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A classification of the weighting schemes in reference point procedures for multiobjective programming

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  • F Ruiz

    (University of Málaga)

  • M Luque

    (University of Málaga)

  • J M Cabello

    (University of Málaga)

Abstract

The reference point-based methods form one of the most widely used class of interactive procedures for multiobjective programming problems. The achievement scalarizing functions used to determine the solutions at each iteration usually include weights. In this paper, we have analysed nine weighting schemes from the preferential point of view, that is, examining their performance in terms of which reference values are given more importance and why. As a result, we have carried out a systematic classification of the schemes attending to their preferential meaning. This way, we distinguish pure normalizing schemes from others where the weights have a preferential interpretation. This preferential behaviour can be either designed (thus, predetermined) by the method, or decided by the decision maker. Besides, several figures have been used to illustrate the way each scheme works. This paper enables the potential users to choose the most appropriate scheme for each case.

Suggested Citation

  • F Ruiz & M Luque & J M Cabello, 2009. "A classification of the weighting schemes in reference point procedures for multiobjective programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(4), pages 544-553, April.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:4:d:10.1057_palgrave.jors.2602577
    DOI: 10.1057/palgrave.jors.2602577
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    References listed on IDEAS

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    1. Miettinen, Kaisa & Makela, Marko M., 2006. "Synchronous approach in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 170(3), pages 909-922, May.
    2. 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.
    3. Ehrgott, Matthias & Tenfelde-Podehl, Dagmar, 2003. "Computation of ideal and Nadir values and implications for their use in MCDM methods," European Journal of Operational Research, Elsevier, vol. 151(1), pages 119-139, November.
    4. K Miettinen & M M Mäkelä, 1999. "Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(9), pages 949-959, September.
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    Cited by:

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    2. Carrizosa, Emilio & Ramírez-Ayerbe, Jasone & Romero Morales, Dolores, 2024. "Mathematical optimization modelling for group counterfactual explanations," European Journal of Operational Research, Elsevier, vol. 319(2), pages 399-412.
    3. Włodzimierz Ogryczak & Bartosz Kozłowski, 2011. "Reference point method with importance weighted ordered partial achievements," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 380-401, December.
    4. Cabello, J.M. & Ruiz, F. & Pérez-Gladish, B. & Méndez-Rodríguez, P., 2014. "Synthetic indicators of mutual funds’ environmental responsibility: An application of the Reference Point Method," European Journal of Operational Research, Elsevier, vol. 236(1), pages 313-325.
    5. Figueira, J.R. & Liefooghe, A. & Talbi, E.-G. & Wierzbicki, A.P., 2010. "A parallel multiple reference point approach for multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 205(2), pages 390-400, September.
    6. José M. Cabello & Enrique Navarro-Jurado & Beatriz Rodríguez & Daniela Thiel-Ellul & Francisco Ruiz, 2019. "Dual weak–strong sustainability synthetic indicators using a double reference point scheme: the case of Andalucía, Spain," Operational Research, Springer, vol. 19(3), pages 757-782, September.
    7. Stelios Rozakis & Athanasios Kampas, 2022. "An interactive multi-criteria approach to admit new members in international environmental agreements," Operational Research, Springer, vol. 22(4), pages 3461-3487, September.
    8. Ana Ruiz & Rubén Saborido & Mariano Luque, 2015. "A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm," Journal of Global Optimization, Springer, vol. 62(1), pages 101-129, May.
    9. Navarro Jurado, E. & Tejada Tejada, M. & Almeida García, F. & Cabello González, J. & Cortés Macías, R. & Delgado Peña, J. & Fernández Gutiérrez, F. & Gutiérrez Fernández, G. & Luque Gallego, M. & Málv, 2012. "Carrying capacity assessment for tourist destinations. Methodology for the creation of synthetic indicators applied in a coastal area," Tourism Management, Elsevier, vol. 33(6), pages 1337-1346.
    10. Mariano Luque & Ana Ruiz & Rubén Saborido & Óscar Marcenaro-Gutiérrez, 2015. "On the use of the $$L_{p}$$ L p distance in reference point-based approaches for multiobjective optimization," Annals of Operations Research, Springer, vol. 235(1), pages 559-579, December.
    11. Jiménez, Mariano & Bilbao-Terol, Amelia & Arenas-Parra, Mar, 2021. "Incorporating preferential weights as a benchmark into a Sequential Reference Point Method," European Journal of Operational Research, Elsevier, vol. 291(2), pages 575-585.
    12. Marcenaro-Gutierrez, O.D. & Luque, M. & Ruiz, F., 2010. "An application of multiobjective programming to the study of workers' satisfaction in the Spanish labour market," European Journal of Operational Research, Elsevier, vol. 203(2), pages 430-443, June.
    13. Ruiz, Francisco & Cabello, José M. & Pérez-Gladish, Blanca, 2018. "Building Ease-of-Doing-Business synthetic indicators using a double reference point approach," Technological Forecasting and Social Change, Elsevier, vol. 131(C), pages 130-140.
    14. F Ruiz & J M Cabello & M Luque, 2011. "An application of reference point techniques to the calculation of synthetic sustainability indicators," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 189-197, January.
    15. Shicheng Hu & Danping Li & Junmin Jia & Yang Liu, 2021. "A Self-Learning Based Preference Model for Portfolio Optimization," Mathematics, MDPI, vol. 9(20), pages 1-17, October.

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