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A Combined Tchebycheff/Aspiration Criterion Vector Interactive Multiobjective Programming Procedure

Author

Listed:
  • Ralph E. Steuer

    (Department of Management Science and Information Technology, University of Georgia, Athens, Georgia 30602)

  • Joe Silverman

    (Navy Personnel Research & Development Center, San Diego, California 92152)

  • Alan W. Whisman

    (Navy Personnel Research & Development Center, San Diego, California 92152)

Abstract

In this paper we combine the Tchebycheff method of Steuer and Choo with Wierzbicki's Aspiration Criterion Vector method in order to form an improved procedure for interactive multiple objective programming. The Combined procedure is sensible because the Tchebycheff and Aspiration Criterion Vector methods possess complementary distinguishing characteristics, solve similar optimization problems to probe the nondominated set, and share a similar computer/user interface. In the early iterations, Tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search. In later iterations, Aspiration Criterion Vector probes might be used to pinpoint a final solution. Computational experience is reported showing the improved effectiveness of the Combined Procedure when employed in this fashion when compared against the Tchebycheff and Aspiration Criterion Vector methods run separately.

Suggested Citation

  • Ralph E. Steuer & Joe Silverman & Alan W. Whisman, 1993. "A Combined Tchebycheff/Aspiration Criterion Vector Interactive Multiobjective Programming Procedure," Management Science, INFORMS, vol. 39(10), pages 1255-1260, October.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:10:p:1255-1260
    DOI: 10.1287/mnsc.39.10.1255
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    Citations

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    Cited by:

    1. Jaszkiewicz, Andrzej & Slowinski, Roman, 1999. "The `Light Beam Search' approach - an overview of methodology and applications," European Journal of Operational Research, Elsevier, vol. 113(2), pages 300-314, March.
    2. Banu Lokman & Murat Köksalan & Pekka J. Korhonen & Jyrki Wallenius, 2016. "An interactive algorithm to find the most preferred solution of multi-objective integer programs," Annals of Operations Research, Springer, vol. 245(1), pages 67-95, October.
    3. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    4. Mingue SUn, 2010. "A Branch-and-Bound Algorithm for Representative Integer Efficient Solutions in Multiple Objective Network Programming Problems," Working Papers 0007, College of Business, University of Texas at San Antonio.
    5. M Köksalan & E Karasakal, 2006. "An interactive approach for multiobjective decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 532-540, May.
    6. Bilge Bozkurt & John W. Fowler & Esma S. Gel & Bosun Kim & Murat Köksalan & Jyrki Wallenius, 2010. "Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function," Operations Research, INFORMS, vol. 58(3), pages 650-659, June.
    7. Rafael Lazimy, 2013. "Interactive Polyhedral Outer Approximation (IPOA) strategy for general multiobjective optimization problems," Annals of Operations Research, Springer, vol. 210(1), pages 73-99, November.
    8. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    9. Sun, Minghe, 2002. "A multiple objective programming approach for determining faculty salary equity adjustments," European Journal of Operational Research, Elsevier, vol. 138(2), pages 302-319, April.
    10. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    11. Minghe Sun, 2003. "Procedures for Finding Nondominated Solutions for Multiple Objective Network Programming Problems," Transportation Science, INFORMS, vol. 37(2), pages 139-152, May.
    12. Sun, Minghe & Steuer, Ralph E., 1996. "InterQuad: An interactive quad tree based procedure for solving the discrete alternative multiple criteria problem," European Journal of Operational Research, Elsevier, vol. 89(3), pages 462-472, March.
    13. Buchanan, John & Gardiner, Lorraine, 2003. "A comparison of two reference point methods in multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 149(1), pages 17-34, August.
    14. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    15. Marmol, Amparo M. & Puerto, Justo & Fernandez, Francisco R., 2002. "Sequential incorporation of imprecise information in multiple criteria decision processes," European Journal of Operational Research, Elsevier, vol. 137(1), pages 123-133, February.

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