Inferring parameters of a relational system of preferences from assignment examples using an evolutionary algorithm
Abstract
Most evolutionary multi-objective algorithms perform poorly in many objective problems. They normally do not make selective pressure towards the Region of Interest (RoI), the privileged zone in the Pareto frontier that contains solutions important to a DM. Several works have proved that a priori incorporation of preferences improves convergence towards the RoI. The work of (E. Fernandez, E. Lopez, F. Lopez & C.A. Coello Coello, 2011) uses a binary fuzzy outranking relational system to map many-objective problems into a tri-objective optimization problem that searches the RoI; however, it requires the elicitation of many preference parameters, a very hard task. The use of an indirect elicitation approach overcomes such situation by allowing the parameter inference from a battery of examples. Even though the relational system of Fernandez et al. (2011) is based on binary relations, it is more convenient to elicit its parameters from assignment examples. In this sense, this paper proposes an evolutionary-based indirect parameter elicitation method that uses preference information embedded in assignment examples, and it offers an analysis of their impact in a priori incorporation of DM’s preferences. Results show, through an extensive computer experiment over random test sets, that the method estimates properly the model parameter’s values.
First published online 7 May 2019
Keyword : decision making, multi-objective optimization, outranking methods, fuzzy preferences, parameter elicitation, evolutionary algorithms
How to Cite
Fernandez, E., Rangel-Valdez, N., Cruz-Reyes, L., Gomez-Santillan, C., Rivera-Zarate, G., & Sanchez-Solis, P. (2019). Inferring parameters of a relational system of preferences from assignment examples using an evolutionary algorithm. Technological and Economic Development of Economy, 25(4), 693-715. https://doi.org/10.3846/tede.2019.9475
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Branke, J., Greco, S., Słowiński, R., & Zielniewicz, P. (2015). Learning value functions in interactive evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation, 19(1), 88-102. https://doi.org/10.1109/TEVC.2014.2303783
Branke, J., Salvatore, C., Greco, S., Slowiński, & Zielniewicz, P. (2016). Using Choquet integral as preference model in interactive evolutionary multiobjective optimization. European Journal of Operational Research, 250, 884-901. https://doi.org/10.1016/j.ejor.2015.10.027
Coello, C. A. (1999). A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowledge and Information Systems, an International Journal, 1(3), 269-308. https://doi.org/10.1007/BF03325101
Coello, C. A., Lamont, G. B., & Van Veldhuizen, D. A. (2007). Evolutionary algorithms for solving multi-objective problems (2nd ed.). New York: Springer. Retrieved from http://www.springer.com/us/book/9780387332543
Cruz-Reyes, L., Fernandez, E., Sanchez, P., Coello Coello, C. A., & Gomez, C. (2017). Incorporation of implicit decision-maker preferences in multi-objective evolutionary optimization using a multicriteria classification method. Applied Soft Computing, 50, 48-57. https://doi.org/10.1016/j.asoc.2016.10.037
Deb, K., & Agrawal, R. B. (1995). Simulated binary crossover for continuous search space. Complex Systems, 9, 115-148.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester-New York-Weinheim-Brisbane-Singapore-Toronto: John Wiley & Sons. Retrieved from http://dl.acm.org/citation.cfm?id=559152
Deb, K. (2007). Current trends in evolutionary multi-objective optimization. International Journal for Simulation and Multidisciplinary Design Optimisation, 1(1), 1-8. https://doi.org/10.1051/ijsmdo:2007001
Deb, K., & Tiwari, S. (2008). Omni-optimizer: A generic evolutionary algorithm for single and multiobjective optimization. European Journal of Operational Research, 185, 1062-1087. https://doi.org/10.1016/j.ejor.2006.06.042
Deb, K., Sinha, A., Korhonen, P., & Wallenius, J. (2010). An interactive evolutionary multiobjective optimization method based on progressively approximated value functions. IEEE T Evolut Comput, 14(5), 723-739. https://doi.org/10.1109/TEVC.2010.2064323
Dias, L., & Mousseau, V. (2006). Inferring electre’s veto-related parameters from outranking examples. European Journal of Operational Research, 170, 172-191. https://doi.org/10.1016/j.ejor.2004.07.044
Doumpos, M., Marinakis, Y., Marimaki, M., & Zopounidis, C. (2009). An evolutionary approach to construction of outranking models for multicriteria classification: The case of ELECTRE TRI method.
European Journal of Operational Research, 199, 496-505. https://doi.org/10.1016/j.ejor.2008.11.035
Fernandez, E., Navarro, J., & Bernal, S. (2009). Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm. European Journal of Operational Research, 192, 602-609. https://doi.org/10.1016/j.ejor.2008.09.020
Fernandez, E., Lopez, E., Lopez, F., & Coello Coello, C. A. (2011). Increasing selective pressure towards the best compromise in evolutionary multiobjective optimization: The extended NOSGA method. Information Science, 181, 44-56. https://doi.org/10.1016/j.ins.2010.09.007
Fernandez, E., Navarro, J., & Mazcorro, G. (2012). Evolutionary multi-objective optimization for inferring outranking model’s parameters under scarce reference information and effects of reinforced preference. Foundations of Computing and Decision Sciencesm, 37, 163-197. https://doi.org/10.2478/v10209-011-0010-0
Fernandez, E., Lopez, E., Mazcorro, G., Olmedo, R., & Coello, C. (2013). Application of the nonoutranked sorting genetic algorithm to public project portfolio selection. Information Sciences, 228, 131-149. https://doi.org/10.1016/j.ins.2012.11.018
Fernandez, E., Gomez, C., Rivera, G., & Cruz-Reyes, L. (2015). Hybrid Metaheuristic approach for handling many objectives and decisions on partial support in project portfolio optimization. Information Sciences, 315, 102-122. https://doi.org/10.1016/j.ins.2015.03.064
Gastelum Chavira, D. A., Leyva Lopez, J. C., Solano Noriega, J. J., Ahumada Valenzuela, O., & Alvarez Carrillo, P. A. (2017). A credit ranking model for a parafinancial company based on the ELECTRE-III method and a multiobjective evolutionary algorithm. Applied Soft Computing, 60(1), 190-201. https://doi.org/10.1016/j.asoc.2017.06.021
Greco, S., Mousseau, V., & Slowinski, R. (2008). Ordinal regression revisited: Multiple criteria ranking with a set of additive value functions. European Journal of Operational Research, 191, 415-435. https://doi.org/10.1016/j.ejor.2007.08.013
Greco, S., Slowinski, R., Figueira, J. R., & Mousseau, V. (2010). Robust ordinal regression. Trends in Multiple Criteria Decision Analysis, 142, 241-283. https://doi.org/10.1007/978-1-4419-5904-1_9
Kahraman, C., Engin, O., Kaya, İ., & Kerim Yilmaz, M. (2012). An application of effective genetic algorithms for solving hybrid flow shop scheduling problems. International Journal of Computational Intelligence Systems, 1(2), 134-147. https://doi.org/10.1080/18756891.2008.9727611
Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37(1), 104-125. https://doi.org/10.1016/j.swevo.2017.06.005
Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 63(2), 81-97. https://doi.org/10.1037/h0043158
Molina, J., Santana-Quintero, L. V., Hernández-Díaz, A. G., Coello Coello, C. A., & Caballero, R. (2009). g-dominance: Reference point based dominance for multiobjective metaheuristics. European Journal of Operational Research, 197(2), 685-692. https://doi.org/10.1016/j.ejor.2008.07.015
Mousseau, V., & Slowinski, R. (1998). Inferring an electre-tri model from assignment examples. Journal of Global Optimization, 12, 157-174. https://doi.org/10.1023/A:1008210427517
Mousseau, V., Figueira, J., & Naux, J. P. (2001). Using assignment examples to infer weights for ELECTRE TRI method: some experimental results. European Journal of Operational Research, 130(2), 263-275. https://doi.org/10.1016/S0377-2217(00)00041-2
Mousseau, V., & Dias, L. C. (2004). Valued outranking relations in ELECTRE providing manageable disaggregation procedures. European Journal of Operational Research, 156(2), 467-482. https://doi.org/10.1016/S0377-2217(03)00120-6
Phelps, S., & Koksalan, M. (2003). An interactive evolutionary metaheuristic for multiobjective combinatorial optimization. Management Science, 49(12), 1617-1770. https://doi.org/10.1287/mnsc.49.12.1726.25117
Roy, B. (1991). The outranking approach and the foundations of electre methods. Theory and Decisions, 31(1), 49-73. https://doi.org/10.1007/BF00134132
Roy, B. (1996). Multicriteria methodology for decision aiding. Boston, MA: Springer. https://doi.org/10.1007/978-1-4757-2500-1
Wagner, T., & Trautmann, H. (2010). Integration of preferences in hypervolume-based multiobjective evolutionary algorithms by means of desirability functions. IEEE Transactions on Evolutionary Computation, 14, 688-701. https://doi.org/10.1109/TEVC.2010.2058119
Xiaohan, Y., Suojan, Z., Xianglin, L., & Xiuli, Q. (2018). ELECTRE methods in prioritized MCDM environment. Information Sciences, 424(1), 301-316. https://doi.org/10.1016/j.ins.2017.09.061
Xiong, N., Molina, D., Leon Ortiz, M., & Herrera, F. (2015). A walk into metaheuristics for engineering optimization: principles, methods and recent trends. International Journal of Computational Intelligence Systems, 8(4), 606-636. https://doi.org/10.1080/18756891.2015.1046324
Zhu, Y., & Luo, Y. (2016). Multi-objective optimisation and decision-making of space station logistics strategies. International Journal of Systems Science, 47(13), 3132-3148. https://doi.org/10.1080/00207721.2015.1091898
Zolfani, S. H., Maknoon, R., & Zavadskas, E. K. (2016). An introduction to prospective multiple attribute decision making (PMADM). Technological and Economic Development of Economy, 22(2), 309-326. https://doi.org/10.3846/20294913.2016.1150363
Bechikh, S. (2013). Incorporating decision maker’s preference information in evolutionary multi-objective optimization (Doctoral dissertation, High Institute of Management of Tunis, University of Tunis, Tunisia). Retrieved from http://delta.cs.cinvestav.mx/~ccoello/EMOO/thesis-bechikh.pdf.gz
Branke, J. (2015). MCDA and multiobjective evolutionary algorithms. In S. Greco, M. Ehrgott, & J. Figueira (Eds.), Multiple criteria decision analysis: state of the art surveys (2nd ed.). Springer. https://doi.org/10.1007/978-1-4939-3094-4_23
Branke, J., Greco, S., Słowiński, R., & Zielniewicz, P. (2015). Learning value functions in interactive evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation, 19(1), 88-102. https://doi.org/10.1109/TEVC.2014.2303783
Branke, J., Salvatore, C., Greco, S., Slowiński, & Zielniewicz, P. (2016). Using Choquet integral as preference model in interactive evolutionary multiobjective optimization. European Journal of Operational Research, 250, 884-901. https://doi.org/10.1016/j.ejor.2015.10.027
Coello, C. A. (1999). A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowledge and Information Systems, an International Journal, 1(3), 269-308. https://doi.org/10.1007/BF03325101
Coello, C. A., Lamont, G. B., & Van Veldhuizen, D. A. (2007). Evolutionary algorithms for solving multi-objective problems (2nd ed.). New York: Springer. Retrieved from http://www.springer.com/us/book/9780387332543
Cruz-Reyes, L., Fernandez, E., Sanchez, P., Coello Coello, C. A., & Gomez, C. (2017). Incorporation of implicit decision-maker preferences in multi-objective evolutionary optimization using a multicriteria classification method. Applied Soft Computing, 50, 48-57. https://doi.org/10.1016/j.asoc.2016.10.037
Deb, K., & Agrawal, R. B. (1995). Simulated binary crossover for continuous search space. Complex Systems, 9, 115-148.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester-New York-Weinheim-Brisbane-Singapore-Toronto: John Wiley & Sons. Retrieved from http://dl.acm.org/citation.cfm?id=559152
Deb, K. (2007). Current trends in evolutionary multi-objective optimization. International Journal for Simulation and Multidisciplinary Design Optimisation, 1(1), 1-8. https://doi.org/10.1051/ijsmdo:2007001
Deb, K., & Tiwari, S. (2008). Omni-optimizer: A generic evolutionary algorithm for single and multiobjective optimization. European Journal of Operational Research, 185, 1062-1087. https://doi.org/10.1016/j.ejor.2006.06.042
Deb, K., Sinha, A., Korhonen, P., & Wallenius, J. (2010). An interactive evolutionary multiobjective optimization method based on progressively approximated value functions. IEEE T Evolut Comput, 14(5), 723-739. https://doi.org/10.1109/TEVC.2010.2064323
Dias, L., & Mousseau, V. (2006). Inferring electre’s veto-related parameters from outranking examples. European Journal of Operational Research, 170, 172-191. https://doi.org/10.1016/j.ejor.2004.07.044
Doumpos, M., Marinakis, Y., Marimaki, M., & Zopounidis, C. (2009). An evolutionary approach to construction of outranking models for multicriteria classification: The case of ELECTRE TRI method.
European Journal of Operational Research, 199, 496-505. https://doi.org/10.1016/j.ejor.2008.11.035
Fernandez, E., Navarro, J., & Bernal, S. (2009). Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm. European Journal of Operational Research, 192, 602-609. https://doi.org/10.1016/j.ejor.2008.09.020
Fernandez, E., Lopez, E., Lopez, F., & Coello Coello, C. A. (2011). Increasing selective pressure towards the best compromise in evolutionary multiobjective optimization: The extended NOSGA method. Information Science, 181, 44-56. https://doi.org/10.1016/j.ins.2010.09.007
Fernandez, E., Navarro, J., & Mazcorro, G. (2012). Evolutionary multi-objective optimization for inferring outranking model’s parameters under scarce reference information and effects of reinforced preference. Foundations of Computing and Decision Sciencesm, 37, 163-197. https://doi.org/10.2478/v10209-011-0010-0
Fernandez, E., Lopez, E., Mazcorro, G., Olmedo, R., & Coello, C. (2013). Application of the nonoutranked sorting genetic algorithm to public project portfolio selection. Information Sciences, 228, 131-149. https://doi.org/10.1016/j.ins.2012.11.018
Fernandez, E., Gomez, C., Rivera, G., & Cruz-Reyes, L. (2015). Hybrid Metaheuristic approach for handling many objectives and decisions on partial support in project portfolio optimization. Information Sciences, 315, 102-122. https://doi.org/10.1016/j.ins.2015.03.064
Gastelum Chavira, D. A., Leyva Lopez, J. C., Solano Noriega, J. J., Ahumada Valenzuela, O., & Alvarez Carrillo, P. A. (2017). A credit ranking model for a parafinancial company based on the ELECTRE-III method and a multiobjective evolutionary algorithm. Applied Soft Computing, 60(1), 190-201. https://doi.org/10.1016/j.asoc.2017.06.021
Greco, S., Mousseau, V., & Slowinski, R. (2008). Ordinal regression revisited: Multiple criteria ranking with a set of additive value functions. European Journal of Operational Research, 191, 415-435. https://doi.org/10.1016/j.ejor.2007.08.013
Greco, S., Slowinski, R., Figueira, J. R., & Mousseau, V. (2010). Robust ordinal regression. Trends in Multiple Criteria Decision Analysis, 142, 241-283. https://doi.org/10.1007/978-1-4419-5904-1_9
Kahraman, C., Engin, O., Kaya, İ., & Kerim Yilmaz, M. (2012). An application of effective genetic algorithms for solving hybrid flow shop scheduling problems. International Journal of Computational Intelligence Systems, 1(2), 134-147. https://doi.org/10.1080/18756891.2008.9727611
Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37(1), 104-125. https://doi.org/10.1016/j.swevo.2017.06.005
Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 63(2), 81-97. https://doi.org/10.1037/h0043158
Molina, J., Santana-Quintero, L. V., Hernández-Díaz, A. G., Coello Coello, C. A., & Caballero, R. (2009). g-dominance: Reference point based dominance for multiobjective metaheuristics. European Journal of Operational Research, 197(2), 685-692. https://doi.org/10.1016/j.ejor.2008.07.015
Mousseau, V., & Slowinski, R. (1998). Inferring an electre-tri model from assignment examples. Journal of Global Optimization, 12, 157-174. https://doi.org/10.1023/A:1008210427517
Mousseau, V., Figueira, J., & Naux, J. P. (2001). Using assignment examples to infer weights for ELECTRE TRI method: some experimental results. European Journal of Operational Research, 130(2), 263-275. https://doi.org/10.1016/S0377-2217(00)00041-2
Mousseau, V., & Dias, L. C. (2004). Valued outranking relations in ELECTRE providing manageable disaggregation procedures. European Journal of Operational Research, 156(2), 467-482. https://doi.org/10.1016/S0377-2217(03)00120-6
Phelps, S., & Koksalan, M. (2003). An interactive evolutionary metaheuristic for multiobjective combinatorial optimization. Management Science, 49(12), 1617-1770. https://doi.org/10.1287/mnsc.49.12.1726.25117
Roy, B. (1991). The outranking approach and the foundations of electre methods. Theory and Decisions, 31(1), 49-73. https://doi.org/10.1007/BF00134132
Roy, B. (1996). Multicriteria methodology for decision aiding. Boston, MA: Springer. https://doi.org/10.1007/978-1-4757-2500-1
Wagner, T., & Trautmann, H. (2010). Integration of preferences in hypervolume-based multiobjective evolutionary algorithms by means of desirability functions. IEEE Transactions on Evolutionary Computation, 14, 688-701. https://doi.org/10.1109/TEVC.2010.2058119
Xiaohan, Y., Suojan, Z., Xianglin, L., & Xiuli, Q. (2018). ELECTRE methods in prioritized MCDM environment. Information Sciences, 424(1), 301-316. https://doi.org/10.1016/j.ins.2017.09.061
Xiong, N., Molina, D., Leon Ortiz, M., & Herrera, F. (2015). A walk into metaheuristics for engineering optimization: principles, methods and recent trends. International Journal of Computational Intelligence Systems, 8(4), 606-636. https://doi.org/10.1080/18756891.2015.1046324
Zhu, Y., & Luo, Y. (2016). Multi-objective optimisation and decision-making of space station logistics strategies. International Journal of Systems Science, 47(13), 3132-3148. https://doi.org/10.1080/00207721.2015.1091898
Zolfani, S. H., Maknoon, R., & Zavadskas, E. K. (2016). An introduction to prospective multiple attribute decision making (PMADM). Technological and Economic Development of Economy, 22(2), 309-326. https://doi.org/10.3846/20294913.2016.1150363