Abstract
The design of water networks consists of selecting pipe connections and pumps to ensure a given water demand to minimize investment and operating costs. Of particular importance is the modeling of variable speed pumps, which are usually represented by degree two and three polynomials approximating the characteristic diagrams. In total, this yields complex mixed-integer (non-convex) nonlinear programs.
This work investigates a reformulation of these characteristic diagrams, eliminating rotating speed variables and determining power usage in terms of volume flow and pressure increase. We characterize when this formulation is convex in the pressure variables. This structural observation is applied to design the water network of a high-rise building in which the piping is tree-shaped. For these problems, the volume flow can only attain finitely many values. We branch on these flow values, eliminating the non-convexities of the characteristic diagrams. Then we apply perspective cuts to strengthen the formulation. Numerical results demonstrate the advantage of the proposed approach.
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References
Altherr, L.C., Leise, P., Pfetsch, M.E., Schmitt, A.: Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP. Optim. Eng. 20(2), 605–645 (2019)
D’Ambrosio, C., Lodi, A., Wiese, S., Bragalli, C.: Mathematical programming techniques in water network optimization. Eur. J. Oper. Res. 243(3), 774–788 (2015)
Frangioni, A., Gentile, C.: Perspective cuts for a class of convex 0–1 mixed integer programs. Math. Program. 106(2), 225–236 (2006)
Gleixner, A., Bastubbe, M., Eifler, L., Gally, T., Gamrath, G., Gottwald, R.L., Hendel, G., Hojny, C., Koch, T., Lübbecke, M.E., Maher, S.J., Miltenberger, M., Müller, B., Pfetsch, M.E., Puchert, C., Rehfeldt, D., Schlösser, F., Schubert, C., Serrano, F., Shinano, Y., Viernickel, J.M., Walter, M., Wegscheider, F., Witt, J.T., Witzig, J.: The SCIP Optimization Suite 6.0. Technical report, Optimization Online (2018)
Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program 106(1), 25–57 (2006)
Acknowledgements
We thank Tim Müller (TU Darmstadt) for the pump approximations. This research was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Number 57157498—SFB 805.
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Pfetsch, M.E., Schmitt, A. (2020). Exploiting Partial Convexity of Pump Characteristics in Water Network Design. In: Neufeld, J.S., Buscher, U., Lasch, R., Möst, D., Schönberger, J. (eds) Operations Research Proceedings 2019. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-48439-2_60
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DOI: https://doi.org/10.1007/978-3-030-48439-2_60
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