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Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems

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  • Selçuklu, Saltuk Buğra
  • Coit, David W.
  • Felder, Frank A.

Abstract

Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality to show the trade-off between objectives. Pareto optimality involves the identification of solutions that are not dominated by other solutions based on their respective objective functions. However, the Pareto optimality concept does not contain any information about the uncertainty of solutions. Evaluation and comparison of solutions becomes difficult when the objective functions are subjected to uncertainty. A new metric, the Pareto Uncertainty Index (PUI), is presented. This metric includes uncertainty due to the stochastic coefficients in the objective functions as part of the Pareto optimality concept to form an extended probabilistic Pareto set, we define as the p-Pareto set. The decision maker can observe and assess the randomness of solutions and compare the promising solutions according to their performance of satisfying objectives and any undesirable uncertainty. The PUI is an effective and convenient decision-making tool to compare promising solutions with multiple uncertain objectives.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:2:p:644-659
    DOI: 10.1016/j.ejor.2020.01.004
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    1. Konak, Abdullah & Coit, David W. & Smith, Alice E., 2006. "Multi-objective optimization using genetic algorithms: A tutorial," Reliability Engineering and System Safety, Elsevier, vol. 91(9), pages 992-1007.
    2. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    3. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    4. Caballero, Rafael & Cerda, Emilio & del Mar Munoz, Maria & Rey, Lourdes, 2004. "Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 158(3), pages 633-648, November.
    5. A. Charnes & W. W. Cooper & R. O. Ferguson, 1955. "Optimal Estimation of Executive Compensation by Linear Programming," Management Science, INFORMS, vol. 1(2), pages 138-151, January.
    6. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    7. Hu, Mengqi & Cho, Heejin, 2014. "A probability constrained multi-objective optimization model for CCHP system operation decision support," Applied Energy, Elsevier, vol. 116(C), pages 230-242.
    8. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    9. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    10. Kulturel-Konak, Sadan & Smith, Alice E. & Norman, Bryan A., 2006. "Multi-objective tabu search using a multinomial probability mass function," European Journal of Operational Research, Elsevier, vol. 169(3), pages 918-931, March.
    11. 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.
    12. Konak, Abdullah & Kulturel-Konak, Sadan & Levitin, Gregory, 2012. "Multi-objective optimization of linear multi-state multiple sliding window system," Reliability Engineering and System Safety, Elsevier, vol. 98(1), pages 24-34.
    13. 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.
    14. Abdelaziz, Fouad Ben & Aouni, Belaid & Fayedh, Rimeh El, 2007. "Multi-objective stochastic programming for portfolio selection," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1811-1823, March.
    15. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    16. Jaszkiewicz, Andrzej, 2002. "Genetic local search for multi-objective combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 137(1), pages 50-71, February.
    17. Teghem, J. & Dufrane, D. & Thauvoye, M. & Kunsch, P., 1986. "Strange: An interactive method for multi-objective linear programming under uncertainty," European Journal of Operational Research, Elsevier, vol. 26(1), pages 65-82, July.
    18. Jones, D. F. & Mirrazavi, S. K. & Tamiz, M., 2002. "Multi-objective meta-heuristics: An overview of the current state-of-the-art," European Journal of Operational Research, Elsevier, vol. 137(1), pages 1-9, February.
    19. 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.
    20. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    21. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    22. Taboada, Heidi A. & Baheranwala, Fatema & Coit, David W. & Wattanapongsakorn, Naruemon, 2007. "Practical solutions for multi-objective optimization: An application to system reliability design problems," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 314-322.
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    2. Selçuklu, Saltuk Buğra & Coit, D.W. & Felder, F.A., 2023. "Electricity generation portfolio planning and policy implications of Turkish power system considering cost, emission, and uncertainty," Energy Policy, Elsevier, vol. 173(C).

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