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Stochastic Approach versus Multiobjective Approach for Obtaining Efficient Solutions in Stochastic Multiobjective Programming Problems

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In this work, we deal with obtaining efficient solutions for stochastic multiobjective programming problems. In general, these solutions are obtained in two stages: in one of them, the stochastic problem is transformed into its equivalent deterministic problem, and in the other one, some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions, which involves transforming the multiobjective problem into a problem with only one objective function. Our aim is to determine whether the order in which these two transformations are carried out influences, in any way, the efficient solution obtained. Our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem, the order can have an influence on the final set of efficient solutions obtained for a given problem.

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  • Rafael Caballero & Emilio Cerdá & Mª del Mar Muñoz & Lourdes Rey, 2002. "Stochastic Approach versus Multiobjective Approach for Obtaining Efficient Solutions in Stochastic Multiobjective Programming Problems," Documentos de Trabajo del ICAE 0217, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:0217
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    1. Liu, Baoding & Iwamura, Kakuzo, 1997. "Modelling stochastic decision systems using dependent-chance programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 193-203, August.
    2. R. Caballero & E. Cerdá & M. M. Muñoz & L. Rey & I. M. Stancu-Minasian, 2001. "Efficient Solution Concepts and Their Relations in Stochastic Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 53-74, July.
    3. F. Ben Abdelaziz & P. Lang & R. Nadeau, 1999. "Dominance and Efficiency in Multicriteria Decision under Uncertainty," Theory and Decision, Springer, vol. 47(3), pages 191-211, December.
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    1. Javier León & Justo Puerto & Begoña Vitoriano, 2020. "A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    2. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    3. Sophie N. Parragh & Fabien Tricoire & Walter J. Gutjahr, 2022. "A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 419-459, June.
    4. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    5. Mercier, Quentin & Poirion, Fabrice & Désidéri, Jean-Antoine, 2018. "A stochastic multiple gradient descent algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 808-817.
    6. Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    7. Mingfa Zheng & Yuan Yi & Zutong Wang & Tianjun Liao, 2017. "Relations among efficient solutions in uncertain multiobjective programming," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 329-357, September.
    8. T Peña & P Lara & C Castrodeza, 2009. "Multiobjective stochastic programming for feed formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1738-1748, December.
    9. Fouad Ben Abdelaziz & Cinzia Colapinto & Davide La Torre & Danilo Liuzzi, 2020. "A stochastic dynamic multiobjective model for sustainable decision making," Annals of Operations Research, Springer, vol. 293(2), pages 539-556, October.
    10. S. Rangavajhala & A. A. Mullur & A. Messac, 2009. "Equality Constraints in Multiobjective Robust Design Optimization: Decision Making Problem," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 315-337, February.
    11. Emilio Cerdá & Julio Moreno Lorente, 2009. "Chance Constrained Programming with one Discrete Random Variable in Each Constraint," Working Papers 2009-05, FEDEA.
    12. Zarghami, Mahdi & Szidarovszky, Ferenc, 2009. "Revising the OWA operator for multi criteria decision making problems under uncertainty," European Journal of Operational Research, Elsevier, vol. 198(1), pages 259-265, October.
    13. Tiong, Achara & Vergara, Hector A., 2023. "A two-stage stochastic multi-objective resilience optimization model for network expansion of interdependent power–water networks under disruption," International Journal of Critical Infrastructure Protection, Elsevier, vol. 40(C).
    14. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    15. Chaabane Djamal & Mebrek Fatma, 2014. "Optimization of a linear function over the set of stochastic efficient solutions," Computational Management Science, Springer, vol. 11(1), pages 157-178, January.
    16. Mahdi Zarghami, 2010. "Urban Water Management Using Fuzzy-Probabilistic Multi-Objective Programming with Dynamic Efficiency," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(15), pages 4491-4504, December.
    17. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    18. Belaid AOUNI & Cinzia COLAPINTO & Davide LA TORRE, 2008. "Solving stochastic multi-objective programming through the GP model," Departmental Working Papers 2008-18, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    19. Suyun Liu & Luis Nunes Vicente, 2023. "Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 165-186, July.
    20. Selçuklu, Saltuk Buğra & Coit, David W. & Felder, Frank A., 2020. "Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems," European Journal of Operational Research, Elsevier, vol. 284(2), pages 644-659.
    21. Fatima Bellahcene, 2019. "Decision maker's preferences modeling for multiple objective stochastic linear programming problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(3), pages 5-16.

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    Keywords

    Stochastic Multiobjective Programming; Efficiency; Stochastic Approach; Multiobjective Approach.;
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