Numerical Algebra, Control and Optimization (NACO)

Towards globally optimal operation of water supply networks

Pages: 695 - 711, Volume 2, Issue 4, December 2012      doi:10.3934/naco.2012.2.695

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Ambros M. Gleixner - Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany (email)
Harald Held - Siemens AG, Corporate Technology (CT RTC AUC SIM-DE), Otto-Hahn-Ring 6, 81739 Munich, Germany (email)
Wei Huang - Technische Universität München, International School of Applied Mathematics, Boltzmannstr. 3, 85748 Garching b. Munich, Germany (email)
Stefan Vigerske - Humboldt-Universität, Department of Mathematics, Unter den Linden 6, 10099 Berlin, Germany (email)

Abstract: 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.

Keywords:  Nonconvex MINLP, global optimization, operative planning, water supply networks.
Mathematics Subject Classification:  Primary: 90C26; Secondary: 90C11, 90C90.

Received: March 2012;      Revised: October 2012;      Available Online: November 2012.