-
Previous Article
Two-stage stochastic programs: Integer variables, dominance relations and PDE constraints
- NACO Home
- This Issue
-
Next Article
The integrated size and price optimization problem
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 |
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.
References:
[1] |
Tobias Achterberg, "Constraint Integer Programming,", PhD thesis, (2007). Google Scholar |
[2] |
Tobias Achterberg, SCIP: Solving constraint integer programs,, Mathematical Programming Computation, 1 (2009), 1.
doi: 10.1007/s12532-008-0001-1. |
[3] |
Pietro Belotti, Jon Lee, Leo Liberti, Francois Margot and Andreas Wächter, Branching and bounds tightening techniques for non-convex MINLP,, Optimization Methods and Software, 24 (2009), 597.
doi: 10.1080/10556780903087124. |
[4] |
Timo Berthold, "Primal Heuristics for Mixed Integer Programs,", Master's thesis, (2006). Google Scholar |
[5] |
Timo Berthold and Ambros M. Gleixner, Undercover - a primal heuristic for MINLP based on sub-MIPs generated by set covering,, in, (2010), 103. Google Scholar |
[6] |
Timo Berthold and Ambros M. Gleixner, Undercover - a primal MINLP heuristic exploring a largest sub-MIP,, ZIB-Report 12-07 (2012), (2012), 12. Google Scholar |
[7] |
Timo Berthold, Stefan Heinz, Marc E. Pfetsch and Stefan Vigerske, Large neighborhood search beyond MIP,, in, (2011), 51. Google Scholar |
[8] |
Timo Berthold, Stefan Heinz and Stefan Vigerske, Extending a CIP framework to solve MIQCPs,, in, 154 (2012), 427.
doi: 10.1007/978-1-4614-1927-3_15. |
[9] |
Cristiana Bragalli, Claudia D'mbrosio, Jon Lee, Andrea Lodi and Paolo Toth, On the optimal design of water distribution networks: a practical MINLP approach,, Optimization and Engineering, 13 (2012), 219.
doi: 10.1007/s11081-011-9141-7. |
[10] |
Jens Burgschweiger, Bernd Gnädig and Marc C. Steinbach, Optimization models for operative planning in drinking water networks,, ZIB-Report 04-48 (2004), (2004), 04. Google Scholar |
[11] |
Björn Geißler, Oliver Kolb, Jens Lang, Günter Leugering, Alexander Martin and Antonio Morsi, Mixed integer linear models for the optimization of dynamical transport networks,, Mathematical Methods of Operations Research, 73 (2011), 339.
doi: 10.1007/s00186-011-0354-5. |
[12] |
Wei Huang, "Operative Planning of Water Supply Networks by Mixed Integer Nonlinear Programming,", Master's thesis, (2011). Google Scholar |
[13] |
Kathrin Klamroth, Jens Lang, Günter Leugering, Alexander Martin, Antonio Morsi, Martin Oberlack, Manfred Ostrowski and Roland Rosen, "Mathematical Optimization of Water Networks,", International Series of Numerical Mathematics, 162 (2012). Google Scholar |
[14] |
Oliver Kolb, "Simulation and Optimization of Gas and Water Supply Networks,", PhD thesis, (2011). Google Scholar |
[15] |
Ailsa H. Land and Alison G. Doig, An automatic method for solving discrete programming problems,, Econometrica, 28 (1960), 497.
|
[16] |
Youdong Lin and Linus Schrage, The global solver in the LINDO API,, Optimization Methods & Software, 24 (2009), 657.
doi: 10.1080/10556780902753221. |
[17] |
Hanif D. Sherali and Ernest P. Smith, A global optimization approach to a water distribution network design problem,, Journal of Global Optimization, 11 (1997), 107.
doi: 10.1023/A:1008207817095. |
[18] |
Mohit Tawarmalani and Nikolaos V. Sahinidis, Global optimization of mixed-integer nonlinear programs: A theoretical and computational study,, Mathematical Programming, 99 (2004), 563.
doi: 10.1007/s10107-003-0467-6. |
[19] |
Stefan Vigerske, "Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming,", Ph.D thesis, (2012). Google Scholar |
[20] |
Andreas Wächter and Lorenz T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming,, Mathematical Programming, 106 (2006), 125.
doi: 10.1007/s10107-004-0559-y. |
[21] |
CppAD, "A Package for Differentiation of C++ algorithms,", Available from: , (). Google Scholar |
[22] |
EPANET, "A software that models water distribution piping systems,", Available from: , (). Google Scholar |
[23] |
Ipopt, "Interior Point Optimizer,", Available from: , (). Google Scholar |
[24] |
SCIP, "Solving Constraint Integer Programs,", Available from: , (). Google Scholar |
[25] |
SoPlex, "Sequential Object-oriented SimPlex,", Available from: , (). Google Scholar |
[26] |
Zimpl, "Zuse Institute Mathematical Programming Language,", Available from: , (). Google Scholar |
show all references
References:
[1] |
Tobias Achterberg, "Constraint Integer Programming,", PhD thesis, (2007). Google Scholar |
[2] |
Tobias Achterberg, SCIP: Solving constraint integer programs,, Mathematical Programming Computation, 1 (2009), 1.
doi: 10.1007/s12532-008-0001-1. |
[3] |
Pietro Belotti, Jon Lee, Leo Liberti, Francois Margot and Andreas Wächter, Branching and bounds tightening techniques for non-convex MINLP,, Optimization Methods and Software, 24 (2009), 597.
doi: 10.1080/10556780903087124. |
[4] |
Timo Berthold, "Primal Heuristics for Mixed Integer Programs,", Master's thesis, (2006). Google Scholar |
[5] |
Timo Berthold and Ambros M. Gleixner, Undercover - a primal heuristic for MINLP based on sub-MIPs generated by set covering,, in, (2010), 103. Google Scholar |
[6] |
Timo Berthold and Ambros M. Gleixner, Undercover - a primal MINLP heuristic exploring a largest sub-MIP,, ZIB-Report 12-07 (2012), (2012), 12. Google Scholar |
[7] |
Timo Berthold, Stefan Heinz, Marc E. Pfetsch and Stefan Vigerske, Large neighborhood search beyond MIP,, in, (2011), 51. Google Scholar |
[8] |
Timo Berthold, Stefan Heinz and Stefan Vigerske, Extending a CIP framework to solve MIQCPs,, in, 154 (2012), 427.
doi: 10.1007/978-1-4614-1927-3_15. |
[9] |
Cristiana Bragalli, Claudia D'mbrosio, Jon Lee, Andrea Lodi and Paolo Toth, On the optimal design of water distribution networks: a practical MINLP approach,, Optimization and Engineering, 13 (2012), 219.
doi: 10.1007/s11081-011-9141-7. |
[10] |
Jens Burgschweiger, Bernd Gnädig and Marc C. Steinbach, Optimization models for operative planning in drinking water networks,, ZIB-Report 04-48 (2004), (2004), 04. Google Scholar |
[11] |
Björn Geißler, Oliver Kolb, Jens Lang, Günter Leugering, Alexander Martin and Antonio Morsi, Mixed integer linear models for the optimization of dynamical transport networks,, Mathematical Methods of Operations Research, 73 (2011), 339.
doi: 10.1007/s00186-011-0354-5. |
[12] |
Wei Huang, "Operative Planning of Water Supply Networks by Mixed Integer Nonlinear Programming,", Master's thesis, (2011). Google Scholar |
[13] |
Kathrin Klamroth, Jens Lang, Günter Leugering, Alexander Martin, Antonio Morsi, Martin Oberlack, Manfred Ostrowski and Roland Rosen, "Mathematical Optimization of Water Networks,", International Series of Numerical Mathematics, 162 (2012). Google Scholar |
[14] |
Oliver Kolb, "Simulation and Optimization of Gas and Water Supply Networks,", PhD thesis, (2011). Google Scholar |
[15] |
Ailsa H. Land and Alison G. Doig, An automatic method for solving discrete programming problems,, Econometrica, 28 (1960), 497.
|
[16] |
Youdong Lin and Linus Schrage, The global solver in the LINDO API,, Optimization Methods & Software, 24 (2009), 657.
doi: 10.1080/10556780902753221. |
[17] |
Hanif D. Sherali and Ernest P. Smith, A global optimization approach to a water distribution network design problem,, Journal of Global Optimization, 11 (1997), 107.
doi: 10.1023/A:1008207817095. |
[18] |
Mohit Tawarmalani and Nikolaos V. Sahinidis, Global optimization of mixed-integer nonlinear programs: A theoretical and computational study,, Mathematical Programming, 99 (2004), 563.
doi: 10.1007/s10107-003-0467-6. |
[19] |
Stefan Vigerske, "Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming,", Ph.D thesis, (2012). Google Scholar |
[20] |
Andreas Wächter and Lorenz T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming,, Mathematical Programming, 106 (2006), 125.
doi: 10.1007/s10107-004-0559-y. |
[21] |
CppAD, "A Package for Differentiation of C++ algorithms,", Available from: , (). Google Scholar |
[22] |
EPANET, "A software that models water distribution piping systems,", Available from: , (). Google Scholar |
[23] |
Ipopt, "Interior Point Optimizer,", Available from: , (). Google Scholar |
[24] |
SCIP, "Solving Constraint Integer Programs,", Available from: , (). Google Scholar |
[25] |
SoPlex, "Sequential Object-oriented SimPlex,", Available from: , (). Google Scholar |
[26] |
Zimpl, "Zuse Institute Mathematical Programming Language,", Available from: , (). Google Scholar |
[1] |
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 |
[2] |
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 |
[3] |
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 |
[4] |
Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344 |
[5] |
Bing Yu, Lei Zhang. Global optimization-based dimer method for finding saddle points. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 741-753. doi: 10.3934/dcdsb.2020139 |
[6] |
Xiaoxian Tang, Jie Wang. Bistability of sequestration networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1337-1357. doi: 10.3934/dcdsb.2020165 |
[7] |
Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial & Management Optimization, 2021, 17 (1) : 393-408. doi: 10.3934/jimo.2019117 |
[8] |
Robert Stephen Cantrell, King-Yeung Lam. Competitive exclusion in phytoplankton communities in a eutrophic water column. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020361 |
[9] |
Bilal Al Taki, Khawla Msheik, Jacques Sainte-Marie. On the rigid-lid approximation of shallow water Bingham. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 875-905. doi: 10.3934/dcdsb.2020146 |
[10] |
D. R. Michiel Renger, Johannes Zimmer. Orthogonality of fluxes in general nonlinear reaction networks. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 205-217. doi: 10.3934/dcdss.2020346 |
[11] |
Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2020 doi: 10.3934/jcd.2021006 |
[12] |
Honglin Yang, Jiawu Peng. Coordinating a supply chain with demand information updating. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020181 |
[13] |
Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond. A new model for the emergence of blood capillary networks. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2021001 |
[14] |
Leslaw Skrzypek, Yuncheng You. Feedback synchronization of FHN cellular neural networks. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021001 |
[15] |
Linfeng Mei, Feng-Bin Wang. Dynamics of phytoplankton species competition for light and nutrient with recycling in a water column. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020359 |
[16] |
Marta Biancardi, Lucia Maddalena, Giovanni Villani. Water taxes and fines imposed on legal and illegal firms exploiting groudwater. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021008 |
[17] |
Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020165 |
[18] |
Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020173 |
[19] |
Hongfei Yang, Xiaofeng Ding, Raymond Chan, Hui Hu, Yaxin Peng, Tieyong Zeng. A new initialization method based on normed statistical spaces in deep networks. Inverse Problems & Imaging, 2021, 15 (1) : 147-158. doi: 10.3934/ipi.2020045 |
[20] |
Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón, Hong Wan. Loss-averse supply chain decisions with a capital constrained retailer. Journal of Industrial & Management Optimization, 2021, 17 (2) : 711-732. doi: 10.3934/jimo.2019131 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]