Abstract
Different reasons can hinder the application of multiparametric programming formulations to solve optimization problems under uncertainty, as the high nonlinearity of the optimization model, and/or its complicated structure. This work presents a complementary method that can assist in such situations. The proposed tool uses kriging metamodels to provide global multiparametric metamodels that approximate the optimal solutions as functions of the problem uncertain parameters. The method has been tested with two benchmark problems of different characteristics, and applied to a case study. The results show the high accuracy of the methodology to predict the multiparametric behavior of the optimal solution, high robustness to deal with different problem types using small number of data, and significant reduction in the solution procedure complexity in comparison with classical multiparametric programming approaches.
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References
Dua, V., Bozinis, N.A., et al.: A multiparametric programming approach for mixed-integer quadratic engineering problems. Comput. Chem. Eng. 26, 715–733 (2002)
Pistikopoulos E.N., Georgias M.C et al.: Multiparametric programming: Theory, Algorithim, and Application. Wiley, New York (2007)
Pistikopoulos, E.N., et al.: Theoretical and algorithmic advances in multi-parametric programming and control. Comput. Manage. Sci. 9, 183–203 (2012)
Rivotti, P., et al.: Combined model approximation techniques and multiparametric programming for explicit nonlinear model predictive control. Comput. Chem. Eng. 42, 277–287 (2012)
Shokry, A., Bojarski, A.D., Espuna, A.: Using surrogate models for process design and optimization. Uncertainty Modeling in Knowledge Engineering and Decision Making, 483–488 (2012)
Shokry, A., Espuna, A.: Applying Metamodels and Sequential Sampling for Constrained Optimization of Process Operations. LNCS. 8468, 396–407 (2014)
Acknowledgements
Financial support received from the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (both funding the research Project SIGERA, DPI2012-37154-C02-01), and from the Generalitat de Catalunya (2014-SGR-1092-CEPEiMA) is fully appreciated.
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Shokry, A., Espuña, A. (2017). Optimization Under Uncertainty Based on Multiparametric Kriging Metamodels. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_78
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DOI: https://doi.org/10.1007/978-3-319-42902-1_78
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