Fuzzy Multi-Objective Optimization

  • Freerk A. Lootsma
Part of the Applied Optimization book series (APOP, volume 8)


Many features of real-life single-objective optimization problems are imprecise. The values of the coefficients are sometimes merely prototypical, the requirement that the constraints must be satisfied may be somewhat relaxed, and the decision makers are not always very satisfied with the value attained by the objective function. Multi-Objective Optimization introduces a new feature: the degrees of satisfaction with the objective-function values play a major role because they enable the decision makers to control the convergence towards an acceptable compromise solution. Since the objective functions have different weights for the decision maker we also have to control the computational process via weighted degrees of satisfaction.


Objective Function Fuzzy Logic Indifference Curve Nondominated Solution Weighted Degree 
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.

References to Chapter 7

  1. 1.
    Athan, T.W., “A Quasi-Monte Carlo Method for Midticriteria Optimization”. Ph.D. Thesis, Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan 48109, 1994.Google Scholar
  2. 2.
    Benayoun, R., Montgolfier, J. de, Tergny, J., and Larichev, O., “Linear Programming with Multiple Objective Functions: STEP Method”. Mathematical Programming 1, 366–375, 1971.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Chankong, V., and Haimes, Y.Y., “Muliobjective Decision Making”. North-Holland, Amsterdam, 1983.Google Scholar
  4. 4.
    Eschenauer, H., Koski, J., and Osyczka, A. (eds.), “Multicriteria Design Optimization”. Springer, Berlin, 1990.zbMATHGoogle Scholar
  5. 5.
    Geoffrion, A.M., “Proper Efficiency and the Theory of Vector Maximization”. Journal of Mathematical Analysis and Applications 22, 618–630, 1986.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hwang, C.L., and Yoon, K., “Multiple Attribute Decision Making”. Springer, Berlin, 1981.zbMATHCrossRefGoogle Scholar
  7. 7.
    Kok, M., “Conflict Analysis via Multiple Objective Programming”. Ph.D. Thesis, Faculty of Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands, 1986.Google Scholar
  8. 8.
    Kok, M., and Lootsma, F.A., “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.zbMATHCrossRefGoogle Scholar
  9. 9.
    Koski, J., “Multicriterion Structural Optimization”. In H. Adeli (ed.), “Advances in Design Optimization”. Chapman & Hall, London, 1994, pp. 194–221.Google Scholar
  10. 10.
    Lewandowski, A., and Grauer, M., “The Reference Point Optimization Approach”. In M. Grauer, A. Lewandowski, and A.P. Wierzbicki (eds.), “Multiobjective and Stochastic Optimization”. IIASA, Laxenburg, Austria, 1982, pp. 353–376.Google Scholar
  11. 11.
    Lootsma, FA., “Optimization with Multiple Objectives”. In M. Iri and K. Tanabe (eds.), “Mathematical Programming, Recent Developments and Applications”. KTK Scientific Publishers, Tokyo, 1989, pp. 333–364.Google Scholar
  12. 12.
    Lootsma, F.A., Athan, T.W., and Papalambros, P.Y., “Controlling the Search for a Compromise Solution in Multi-Objective Optimization”. Engineering Optimization 25, 65–81, 1995.CrossRefGoogle Scholar
  13. 13.
    Osyczka, A., “Multicriterion Optimization in Engineering”. Wiley, New York, 1984.Google Scholar
  14. 14.
    Papalambros, P.Y., and Wilde, D.J., “Principles of Optimal Design”. Cambridge University Press, Cambridge, UK, 1988.zbMATHGoogle Scholar
  15. 15.
    Schittkowski, K., “NLPQL, a FORTRAN Subroutine for Solving Constrained Nonlinear Programming Problems”. Annals of Operations Research 5, 485–500, 1986.MathSciNetGoogle Scholar
  16. 16.
    Steuer, R.E., “On Sampling the Efficient Set using Weighted Tchebycheff Metrics”. In M. Grauer, A. Lewandowski, and A.P. Wierzbicki (eds), “Multiobjective and Stochastic Optimization”. IIASA, Laxenburg, Austria, 1982, pp. 335–352.Google Scholar
  17. 17.
    Steuer, R.E., “Multiple Criteria Optimization Theory, Computation, and Application”. Wiley, New York, 1986.zbMATHGoogle Scholar
  18. 18.
    Stevens, S.S., “On the Psycho-Physical Law”. Psychological Review 34, 273–286, 1957.Google Scholar
  19. 19.
    Wierzbicki, A.P., “A Mathematical Basis for Satisficing Decision Making”. WP-80–90, IIASA, Laxenburg, Austria, 1980.Google Scholar
  20. 20.
    Yu, P.L., and Zeleny, M, “The Set of All Nondominated Solutions in Linear Cases and a Multicriteria Simplex Method”. Journal of Mathematical Analysis and Applications 49,430–468, 1975.MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Zeleny, M., “Linear Multi-Objective Programming”. Springer, Berlin, 1974.CrossRefGoogle Scholar
  22. 22.
    Zeleny, M., “Multiple Criteria Decision Making”. McGraw-Hill, New York, 1982.zbMATHGoogle Scholar
  23. 23.
    Zionts, S, and Wallenius, J, “An Interactive Programming Method for Solving the Multiple Criteria Problem”. Management Science 22, 652–663, 1976.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Freerk A. Lootsma
    • 1
  1. 1.Delft University of TechnologyThe Netherlands

Personalised recommendations