Abstract
We are interested in the optimal control of sewage networks. It is of high public interest to minimize the overflow of sewage onto the streets and to the natural environment that may occur during periods of heavy rain. The assumption of linear flow in a discrete time setting has proven to be adequate for the practical control of larger systems. However, the possibility of overflow introduces a nonlinear and nondifferentiable element to the formulation, by means of a maximum of linear terms. This particular challenge can be addressed by smoothing methods that result in a nonlinear program (NLP) or by logical constraints that result in a mixed integer linear program (MILP). We discuss both approaches and present a novel tailored branch-and-bound algorithm that outperforms competing methods from the literature for a set of realistic rain scenarios.
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Acknowledgments
This work has been partially funded by the EU Project EFFINET (FP7-ICT-2011-8-31855) and DGR of Generalitat de Catalunya (SAC group Ref. 2009/SGR/1491). Financial support of the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences and of the EU project EMBOCON under grant FP7-ICT-2009-4 248940 is gratefully acknowledged.
The cooperation of CLABSA (Claveguream de Barcelona S.A.) in providing data and useful guidance is also gratefully acknowledged.
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Joseph-Duran, B., Jung, M.N., Ocampo-Martinez, C. et al. Minimization of Sewage Network Overflow. Water Resour Manage 28, 41–63 (2014). https://doi.org/10.1007/s11269-013-0468-z
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DOI: https://doi.org/10.1007/s11269-013-0468-z