Computational Optimization and Applications

, Volume 58, Issue 3, pp 757–779 | Cite as

Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS

Article

Abstract

Interactive multiobjective optimization methods have provided promising results in the literature but still their implementations are rare. Here we introduce a core structure of interactive methods to enable their convenient implementation. We also demonstrate how this core structure can be applied when implementing an interactive method using a modeling environment. Many modeling environments contain tools for single objective optimization but not for interactive multiobjective optimization. Furthermore, as a concrete example, we present GAMS-NIMBUS Tool which is an implementation of the classification-based NIMBUS method for the GAMS modeling environment. So far, interactive methods have not been available in the GAMS environment, but with the GAMS-NIMBUS Tool we open up the possibility of solving multiobjective optimization problems modeled in the GAMS modeling environment. Finally, we give some examples of the benefits of applying an interactive method by using the GAMS-NIMBUS Tool for solving multiobjective optimization problems modeled in the GAMS environment.

Keywords

Multiple objective programming Interactive methods  NIMBUS method Modeling languages Pareto optimality 

Notes

Acknowledgments

The research was partly supported by the Academy of Finland, Grant number 128495 (on the part of Vesa Ojalehto).

Supplementary material

10589_2014_9639_MOESM1_ESM.gms (7 kb)
Supplementary material 1 (gms 6 KB)

References

  1. 1.
    Agrell, P.J., Lence, B.J., Stam, A.: An interactive multicriteria decision model for multipurpose reservoir management: the shellmouth reservoir. J. Multi-Criter. Decis. Anal. 7(2), 61–86 (1998)CrossRefMATHGoogle Scholar
  2. 2.
    Benayoun, R., de Montgolfier, J., Tergny, J., Laritchev, O.: Linear programming with multiple objective functions: step method (STEM). Math. Program. 1, 366–375 (1971)CrossRefMATHGoogle Scholar
  3. 3.
    Bisschop, J., Entriken, R.: AIMMS the Modeling System. Paragon Decision Technology, Haarlem (1993)Google Scholar
  4. 4.
    Branke, J., Deb, K., Miettinen, K., Slowiński R. (eds.): Multiobjective Optimization: Interactive and Evolutionary Approaches. Springer, Berlin (2008)Google Scholar
  5. 5.
    Brooke, A., Kendrick, D., Meeraus, A., Raman, R.: GAMS—A User’s Guide. GAMS Development Corporation, Washington (2008)Google Scholar
  6. 6.
    Buchanan, J.: A naive approach for solving MCDM problems: the GUESS method. J. Oper. Res. Soc. 48(2), 202–206 (1997)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. North-Holland, New York (1983)MATHGoogle Scholar
  8. 8.
    Deb, K., Miettinen, K., Chaudhuri, S.: Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Trans. Evol. Comput. 14(6), 821–841 (2010)CrossRefGoogle Scholar
  9. 9.
    Eskelinen, P., Miettinen, K., Klamroth, K., Hakanen, J.: Pareto Navigator for interactive nonlinear multiobjective optimization. OR Spectrum 32(1), 211–227 (2010)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Fourer, R., Gay, D.M., Kerninghan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Boyd & Fraser Publishing Company, San Francisco (1993)Google Scholar
  11. 11.
    Hakanen, J., Hakala, J., Manninen, J.: An integrated multiobjective design tool for process design. Appl. Therm. Eng. 26(13), 1393–1399 (2006)CrossRefGoogle Scholar
  12. 12.
    Hakanen, J., Kawajiri, Y., Miettinen, K., Biegler, L.: Interactive multi-objective optimization for simulated moving bed processes. Control Cybern. 36(2), 282–320 (2007)MathSciNetGoogle Scholar
  13. 13.
    Hakanen, J., Miettinen, K., Mäkelä, M.M., Manninen, J.: On interactive multiobjective optimization with NIMBUS in chemical process design. J. Multi-Criter. Decis. Anal. 13(2–3), 125–134 (2005)CrossRefMATHGoogle Scholar
  14. 14.
    Hakanen, J., Miettinen, K., Sahlstedt, K.: Wastewater treatment: new insight provided by interactive multiobjective optimization. Decis. Support Syst. 51(2), 328–337 (2011)CrossRefGoogle Scholar
  15. 15.
    Hakanen, J., Sahlstedt, K., Miettinen, K.: Wastewater treatment plant design and operation under multiple conflicting objective functions. Environ. Model. Softw. 46, 240–249 (2013)CrossRefGoogle Scholar
  16. 16.
    Hämäläinen, J., Miettinen, K., Tarvainen, P., Toivanen, J.: Interactive solution approach to a multiobjective optimization problem in paper machine headbox design. J. Optim. Theory Appl. 116, 265–281 (2003)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Hartikainen, M., Miettinen, K., Wiecek, M.: PAINT: pareto front interpolation for nonlinear multiobjective optimization. Comput. Optim. Appl. 52, 845–867 (2012)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Heikkola, E., Miettinen, K., Nieminen, P.: Multiobjective optimization of an ultrasonic transducer using NIMBUS. Ultrasonics 44(4), 368–380 (2006)CrossRefGoogle Scholar
  19. 19.
    Hentenryck, P.V.: The OPL Optimization Programming Language. MIT Press, Cambridge (1999)Google Scholar
  20. 20.
    Kaliszewski, I.: Out of the mist-towards decision-maker-friendly multiple criteria decision making support. Eur. J. Oper. Res. 158(2), 293–307 (2004)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Laukkanen, T., Tveit, T.M., Ojalehto, V., Miettinen, K., Fogelholm, C.J.: An interactive multi-objective approach to heat exchanger network synthesis. Comput. Chem. Eng. 34(6), 943–952 (2010)CrossRefGoogle Scholar
  22. 22.
    Luque, M., Ruiz, F., Miettinen, K.: Global formulation for interactive multiobjective optimization. OR Spectrum 33, 27–48 (2011)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Madetoja, E., Miettinen, K., Tarvainen, P.: Issues related to the computer realization of a multidisciplinary and multiobjective optimization system. Eng. Comput. 22(1), 33–46 (2006)CrossRefGoogle Scholar
  24. 24.
    Mavrotas G (2006) Generation of Efficient Solutions in Multiobjective Mathematical Programming Problems Using GAMS. School of Chemical Engineering, National Technical University of Athens, AthensGoogle Scholar
  25. 25.
    Mavrotas, G.: Effective implementation of the \(\epsilon \)-constraint method in multi-objective mathematical programming problems. Appl. Math. Comput. 213(2), 455–465 (2009)CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic, Boston (1999)MATHGoogle Scholar
  27. 27.
    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 in Katowice, Katowice (2006)Google Scholar
  28. 28.
    Miettinen, K.: Using interactive multiobjective optimization in continuous casting of steel. Mater. Manuf. Process. 22(5), 585–593 (2007)CrossRefGoogle Scholar
  29. 29.
    Miettinen, K.: Survey of methods to visualize alternatives in multiple criteria decision making problems. OR Spectrum. 36(1), 3–37 (2014)Google Scholar
  30. 30.
    Miettinen, K., Eskelinen, P., Ruiz, F., Luque, M.: NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point. Eur. J. Oper. Res. 206(2), 426–434 (2010)CrossRefMATHMathSciNetGoogle Scholar
  31. 31.
    Miettinen, K. Hakanen, J.: Why use interactive multi-objective optimization in chemical process design. In: Rangaiah, G.P. (ed.) Multi-Objective Optimization: Techniques and Applications in Chemical Engineering, pp. 153–188. World Scientific, Singapore (2008)Google Scholar
  32. 32.
    Miettinen, K., Kaario, K.: Comparing graphic and symbolic classification in interactive multiobjective optimization. J. Multi-Criter. Decis. Anal. 12(6), 331–335 (2003)Google Scholar
  33. 33.
    Miettinen, K., Mäkelä, M.M.: Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. Optimization 34, 231–246 (1995)CrossRefMATHMathSciNetGoogle Scholar
  34. 34.
    Miettinen, K., Mäkelä, M.M.: Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation. J. Oper. Res. Soc. 50, 949–959 (1999)CrossRefMATHGoogle Scholar
  35. 35.
    Miettinen, K., Mäkelä, M.M.: Interactive multiobjective optimization system WWW-NIMBUS on the internet. Comput. Oper. Res. 27(7–8), 709–723 (2000)CrossRefMATHGoogle Scholar
  36. 36.
    Miettinen, K., Mäkelä, M.M.: On scalarizing functions in multiobjective optimization. OR Spectrum 24(2), 193–213 (2002)CrossRefMATHGoogle Scholar
  37. 37.
    Miettinen, K., Mäkelä, M.M.: Synchronous approach in interactive multiobjective optimization. Eur. J. Oper. Res. 170(3), 909–922 (2006)CrossRefMATHGoogle Scholar
  38. 38.
    Miettinen, K., Mäkelä, M.M., Männikkö, T.: Optimal control of continuous casting by nondifferentiable multiobjective optimization. Comput. Optim. Appl. 11, 177–194 (1998)CrossRefMATHMathSciNetGoogle Scholar
  39. 39.
    Miettinen, K., Ruiz, F., Wierzbicki, A.P.: Introduction to multiobjective optimization: Interactive approaches. In: Branke, J., Deb, K., Miettinen, K., Slowinski, R. (eds.) Multiobjective Optimization: Interactive and Evolutionary Approaches, pp. 27–57. Springer, Berlin (2008)CrossRefGoogle Scholar
  40. 40.
    Nakayama, H., Kaneshige, K., Takemoto, S., Watada, Y.: Application of a multi-objective programming technique to construction accuracy control of cable-stayed bridges. Eur. J. Oper. Res. 87(3), 731–738 (1995)CrossRefMATHGoogle Scholar
  41. 41.
    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, Berlin (1984)CrossRefGoogle Scholar
  42. 42.
    Ruiz, F., Luque, M., Miettinen, K.: Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization. Ann. Oper. Res. 197(1), 47–70 (2012)CrossRefMATHMathSciNetGoogle Scholar
  43. 43.
    Ruotsalainen, H., Boman, E., Miettinen, K., Tervo, J.: Nonlinear interactive multiobjective optimization method for radiotherapy treatment planning with Boltzmann transport equation. Contemp. Eng. Sci. 2(9), 391–422 (2009)Google Scholar
  44. 44.
    Ruotsalainen, H., Miettinen, K., Palmgren, J.E.: Interactive multiobjective optimization for 3D HDR brachytherapy applying IND-NIMBUS. In: Jones, D., Tamiz, M., Ries, J. (eds.) New Developments in Multiple Objective and Goal Programming, pp. 117–131. Springer, Berlin Heidelberg (2010)CrossRefGoogle Scholar
  45. 45.
    Ruotsalainen, H., Miettinen, K., Palmgren, J.E., Lahtinen, T.: Interactive multiobjective optimization for anatomy-based three-dimensional HDR brachytherapy. Phys. Med. Biol. 55(16), 4703–4719 (2010)CrossRefGoogle Scholar
  46. 46.
    Stam, A., Kuula, M., Cesar, H.: Transboundary air pollution in Europe: an interactive multicriteria tradeoff analysis. Eur. J. Oper. Res. 56(2), 263–277 (1992)CrossRefGoogle Scholar
  47. 47.
    Steuer, R.E.: Multiple Criteria Optimization; Theory, Computation, and Application. Wiley, New York (1986)MATHGoogle Scholar
  48. 48.
    Tarkkanen, S., Miettinen, K., Hakanen, J., Isomäki, H.: Incremental user-interface development for interactive multiobjective optimization. Expert. Syst. Appl. 40, 3220–3232 (2013)CrossRefGoogle Scholar
  49. 49.
    Wierzbicki, A.: A mathematical basis for satisficing decision making. Math. Model. 3, 391–405 (1982)CrossRefMATHMathSciNetGoogle Scholar
  50. 50.
    Wierzbicki, A.: Reference point approaches. In: Gal, T., Stewart, T., Hanne, T. (eds.) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications, pp. 9-9–9-39. Kluwer Academic, Boston (1999)Google Scholar
  51. 51.
    Yee, T., Grossmann, I.: Simultaneous optimization models for heat integration. Comput. Chem. Eng. 14(10), 1165–1184 (1990)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Vesa Ojalehto
    • 1
  • Kaisa Miettinen
    • 1
  • Timo Laukkanen
    • 2
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläJyvaskylaFinland
  2. 2.Department of Energy TechnologyAalto University School of EngineeringAaltoFinland

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