Abstract
In this paper, we study the use of exact approaches based on constraint programming and mixed integer programming, to tackle the parameter elicitation problem in the lexicographic ordering approach (LO). Like all multicriteria optimization methods, the LO method has the criteria order parameter that should be fixed carefully. Indeed, the criteria usually conflict with each other, and thus, finding an appropriate order between the criteria is challenging. This is why we propose elicitation methods in order to assist the Decision Maker (DM) in fixing this parameter. These methods require some prior knowledge, that the DM can give easily. We present some numerical experiments, showing the effectiveness of our approaches.
This work is supported by TASSILI research program 11MDU839 (France, Algeria). This work is also supported by PNR research project 70/TIC/2011 (Algeria).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aribi, N., Lebbah, Y.: Approches d’élicitation basées sur le coefficient de Spearman pour l’optimisation multicritère par ordre lexicographique. In: JFPC 2013 - Neuvièmes Journées Francophones de Programmation par Contraintes, Aix-en-Provence, France, pp. 51–60 (2013)
Aribi, N., Lebbah, Y.: Statistical and constraint programming approaches for parameter elicitation in lexicographic ordering. In: Amine, A., Mohamed, O.A., Bellatreche, L. (eds.) Modeling Approaches and Algorithms. SCI, vol. 488, pp. 47–56. Springer, Heidelberg (2013)
Beliakov, G.: How to build aggregation operators from data. International Journal of Intelligent Systems 18, 903–923 (2003)
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), Atlanta, GA, USA, pp. 1160–1167. AAAI Press (July 2010)
Brase, C.H., Brase, C.P.: Understandable Statistics: Concepts and Methods. Cengage Learning (2011)
Corder, G.W., Foreman, D.I.: Nonparametric Statistics for Non-Statisticians: A Step-By-Step Approach. Wiley (2009)
Delecroix, F., Morge, M., Routier, J.-C.: 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)
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)
Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Boston (2005)
Van Hentenryck, P.: Constraint satisfaction in logic programming. MIT Press (1989)
Hooker, J.: Integrated Methods for Optimization. International series in operations research & management science. Springer, US (2012)
Hutter, F., Hoos, H.H., Leyton-Brown, K.: Automated configuration of mixed integer programming solvers. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 186–202. Springer, Heidelberg (2010)
Kendall, M.G.: A New Measure of Rank Correlation. Biometrika 30(1/2), 81–93 (1938)
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/s00158-003-0368-6
Montanari, U.: Networks of constraints: Fundamental properties and applications to picture processing. Information Sciences 7, 95–132 (1974)
Refalo, P.: Linear formulation of constraint programming models and hybrid solvers. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 369–383. Springer, Heidelberg (2000)
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)
Régin, J.-C.: Global Constraints: a survey. In: Milano, M., Van Hentenryck, P. (eds.) Hybrid Optimization. Springer (2011)
Rossi, F., van Beek, P., Walsh, T. (eds.): The Handbook of Constraint Programming. Elsevier (2006)
Roy, B., Bouyssou, D.: Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy. International Series in Operations Research & Management Science. Springer (2002)
Sedgewick, R., Wayne, K.: Algorithms, 4th edn. Addison-Wesley (2011)
Tabachnick, B.G., Fidell, L.S.: Using Multivariate Statistics, 5th edn. Allyn & Bacon, Inc., Needham Heights (2006)
Wolsey, L.A.: Integer Programming. A Wiley-Interscience Publication, Wiley (1998)
Xu, W., Chang, C., Hung, Y.S., Kwan, S.K., Fung, P.C.W.: Order statistics correlation coefficient as a novel association measurement with applications to biosignal analysis. IEEE Transactions on Signal Processing 55(12), 5552–5563 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aribi, N., Lebbah, Y. (2013). Exact Approaches for Parameter Elicitation in Lexicographic Ordering. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds) Algorithmic Decision Theory. ADT 2013. Lecture Notes in Computer Science(), vol 8176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41575-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-41575-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41574-6
Online ISBN: 978-3-642-41575-3
eBook Packages: Computer ScienceComputer Science (R0)