Scholar 

  • Korhonen, P., Laakso, J.: A visual interactive method for solving the multiple criteria problem. European Journal of Operational Research 24, 277–287 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Korhonen, P., Wallenius, J.: A Pareto race. Naval Research Logistics 35, 615–623 (1988)

    Article  MATH  Google Scholar 

  • Korhonen, P., Wallenius, J., Zionts, S.: A bargaining model for solving the multiple criteria problem. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Application, pp. 178–188. Springer, Berlin (1980)

    Chapter  Google Scholar 

  • Levine, D.M., Krehbiel, T.C., Berenson, M.L.: Business Statistics: A First Course. Prentice-Hall, Englewood Cliffs (2006)

    MATH  Google Scholar 

  • Lotov, A.V., Bushenkov, V.A., Chernov, A.V., Gusev, D.V., Kamenev, G.K.: Internet, GIS and interactive decision maps. Journal of Geographic Information and Decision Analysis 1, 118–143 (1997)

    Google Scholar 

  • Lotov, A.V., Bushenkov, V.A., Kamenev, G.K.: Interactive Decision Maps. Approximation and Visualization of Pareto Frontier. Kluwer Academic Publishers, Boston (2004)

    Book  MATH  Google Scholar 

  • Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic Press, San Diego (1979)

    MATH  Google Scholar 

  • Mareschal, B., Brans, J.: Geometrical representations for mcda. European Journal of Operational Research 34, 69–77 (1988)

    Article  MathSciNet  Google Scholar 

  • Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston (1999)

    MATH  Google Scholar 

  • Miettinen, K.: Graphical illustration of Pareto optimal solutions. In: Tanino, T., Tanaka, T., Inuiguchi, M. (eds.) Multi-Objective Programming and Goal Programming: Theory and Applications, pp. 197–202. Springer, Berlin (2003)

    Chapter  Google Scholar 

  • Miettinen, K., Mäkelä, M.M.: Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. Optimization 34, 231–246 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Miettinen, K., Mäkelä, M.M.: Interactive multiobjective optimization system WWW-NIMBUS on the Internet. Computers & Operations Research 27, 709–723 (2000)

    Article  MATH  Google Scholar 

  • Miettinen, K., Mäkelä, M.M.: Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research 170, 909–922 (2006)

    Article  MATH  Google Scholar 

  • R Graph Gallery (2007), http://addictedtor.free.fr/graphiques/RGraphGallery.php?graph=47

  • Saaty, T.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)

    MATH  Google Scholar 

  • Salo, A., Hämäläinen, R.P.: Preference assessment by imprecise ratio statements. Operations Research 40, 1053–1061 (1992)

    Article  MATH  Google Scholar 

  • Schilling, D., Revelle, C., Cohon, J.: An approach to the display and analysis of multiobjective problems. Socio-Economic Planning Sciences 17, 57–63 (1983)

    Article  Google Scholar 

  • Silverman, J., Steuer, R.E., Whisman, A.: Computer graphics at the multicriterion computer/user interface. In: Haimes, Y., Chankong, V. (eds.) Decision Making with Multiple Objectives, vol. 242, pp. 201–213. Springer, Berlin (1985)

    Chapter  Google Scholar 

  • Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation, and Application. John Wiley and Sons, New York (1986)

    MATH  Google Scholar 

  • Wainer, H.: How to display data badly. The American Statistician 38, 137–147 (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Business Technology, Helsinki School of Economics, P.O. Box 1210, FI-00101, Helsinki, Finland

    Pekka Korhonen & Jyrki Wallenius

Authors
  1. Pekka Korhonen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jyrki Wallenius
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute AIFB, University of Karlsruhe, Germany

    Jürgen Branke

  2. Department of Business Technology, Helsinki School of Economics, P.O. Box 1210, FI-00101, Helsinki, Finland

    Kalyanmoy Deb

  3. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, (Agora), FI-40014, Finland

    Kaisa Miettinen

  4. Institute of Computing Science Poznan, University of Technology, 60-965, Poznan, Poland

    Roman Słowiński

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Korhonen, P., Wallenius, J. (2008). Visualization in the Multiple Objective Decision-Making Framework. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds) Multiobjective Optimization. Lecture Notes in Computer Science, vol 5252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88908-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88908-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88907-6

  • Online ISBN: 978-3-540-88908-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics