Skip to main content

Introduction to Multiobjective Optimization: Noninteractive Approaches

  • Chapter
Multiobjective Optimization

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

Abstract

We give an introduction to nonlinear multiobjective optimization by covering some basic concepts as well as outlines of some methods. Because Pareto optimal solutions cannot be ordered completely, we need extra preference information coming from a decision maker to be able to select the most preferred solution for a problem involving multiple conflicting objectives. Multiobjective optimization methods are often classified according to the role of a decision maker in the solution process. In this chapter, we concentrate on noninteractive methods where the decision maker either is not involved or specifies preference information before or after the actual solution process. In other words, the decision maker is not assumed to devote too much time in the solution process.

Reviewed by: Nirupam Chakraborti, Indian Institute of Technology, India; Hirotaka Nakayama, Konan University, Japan; Roman Słowiński, Poznan University of Technology, Poland

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ballestero, E., Romero, C.: A theorem connecting utility function optimization and compromise programming. Operations Research Letters 10(7), 421–427 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Benayoun, R., de Montgolfier, J., Tergny, J., Laritchev, O.: Programming with multiple objective functions: Step method (STEM). Mathematical Programming 1(3), 366–375 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  • Benson, H.P.: Existence of efficient solutions for vector maximization problems. Journal of Optimization Theory and Application 26(4), 569–580 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • Benson, H.P.: Vector maximization with two objective functions. Journal of Optimization Theory and Applications 28(3), 253–257 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • Censor, Y.: Pareto optimality in multiobjective problems. Applied Mathematics and Optimization 4(1), 41–59 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  • Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making: Theory and Methodology. Elsevier Science Publishing, New York (1983)

    MATH  Google Scholar 

  • Charnes, A., Cooper, W.W.: Management Models and Industrial Applications of Linear Programming, vol. 1. Wiley, New York (1961)

    MATH  Google Scholar 

  • Charnes, A., Cooper, W.W.: Goal programming and multiple objective optimization; part 1. European Journal of Operational Research 1(1), 39–54 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  • Charnes, A., Cooper, W.W., Ferguson, R.O.: Optimal estimation of executive compensation by linear programming. Management Science 1(2), 138–151 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  • Cohon, J.L.: Multicriteria programming: Brief review and application. In: Gero, J.S. (ed.) Design Optimization, pp. 163–191. Academic Press, London (1985)

    Chapter  Google Scholar 

  • Das, I., Dennis, J.E.: A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural Optimization 14(1), 63–69 (1997)

    Article  Google Scholar 

  • Deb, K., Chaudhuri, S., Miettinen, K.: Towards estimating nadir objective vector using evolutionary approaches. In: Keijzer, M., et al. (eds.) Proceedings of the 8th Annual Genetic and Evolutionary Computation Conference (GECCO-2006), Seattle, vol. 1, pp. 643–650. ACM Press, New York (2006)

    Google Scholar 

  • deNeufville, R., McCord, M.: Unreliable measurement of utility: Significant problems for decision analysis. In: Brans, J.P. (ed.) Operational Research ’84, pp. 464–476. Elsevier, Amsterdam (1984)

    Google Scholar 

  • Edgeworth, F.Y.: Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences. C. Kegan Paul & Co., London (1881), University Microfilms International (Out-of-Print Books on Demand) (1987)

    MATH  Google Scholar 

  • Fandel, G.: Group decision making: Methodology and applications. In: Bana e Costa, C. (ed.) Readings in Multiple Criteria Decision Aid, pp. 569–605. Berlin (1990)

    Google Scholar 

  • Fishburn, P.C.: Lexicographic orders, utilities and decision rules: A survey. Management Science 20(11), 1442–1471 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • Flavell, R.B.: A new goal programming formulation. Omega 4(6), 731–732 (1976)

    Article  Google Scholar 

  • Gass, S., Saaty, T.: The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly 2, 39–45 (1955)

    Article  MathSciNet  Google Scholar 

  • Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications 22(3), 618–630 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  • Haimes, Y.Y., Lasdon, L.S., Wismer, D.A.: On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man, and Cybernetics 1, 296–297 (1971)

    MathSciNet  MATH  Google Scholar 

  • Hwang, C.-L., Lin, M.-J.: Group Decision Making under Multiple Criteria: Methods and Applications. Springer, New York (1987)

    Book  MATH  Google Scholar 

  • Hwang, C.L., Masud, A.S.M.: Multiple Objective Decision Making – Methods and Applications: A State-of-the-Art Survey. Springer, Berlin (1979)

    Book  MATH  Google Scholar 

  • Ignizio, J.P.: Introduction to Linear Goal Programming. Sage Publications, Beverly Hills (1985)

    Book  MATH  Google Scholar 

  • Jahn, J.: Vector Optimization. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  • Jones, D.F., Tamiz, M., Mirrazavi, S.K.: Intelligent solution and analysis of goal programmes: the GPSYS system. Decision Support Systems 23(4), 329–332 (1998)

    Article  Google Scholar 

  • Kaliszewski, I.: Quantitative Pareto Analysis by Cone Separation Technique. Kluwer, Dordrecht (1994)

    Book  MATH  Google Scholar 

  • Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, Chichester (1976)

    MATH  Google Scholar 

  • Koopmans, T.: Analysis and production as an efficient combination of activities. In: Koopmans, T. (ed.) Activity Analysis of Production and Allocation: Proceedings of a Conference, pp. 33–97. Wiley, New York (1951), Yale University Press, London (1971)

    Google Scholar 

  • Korhonen, P., Salo, S., Steuer, R.E.: A heuristic for estimating nadir criterion values in multiple objective linear programming. Operations Research 45(5), 751–757 (1997)

    Article  MATH  Google Scholar 

  • Kuhn, H., Tucker, A.: Nonlinear programming. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. University of California Press, Berkeley (1951)

    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 

  • Luc, D.T.: Theory of Vector Optimization. Springer, Berlin (1989)

    Book  Google Scholar 

  • Luque, M., Miettinen, K., Eskelinen, P., Ruiz, F.: Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega 37(2), 450–462 (2009)

    Article  Google Scholar 

  • Makarov, E.K., Rachkovski, N.N.: Unified representation of proper efficiency by means of dilating cones. Journal of Optimization Theory and Applications 101(1), 141–165 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Marler, R., Arora, J.: Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization 26(6), 369–395 (2004)

    Article  MathSciNet  MATH  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., Kaario, K.: Experiments with classification-based scalarizing functions in interactive multiobjective optimization. European Journal of Operational Research 175(2), 931–947 (2006)

    Article  MATH  Google Scholar 

  • Miettinen, K., Molina, J., González, M., Hernández-Díaz, A., Caballero, R.: Using box indices in supporting comparison in multiobjective optimization. European Journal of Operational Research, to appear (2008), doi:10.1016/j.ejor.2008.05.103

    Google Scholar 

  • Pareto, V.: Cours d’Economie Politique. Rouge, Lausanne (1896)

    Google Scholar 

  • Pareto, V.: Manuale di Economia Politica. Piccola Biblioteca Scientifica, Milan (1906), Translated into English by Schwier, A.S., Manual of Political Economy, MacMillan, London (1971)

    Google Scholar 

  • Podinovski, V.V.: Criteria importance theory. Mathematical Social Sciences 27(3), 237–252 (1994)

    Article  MathSciNet  Google Scholar 

  • Rodríguez Uría, M., Caballero, R., Ruiz, F., Romero, C.: Meta-goal programming. European Journal of Operational Research 136(2), 422–429 (2002)

    Article  MATH  Google Scholar 

  • Romero, C.: Handbook of Critical Issues in Goal Programming. Pergamon Press, Oxford (1991)

    MATH  Google Scholar 

  • Rommelfanger, H., Slowinski, R.: Fuzzy linear programming with single or multiple objective functions. In: Slowinski, R. (ed.) Fuzzy Sets in Decision Analysis, Operations Research and Statistics, pp. 179–213. Kluwer Academic Publishers, Boston (1998)

    Chapter  Google Scholar 

  • Rosenthal, R.E.: Principles of Multiobjective Optimization. Decision Sciences 16(2), 133–152 (1985)

    Article  Google Scholar 

  • Roy, B., Mousseau, V.: A theoretical framework for analysing the notion of relative importance of criteria. Journal of Multi-Criteria Decision Analysis 5(2), 145–159 (1996)

    Article  MATH  Google Scholar 

  • Ruzika, S., Wiecek, M.M.: Approximation methods in multiobjective programming. Journal of Optimization Theory and Applications 126(3), 473–501 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Orlando (1985)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Tanner, L.: Selecting a text-processing system as a qualitative multiple criteria problem. European Journal of Operational Research 50(2), 179–187 (1991)

    Article  Google Scholar 

  • Vincke, P.: Multicriteria Decision-Aid. Wiley, Chichester (1992)

    MATH  Google Scholar 

  • Weistroffer, H.R.: Careful usage of pessimistic values is needed in multiple objectives optimization. Operations Research Letters 4(1), 23–25 (1985)

    Article  MATH  Google Scholar 

  • Wierzbicki, A.P.: A mathematical basis for satisficing decision making. Mathematical Modelling 3, 391–405 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  • Wierzbicki, A.P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectrum 8(2), 73–87 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • 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, Boston (1999)

    Google Scholar 

  • Wierzbicki, A.P.: Reference point methodology. In: Wierzbicki, A.P., Makowski, M., Wessels, J. (eds.) Model-Based Decision Support Methodology with Environmental Applications, pp. 71–89. Kluwer Academic Publishers, Dordrecht (2000)

    Chapter  Google Scholar 

  • Yu, P.L.: A class of solutions for group decision problems. Management Science 19(8), 936–946 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh, L.: Optimality and non-scalar-valued performance criteria. IEEE Transactions on Automatic Control 8, 59–60 (1963)

    Article  Google Scholar 

  • Zeleny, M.: Compromise programming. In: Cochrane, J.L., Zeleny, M. (eds.) Multiple Criteria Decision Making, pp. 262–301. University of South Carolina, Columbia, SC (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Miettinen, K. (2008). Introduction to Multiobjective Optimization: Noninteractive Approaches. 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_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88908-3_1

  • 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