# 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
##### References:

show all references

##### References:
 [1] Chunrong Chen, T. C. Edwin Cheng, Shengji Li, Xiaoqi Yang. Nonlinear augmented Lagrangian for nonconvex multiobjective optimization. Journal of Industrial & Management Optimization, 2011, 7 (1) : 157-174. doi: 10.3934/jimo.2011.7.157 [2] Juan Carlos López Alfonso, Giuseppe Buttazzo, Bosco García-Archilla, Miguel A. Herrero, Luis Núñez. A class of optimization problems in radiotherapy dosimetry planning. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1651-1672. doi: 10.3934/dcdsb.2012.17.1651 [3] Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 [4] Radu C. Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo. Flow optimization in vascular networks. Mathematical Biosciences & Engineering, 2017, 14 (3) : 607-624. doi: 10.3934/mbe.2017035 [5] Zehui Jia, Xue Gao, Xingju Cai, Deren Han. The convergence rate analysis of the symmetric ADMM for the nonconvex separable optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1943-1971. doi: 10.3934/jimo.2020053 [6] Liping Tang, Ying Gao. Some properties of nonconvex oriented distance function and applications to vector optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (1) : 485-500. doi: 10.3934/jimo.2020117 [7] Chunrong Chen. A unified nonlinear augmented Lagrangian approach for nonconvex vector optimization. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 495-508. doi: 10.3934/naco.2011.1.495 [8] Weijun Zhou, Youhua Zhou. On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization. Journal of Industrial & Management Optimization, 2013, 9 (4) : 893-899. doi: 10.3934/jimo.2013.9.893 [9] Qilin Wang, S. J. Li. Higher-order sensitivity analysis in nonconvex vector optimization. Journal of Industrial & Management Optimization, 2010, 6 (2) : 381-392. doi: 10.3934/jimo.2010.6.381 [10] Hui Gao, Jian Lv, Xiaoliang Wang, Liping Pang. An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information. Journal of Industrial & Management Optimization, 2021, 17 (2) : 805-825. doi: 10.3934/jimo.2019135 [11] Qiong Liu, Jialiang Liu, Zhaorui Dong, Mengmeng Zhan, Zhen Mei, Baosheng Ying, Xinyu Shao. Integrated optimization of process planning and scheduling for reducing carbon emissions. Journal of Industrial & Management Optimization, 2021, 17 (3) : 1025-1055. doi: 10.3934/jimo.2020010 [12] Hanyu Gu, Hue Chi Lam, Yakov Zinder. Planning rolling stock maintenance: Optimization of train arrival dates at a maintenance center. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020177 [13] Giuseppe Buttazzo, Filippo Santambrogio. Asymptotical compliance optimization for connected networks. Networks & Heterogeneous Media, 2007, 2 (4) : 761-777. doi: 10.3934/nhm.2007.2.761 [14] Michael Herty, Veronika Sachers. Adjoint calculus for optimization of gas networks. Networks & Heterogeneous Media, 2007, 2 (4) : 733-750. doi: 10.3934/nhm.2007.2.733 [15] Joseph Geunes, Panos M. Pardalos. Introduction to the Special Issue on Supply Chain Optimization. Journal of Industrial & Management Optimization, 2007, 3 (1) : i-ii. doi: 10.3934/jimo.2007.3.1i [16] Yuki Kumagai. Social networks and global transactions. Journal of Dynamics & Games, 2019, 6 (3) : 211-219. doi: 10.3934/jdg.2019015 [17] Yi Jing, Wenchuan Li. Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain. Journal of Industrial & Management Optimization, 2018, 14 (2) : 511-539. doi: 10.3934/jimo.2017058 [18] Gonglin Yuan, Zhan Wang, Pengyuan Li. Global convergence of a modified Broyden family method for nonconvex functions. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021164 [19] Pierre Fabrie, Elodie Jaumouillé, Iraj Mortazavi, Olivier Piller. Numerical approximation of an optimization problem to reduce leakage in water distribution systems. Mathematical Control & Related Fields, 2012, 2 (2) : 101-120. doi: 10.3934/mcrf.2012.2.101 [20] Hamid Norouzi Nav, Mohammad Reza Jahed Motlagh, Ahmad Makui. Modeling and analyzing the chaotic behavior in supply chain networks: a control theoretic approach. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1123-1141. doi: 10.3934/jimo.2018002

Impact Factor: