Skip to main content
Springer Nature Link
Log in

Trade-off analysis approach for interactive nonlinear multiobjective optimization

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off analysis approach that can be connected to various multiobjective optimization methods utilizing a certain type of scalarization to produce Pareto optimal solutions. With this approach, the DM can conveniently learn about local trade-offs between the conflicting objectives and judge whether they are acceptable. The approach is based on an idea where the DM is able to make small changes in the components of a selected Pareto optimal objective vector. The resulting vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set located at the Pareto optimal solution selected. The obtained approximate Pareto optimal solutions can be used to study trade-off information. The approach is especially useful when trade-off analysis must be carried out without increasing computation workload. We demonstrate the usage of the approach through an academic example problem.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chankong V, Haimes YY (1977) The interactive surrogate worth trade-off (ISWT) method for multiobjective decision making. In: Zionts S (eds) Multiple criteria problem solving, vol 155. Springer, Berlin, pp 42–67

    Google Scholar 

  • Chankong V, Haimes YY (1983) Multiobjective decision making theory and methodology. Elsevier Science Publishing Co., Inc., New York

    Google Scholar 

  • Kuk H, Tanino T, Tanaka M (1997) Trade-off analysis for vector optimization problems via scalarization. J Inf Optim Sci 18: 75–87

    Google Scholar 

  • Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, Boston

    Google Scholar 

  • 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 137–150

    Google Scholar 

  • Miettinen K, Mäkelä MM (2006) Synchronous approach in interactive multiobjective optimization. Eur J Oper Res 170(3): 909–922

    Article  Google Scholar 

  • Miettinen K, Ruiz F, Wierzbicki AP (2008) Introduction to multiobjective optimization: interactive approaches. In: Branke J, Deb K, Miettinen K, Slowinski R (eds) Multiobjective optimization: interactive and evolutionary approaches. Springer, Berlin, pp 27–57

    Google Scholar 

  • Nakayama H, Sawaragi Y (1984) Satisficing trade-off method for multiobjective programming. In: Grauer M, Wierzbicki AP (eds) Interactive decision analysis. Springer, New York, pp 113–122

    Google Scholar 

  • Nocedal J, Wright SJ (2006) Numerical Optimization, 2nd edn. Springer, New York

    Google Scholar 

  • Sakawa M (1982) Interactive multiobjective decision making by the sequential proxy optimization technique: SPOT. Eur J Oper Res 9: 386–396

    Article  Google Scholar 

  • Sakawa M, Yano H (1990) Trade-off rates in the hyperplane method for multiobjective optimization problems. Eur J Oper Res 44: 105–118

    Article  Google Scholar 

  • Sindhya K, Deb K, Miettinen K (2011) Improving convergence of evolutionary multi-objective optimization with local search: a concurrent hybrid algorithm. Nat Comput. doi:10.1007/s11047-011-9250-4

  • Tappeta RV, Renaud JE (1999) Interactive multiobjective optimization procedure. AIAA J 37: 881–889

    Article  Google Scholar 

  • Wierzbicki AP (1986) On completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spektrum 8: 73–87

    Article  Google Scholar 

  • Yang J-B (1999) Gradient projection and local region search for multiobjective optimisation. Eur J Oper Res 112: 432–459

    Article  Google Scholar 

  • Yang J-B, Li D (2002) Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimization. IEEE Trans Syst Man Cybern Part A: Syst Hum 32(3): 305–319

    Article  Google Scholar 

  • Yano H, Sakawa M (1987) Trade-off rates in the weighted Tchebycheff norm method. Large Scale Syst 13: 167–177

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Petri Eskelinen & Kaisa Miettinen

Authors
  1. Petri Eskelinen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaisa Miettinen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kaisa Miettinen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eskelinen, P., Miettinen, K. Trade-off analysis approach for interactive nonlinear multiobjective optimization. OR Spectrum 34, 803–816 (2012). https://doi.org/10.1007/s00291-011-0266-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-011-0266-z

Keywords

Search

Navigation