# American Institute of Mathematical Sciences

2012, 2(4): 695-711. doi: 10.3934/naco.2012.2.695

## Towards globally optimal operation of water supply networks

 1 Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany 2 Siemens AG, Corporate Technology (CT RTC AUC SIM-DE), Otto-Hahn-Ring 6, 81739 Munich, Germany 3 Technische Universität München, International School of Applied Mathematics, Boltzmannstr. 3, 85748 Garching b. Munich, Germany 4 Humboldt-Universität, Department of Mathematics, Unter den Linden 6, 10099 Berlin, Germany

Received  March 2012 Revised  October 2012 Published  November 2012

This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to $\epsilon$-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms.
In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem.
Citation: Ambros M. Gleixner, Harald Held, Wei Huang, Stefan Vigerske. Towards globally optimal operation of water supply networks. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 695-711. doi: 10.3934/naco.2012.2.695
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