A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems
Abstract Water distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems....
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| Format: | Article |
| Language: | English |
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Wiley
2024-02-01
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| Series: | Water Resources Research |
| Online Access: | https://doi.org/10.1029/2023WR034526 |
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| _version_ | 1849687119814983680 |
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| author | Meghna Thomas Lina Sela |
| author_facet | Meghna Thomas Lina Sela |
| author_sort | Meghna Thomas |
| collection | DOAJ |
| description | Abstract Water distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations. |
| format | Article |
| id | doaj-art-88466040e712497e8d7358dfbf7a503b |
| institution | DOAJ |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-88466040e712497e8d7358dfbf7a503b2025-08-20T03:22:26ZengWileyWater Resources Research0043-13971944-79732024-02-01602n/an/a10.1029/2023WR034526A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations ProblemsMeghna Thomas0Lina Sela1The University of Texas at Austin Austin TX USAThe University of Texas at Austin Austin TX USAAbstract Water distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.https://doi.org/10.1029/2023WR034526 |
| spellingShingle | Meghna Thomas Lina Sela A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems Water Resources Research |
| title | A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems |
| title_full | A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems |
| title_fullStr | A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems |
| title_full_unstemmed | A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems |
| title_short | A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems |
| title_sort | mixed integer linear programming framework for optimization of water network operations problems |
| url | https://doi.org/10.1029/2023WR034526 |
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