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Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation

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  • Mavrotas, George
  • Pechak, Olena
  • Siskos, Eleftherios
  • Doukas, Haris
  • Psarras, John

Abstract

In most multi-objective optimization problems we aim at selecting the most preferred among the generated Pareto optimal solutions (a subjective selection among objectively determined solutions). In this paper we consider the robustness of the selected Pareto optimal solution in relation to perturbations within weights of the objective functions. For this task we design an integrated approach that can be used in multi-objective discrete and continuous problems using a combination of Monte Carlo simulation and optimization. In the proposed method we introduce measures of robustness for Pareto optimal solutions. In this way we can compare them according to their robustness, introducing one more characteristic for the Pareto optimal solution quality. In addition, especially in multi-objective discrete problems, we can detect the most robust Pareto optimal solution among neighboring ones. A computational experiment is designed in order to illustrate the method and its advantages. It is noteworthy that the Augmented Weighted Tchebycheff proved to be much more reliable than the conventional weighted sum method in discrete problems, due to the existence of unsupported Pareto optimal solutions.

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  • Mavrotas, George & Pechak, Olena & Siskos, Eleftherios & Doukas, Haris & Psarras, John, 2015. "Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 240(1), pages 193-201.
    • Handle: RePEc:eee:ejores:v:240:y:2015:i:1:p:193-201
    DOI: 10.1016/j.ejor.2014.06.039
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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
    3. Lahdelma, Risto & Hokkanen, Joonas & Salminen, Pekka, 1998. "SMAA - Stochastic multiobjective acceptability analysis," European Journal of Operational Research, Elsevier, vol. 106(1), pages 137-143, April.
    4. Liesiö, Juuso & Mild, Pekka & Salo, Ahti, 2008. "Robust portfolio modeling with incomplete cost information and project interdependencies," European Journal of Operational Research, Elsevier, vol. 190(3), pages 679-695, November.
    5. Mareschal, Bertrand, 1988. "Weight stability intervals in multicriteria decision aid," European Journal of Operational Research, Elsevier, vol. 33(1), pages 54-64, January.
    6. Liesio, Juuso & Mild, Pekka & Salo, Ahti, 2007. "Preference programming for robust portfolio modeling and project selection," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1488-1505, September.
    7. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    8. Tervonen, Tommi & van Valkenhoef, Gert & Baştürk, Nalan & Postmus, Douwe, 2013. "Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 224(3), pages 552-559.
    9. Wang, Jingguo & Zionts, Stanley, 2006. "The aspiration level interactive method (AIM) reconsidered: Robustness of solutions," European Journal of Operational Research, Elsevier, vol. 175(2), pages 948-958, December.
    10. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    11. Tervonen, Tommi & Figueira, José Rui & Lahdelma, Risto & Dias, Juscelino Almeida & Salminen, Pekka, 2009. "A stochastic method for robustness analysis in sorting problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 236-242, January.
    12. Wierzbicki, Andrzej P. & Granat, Janusz, 1999. "Multi-objective modeling for engineering applications: DIDASN++ system," European Journal of Operational Research, Elsevier, vol. 113(2), pages 374-389, March.
    13. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
    14. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    15. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    8. Afrasiabi, Ahmadreza & Chalmardi, Mazyar Kaboli & Balezentis, Tomas, 2022. "A novel hybrid evaluation framework for public organizations based on employees’ performance factors," Evaluation and Program Planning, Elsevier, vol. 91(C).

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