Abstract
We introduce a mixed integer linear modeling approach for the optimization of dynamic water supply networks based on the piecewise linearization of nonlinear constraints. One advantage of applying mixed integer linear techniques is that these methods are nowadays very mature, that is, they are fast, robust, and are able to solve problems with up to a huge number of variables. The other major point is that these methods have the potential of finding globally optimal solutions or at least to provide guarantees of the solution quality. We demonstrate the applicability of our approach on examples networks.
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
J. Abreu, E. Cabrera, J. Izquierdo, J. García-Serra, Flow modeling in pressurized systems revisited. J. Hydraul. Eng. 125, 1154–1169 (1999)
P. Domschke, B. Geißler, O. Kolb, J. Lang, A. Martin, A. Morsi, Combination of nonlinear and linear optimization of transient gas networks. INFORMS J. Comput. 23, 605–617 (2011)
A. Fügenschuh, M. Herty, A. Klar, A. Martin, Combinatorial and continuous models for the optimization of traffic flows on networks. SIAM J. Optim. 16, 1155–1176 (2006)
B. Geißler, A. Martin, A. Morsi, L. Schewe, Using piecewise linear functions for solving MINLPs, in Mixed Integer Nonlinear Programming, ed. by J. Lee, S. Leyffer. The IMA Volumes in Mathematics and its Applications, vol. 154 (Springer, Berlin, 2012), pp. 287–314
C.E. Gounaris, C.A. Floudas, Tight convex underestimators for ℂ2-continuous problems: I. Multivariate functions. J. Glob. Optim. 42, 69–89 (2008)
C.E. Gounaris, C.A. Floudas, Tight convex underestimators for ℂ2-continuous problems: I. Univariate functions. J. Glob. Optim. 42, 51–67 (2008)
Gurobi Optimization, Inc., Houston, Texas, USA. Gurobi Optimizer Version 4.0, 2010. Information available at URL http://www.gurobi.com
J. Lee, J. Margot, F. Margot, Min-up/min-down polytopes. Discrete Optim. 1, 77–85 (2004)
H.M. Markowitz, A.S. Manne, On the solution of discrete programming problems. Econometrica 25, 84–110 (1957)
M. Padberg, Approximating separable nonlinear functions via mixed zero-one programs. Oper. Res. Lett. 27(1), 1–5 (2000)
J.P. Vielma, A.B. Keha, G.L. Nemhauser, Nonconvex, lower semicontinuous piecewise linear optimization. Discrete Optim. 5(2), 467–488 (2008)
B. Wendroff, On centered difference equations for hyperbolic systems. J. Soc. Ind. Appl. Math. 8(3), 549–555 (1960)
D. Wilson, Polyhedral methods for piecewise-linear functions. Ph.D. thesis in Discrete Mathematics, University of Kentucky, 1998
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Basel
About this chapter
Cite this chapter
Morsi, A., Geißler, B., Martin, A. (2012). Mixed Integer Optimization of Water Supply Networks. In: Martin, A., et al. Mathematical Optimization of Water Networks. International Series of Numerical Mathematics, vol 162. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0436-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0436-3_3
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0435-6
Online ISBN: 978-3-0348-0436-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)