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Probabilistic constraints via SQP solver: application to a renewable energy management problem

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  • I. Bremer
  • R. Henrion
  • A. Möller

Abstract

This paper aims at illustrating the efficient solution of nonlinear optimization problems with joint probabilistic constraints under multivariate Gaussian distributions. The numerical solution approach is based on Sequential Quadratic Programming (SQP) and is applied to a renewable energy management problem. We consider a coupled system of hydro and wind power production used in order to satisfy some local demand of energy and to sell/buy excessive or missing energy on a day-ahead and intraday market, respectively. A short term planning horizon of 2 days is considered and only wind power is assumed to be random. In the first part of the paper, we develop an appropriate optimization problem involving a probabilistic constraint reflecting demand satisfaction. Major attention will be payed to formulate this probabilistic constraint not directly in terms of random wind energy produced but rather in terms of random wind speed, in order to benefit from a large data base for identifying an appropriate distribution of the random parameter. The second part presents some details on integrating Genz’ code for Gaussian probabilities of rectangles into the environment of the SQP solver SNOPT. The procedure is validated by means of a simplified optimization problem which by its convex structure allows to estimate the gap between the numerical and theoretical optimal values, respectively. In the last part, numerical results are presented and discussed for the original (nonconvex) optimization problem. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    • Handle: RePEc:spr:comgts:v:12:y:2015:i:3:p:435-459
    DOI: 10.1007/s10287-015-0228-z
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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    3. Andrieu, L. & Henrion, R. & Römisch, W., 2010. "A model for dynamic chance constraints in hydro power reservoir management," European Journal of Operational Research, Elsevier, vol. 207(2), pages 579-589, December.
    4. Y.M. Ermoliev & T.Y. Ermolieva & G.J. MacDonald & V.I. Norkin, 2000. "Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks," Annals of Operations Research, Springer, vol. 99(1), pages 207-225, December.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    6. Wim Van Ackooij & René Henrion & Andris Möller & Riadh Zorgati, 2010. "On probabilistic constraints induced by rectangular sets and multivariate normal distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 535-549, June.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    8. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    9. Aksoy, Hafzullah & Fuat Toprak, Z & Aytek, Ali & Erdem Ünal, N, 2004. "Stochastic generation of hourly mean wind speed data," Renewable Energy, Elsevier, vol. 29(14), pages 2111-2131.
    10. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    11. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    12. J. O. Royset & E. Polak, 2007. "Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 1-18, April.
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    Cited by:

    1. Jinxiang Wei & Zhaolin Hu & Jun Luo & Shushang Zhu, 2024. "Enhanced branch-and-bound algorithm for chance constrained programs with Gaussian mixture models," Annals of Operations Research, Springer, vol. 338(2), pages 1283-1315, July.
    2. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    3. Martin Branda & Štěpán Hájek, 2017. "Flow-based formulations for operational fixed interval scheduling problems with random delays," Computational Management Science, Springer, vol. 14(1), pages 161-177, January.
    4. Michel Minoux & Riadh Zorgati, 2019. "Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems," Journal of Global Optimization, Springer, vol. 75(3), pages 735-766, November.
    5. Amarjit Budhiraja & Shu Lu & Yang Yu & Quoc Tran-Dinh, 2021. "Minimization of a class of rare event probabilities and buffered probabilities of exceedance," Annals of Operations Research, Springer, vol. 302(1), pages 49-83, July.

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