Abstract
In this work we describe a good approach to solve chance-constrained programming with mixed-integer variables. We replace a hard chance constrained function by a copula. We prove that Zhang’s copula family satisfies the proprieties request by outer-approximation and we use this algorithm to solve this problem with promising results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arnold, T., Henrion, R., Möller, A., Vigerske, S.: A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints. Pac. J. Optim. 10, 5–25 (2014)
Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (2011)
de Oliveira, W.: Regularized optimization methods for convex MINLP problems. TOP 24, 665–692 (2016)
Delfino, A., de Oliveira, W.: Outer-approximation algorithms for nonsmooth convex MINLP problem. Optimization 67, 797–819 (2018)
Duran, M.A., Grossmann, I.E.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Program. 36, 307–339 (1986)
Eronen, V.P., Mäkelä, M.M., Westerlund, T.: On the generalization of ECP and OA methods to nonsmooth convex MINLP problems. Optimization 63, 1057–1073 (2014)
Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66, 327–349 (1994)
Nelsen, R.B.: An Introduction to Copulas. Springer, New York (2006)
Prékopa, A.: Stochastic Programming. Dordrechet (1995)
Quesada, I., Grossmann, I.E.: An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Comput. Chem. Eng. 16, 937–947 (1992)
Sklar, A.: Fountions de rapartition á dimentisions et leurs marges. Publications and Institut de Statistique de Paris 8, 229–231 (1959)
Song, Y., Luedtke, J., Küçükyavuz, S.: Chance-constrained binary packing problems. INFORMS J. Comput. 26, 735–747 (2014)
Vielma, J.P., Ahmed, S., Nemhauser, G.L.: Mixed integer linear programming formulations for probabilistic constraints. Oper. Res. Lett. 40, 153–158 (2012)
Westerlund, T., Pettersson, F.: An extended cutting plane method for solving convex MINLP problems. Comput. Chem. Eng. 19, 131–136 (1995)
Zhang, Z.: On approximation max-stable process and constructing extremal copula functions. In: Statistical Inference for Stochastic Process, vol. 12, pp. 89–114 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Delfino, A. (2020). Solving an MINLP with Chance Constraint Using a Zhang’s Copula Family. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_48
Download citation
DOI: https://doi.org/10.1007/978-3-030-21803-4_48
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21802-7
Online ISBN: 978-3-030-21803-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)