A Methodological Proposal for an Evolutionary Approach to Parameter Inference in MURAME-Based Problems

Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 26)


In this paper we propose an evolutionary approach in order to infer the values of the parameters for applying the MURAME, a multicriteria method which allows to score/rank a set of alternatives according to a set of evaluation criteria. This problem, known as preference disaggregation, consists in finding the MURAME parameter values that minimize the inconsistency between the model obtained with those parameters and the true preference model on the basis of a reference set of decisions of the Decision Maker. In order to represent a measure of inconsistency of the MURAME model compared to the true preference one, we consider a fitness function which puts emphasis on the distance between the scoring of the alternatives given by the Decision Maker and the one determined by the MURAME. The problem of finding a numerical solution of the involved mathematical programming problem is tackled by using an evolutionary solution algorithm based on the Particle Swarm Optimization. An application is finally provided in order to give an initial assessment of the proposed approach.


Preference disaggregation MURAME Particle Swarm Optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belacel, N., Bhasker Raval, H., Punnen, A.P.: Learning multicriteria fuzzy classification method. PROAFTN from data. Computers & Operations Research 34(7), 1885–1898 (2007)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Blackwell, T., Kennedy, J., Poli, R.: Particle swarm optimization – An overview. Swarm Intelligence 1(1), 33–57 (2007)CrossRefGoogle Scholar
  3. 3.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: From Natural to Artificial Swarm Intelligence. Oxford University Press (1999)Google Scholar
  4. 4.
    Brans, J.P., Vincke, P.: A preference ranking organisation method (The PROMETHEE method for multiple criteria decision-making). Management Science 31(6), 647–656 (1985)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Buchanan, J., Sheppard, P., Vanderpooten, D.: Project ranking using ELECTRE III. Research report 99-01, Department of Management Systems, University of Waikato, New-Zealand (1999)Google Scholar
  6. 6.
    Corazza, M., Fasano, G., Gusso, R.: Portfolio selection with an alternative measure of risk: Computational performances of particle swarm optimization and genetic algorithms. In: Perna, C., Sibillo, M. (eds.) Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 123–130. Springer (2012)Google Scholar
  7. 7.
    Corazza, M., Funari, S., Gusso, R.: Il merito creditizio delle Pmi italiane durante la crisi finanziaria: l’utilizzo di più fonti informative per l’analisi e lo scoring. Bancaria 1(1), 47–63 (2012) (in Italian)Google Scholar
  8. 8.
    Cura, T.: Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications 10(4), 2396–2406 (2009)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Doumpos, M., Marinakis, Y., Marinaki, M., Zopounidis, C.: An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method. European Journal of Operational Research 199(2), 496–505 (2009)CrossRefMATHGoogle Scholar
  10. 10.
    Fletcher, R.: Practical Methods of Optimization. John Wiley & Sons (1991)Google Scholar
  11. 11.
    Goletsis, Y., Askounis, D.T., Psarras, J.: Multicriteria judgments for project ranking: An integrated methodology. Economic Financial Modelling 8(3), 127–148 (2001)Google Scholar
  12. 12.
    Jacquet-Lagrèze, E., Siskos, Y.: Preference disaggregation: 20 years of MCDA experience. European Journal of Operational Research 130(2), 233–245 (2001)CrossRefMATHGoogle Scholar
  13. 13.
    Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. Proceedings of the IEEE International Conference on Neural Networks 4, 1942–1948 (1995)CrossRefGoogle Scholar
  14. 14.
    Mousseau, V., Slowinski, R., Zielniewicz, P.: ELECTRE TRI 2.0a: Methodological guide and user’s documentation. Université de Paris-Dauphine (1999)Google Scholar
  15. 15.
    Di Pillo, G., Grippo, L.: Exact penalty functions in constrained optimization. SIAM Journal on Control and Optimization 27(6), 1333–1360 (1989)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Roy, B.: ELECTRE III: Un algorithme de classements fondé sur une representation floue des préférences en présence de critères multiples. Cahiers du CERO 20(1), 3–24 (1978)MATHGoogle Scholar
  17. 17.
    Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: The 1998 IEEE International Conference on Evolutionary Computation Proceedings, pp. 69–73 (1998)Google Scholar
  18. 18.
    Thomaidis, N., Angelidis, T., Vassiliadis, V., Dounias, G.: Active portfolio management with cardinality constraints: An application of Particle Swarm Optimization. New Mathematics and Natural Computation 5(3), 535–555 (2009)CrossRefMATHGoogle Scholar
  19. 19.
    Zangwill, W.I.: Non-linear programming via penalty functions. Management Science 13(5), 344–358 (1967)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Zhang, W.J., Xie, X.F., Bi, D.C.: Handling boundary constraints for numerical optimization by particle swarm flying in periodic search space. In: Proceedings of the 2004 Congress on Evolutionary Computation IEEE, pp. 2307–2311 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marco Corazza
    • 1
    • 3
  • Stefania Funari
    • 2
  • Riccardo Gusso
    • 1
  1. 1.Department of EconomicsCa’ Foscari University of VeniceVeniceItaly
  2. 2.Department of ManagementCa’ Foscari University of VeniceVeniceItaly
  3. 3.Advanced School of Economics of VeniceCa’ Foscari University of VeniceVeniceItaly

Personalised recommendations