Statistical and Constraint Programming Approaches for Parameter Elicitation in Lexicographic Ordering

Part of the Studies in Computational Intelligence book series (SCI, volume 488)


In this paper, we propose statistical and constraint programming approaches in order to tackle the parameter elicitation problem for the lexicographic ordering (LO) method. Like all multicriteria optimization methods, the LO method have a parameter that should be fixed carefully, either to determine the optimal solution (best tradeoff), or to rank the set of feasible solutions (alternatives). Unfortunately, the criteria usually conflict with each other, and thus, it is unlikely to find a convenient parameter for which the obtained solution will perform best for all criteria. This is why elicitation methods have been populated in order to assist the Decision Maker (DM) in the hard task of fixing the parameters. Our proposed approaches require some prior knowledge that the DM can give straightforwardly. These informations are used in order to get automatically the appropriate parameters. We also present a relevant numerical experimentations, showing the effectiveness of our approaches in solving the elicitation problem.


Parameter Elicitation Multicriteria Optimisation Constraint Programming Statistics Lexicographic ordering 


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  1. 1.
    Beliakov, G.: How to build aggregation operators from data. International Journal of Intelligent Systems 18, 903–923 (2003)CrossRefMATHGoogle Scholar
  2. 2.
    Berry, W.D.: Understanding Regression Assumptions. Quantitative Applications in the Social Sciences, vol. 92. SAGE Publications (1993)Google Scholar
  3. 3.
    Boutilier, C., Regan, K., Viappiani, P.: Simultaneous elicitation of preference features and utility. In: Proceedings of the Twenty-fourth AAAI Conference on Artificial Intelligence (AAAI 2010), pp. 1160–1167. AAAI Press, Atlanta (2010)Google Scholar
  4. 4.
    Brase, C.H., Brase, C.P.: Understandable Statistics: Concepts and Methods. Cengage Learning (2011)Google Scholar
  5. 5.
    Corder, G.W., Foreman, D.I.: Nonparametric Statistics for Non-Statisticians: A Step-By-Step Approach. Wiley (2009)Google Scholar
  6. 6.
    Delecroix, F., Morge, M., Delecroix, F.: An algorithm for active learning of lexicographic preferences. In: Pirlot, M., Mousseau, V. (eds.) Proc. of the Workshop from Multiple Criteria Decision Aiding to Preference Learning, pp. 115–122 (November 2012)Google Scholar
  7. 7.
    Escoffier, B., Lang, J., Öztürk, M.: Single-peaked consistency and its complexity. In: Proceedings of the 2008 Conference on ECAI 2008: 18th European Conference on Artificial Intelligence, pp. 366–370. IOS Press, Amsterdam (2008)Google Scholar
  8. 8.
    Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Boston (2005)Google Scholar
  9. 9.
    Van Hentenryck, P.: Constraint satisfaction in logic programming. Logic Programming. MIT Press (1989)Google Scholar
  10. 10.
    Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization 26, 369–395 (2004), doi:10.1007/s00158-003-0368-6MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Nathans, L.L., Oswald, F.L., Nimon, K.: Interpreting multiple linear regression: A guidebook of variable importance. Practical Assessment, Research & Evaluation 17(9), 21–62 (2012)Google Scholar
  12. 12.
    Pedhazur, E.J.: Multiple regression in behavioral research: explanation and prediction. Harcourt Brace College Publishers (1997)Google Scholar
  13. 13.
    Régin, J.-C.: A filtering algorithm for constraints of difference in csps. In: Hayes-Roth, B., Korf, R.E. (eds.) AAAI, pp. 362–367. AAAI Press, The MIT Press (1994)Google Scholar
  14. 14.
    Rossi, F., Van Beek, P., Walsh, T.: Handbook of Constraint Programming. Foundations of Artificial Intelligence, vol. 35. Elsevier (2006)Google Scholar
  15. 15.
    Roy, B., Bouyssou, D.: Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy. International Series in Operations Research & Management Science. Springer (2002)Google Scholar
  16. 16.
    Tabachnick, B.G., Fidell, L.S.: Using Multivariate Statistics, 5th edn. Allyn & Bacon, Inc., Needham Heights (2006)Google Scholar
  17. 17.
    Zar, J.H.: Significance testing of the spearman rank correlation coefficient. Journal of the American Statistical Association 67(339), 578–580 (1972)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Laboratoire LITIOUniversité d’OranEl-M’NaouerAlgérie
  2. 2.Laboratoire I3S/CNRSUniversité de NiceSophia AntipolisFrance

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