# An Optimal Model and Application of Hydraulic Structure Regulation to Improve Water Quality in Plain River Networks

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) over 0.95. Compared to the two traditional algorithms, the IGSA-BPNN model was, respectively, improved by 1.5% and 0.9% on R

^{2}in the train dataset, and 1.1% and 1.5% in the test dataset. The optimal scheduling model for hydraulic structures led to a reduction of 46~69% in total power consumption while achieving the water quality objectives. With the lowest cost scheme in practice, the proposed intelligent scheduling model is recommended for water diversion projects in plain river networks.

## 1. Introduction

## 2. Methods

#### 2.1. Traditional Gravitational Search Algorithm

#### 2.2. Proposed Algorithm: IPSOGSA

#### 2.2.1. Opposition-Based Learning

#### 2.2.2. Elite Mutation Strategy

#### 2.2.3. Local Search Strategy

#### 2.2.4. Co-Evolution Strategies

#### 2.2.5. Location Update Strategy

#### 2.2.6. The Procedure of IPSOGSA

#### 2.3. Experiment Results and Discussion

^{®}version R2019b.

#### 2.3.1. Classical Benchmark Functions Set

_{1}(x)–${f}_{5}$(x), f

_{7}(x)), as illustrated in Table S5 (in Supplementary Materials). Especially for functions ${f}_{1}$(x)–f

_{4}(x), the IPSOGSA could acquire the theoretical optimal solution, 0, in three different dimensions. For function ${f}_{6}$ (Dim = 30/50), the mean value with the highest precision was obtained by the PSOGSA, while the IPSOGSA showed an improved performance compared to other two algorithms when dealing with the high-dimensional (Dim = 100) problem of function f

_{6}, where the result differed by at least four orders of magnitude. On the other hand, their final ranks point out the superiority of the IPSOGSA over the GSA and PSOGSA, especially high-dimensional problems. the IPSOGSA provided 90% of the best mean values of the unimodal benchmark functions on three different dimensions, followed by the PSOGSA (10%) and the GSA (0%). These results imply that the GSA and PSOGSA suffered from premature convergence.

_{4}(x) is 0, the other three representative results are selected to be exhibited in boxplots, and from left to right, the data distributions of the three algorithms from low-dimensional to high-dimensional are shown. The box-and-whisker diagrams illustrate that the proposed algorithm possesses the shortest distance and lowest altitude in Figure 2, while the GSA and PSOGSA have more discrete data distribution as the dimension increases. For the seven benchmark functions with dimensions 30/50/100, the IPSOGSA not only converged to the global optimal solutions, but also had stronger stability. These results indicate that the proposed algorithm is more competitive and reliable for solving unimodal benchmark functions.

_{12}(x)). For the multimodal benchmark functions ${f}_{9}$(x) and f

_{11}(x) with dimensions 30/50/100, the IPSOGSA could also find the theoretical optimal solution of 0. For function ${f}_{13}$(x), the IPSOGSA performed worse than the PSOGSA for low-dimensional problems (Dim = 30). However, with the increase in the function dimension, the advantages of the proposed algorithm appear more prominent. The IPSOGSA obtained the best mean value compared with the other two algorithms in the high dimension of function f

_{13}(x) (Dim = 100). In addition, the final overall ranking indicated that the IPSOGSA outperformed the GSA and PSOGSA in solving the global solution of multimodal benchmark functions in three different dimensions. The IPSOGSA obtained 89% of the best results on the mean and standard deviation of the multimodal benchmark functions. The PSOGSA was only superior to the IPSOGSA in two (11%) of the test results, while the GSA had the worst performance. According to the convergence curve, the IPSOGSA can obtain optimal results with fastest convergence velocity (Figure S2 in Supplementary Materials). The optimal results of f

_{8}, f

_{12}, and f

_{13}are exhibited in boxplots (Figure 3). The box-and-whisker diagrams indicate that the IPSOGSA had a more concentrated distribution of optimal results over 30 independent runs and still performed well in high-dimensional problems. For the multimodal benchmark functions, the proposed algorithm had a higher probability of finding high-quality solutions compared to other algorithms. Evidently, the hybrid optimization scheme enhanced the exploration competence of the algorithm and prevented precocious convergence.

_{1}–f

_{5}and f

_{8}–f

_{12}with 30 variables [48]. Compared to a novel metaheuristic algorithm, the IPSOGSA outperformed the Chimp Optimization Algorithm (2020) on 10 high-dimensional (Dim = 100) traditional benchmark functions [49]. These findings suggest that the proposed algorithm possesses a strong exploration ability and is effective for high-dimensional (Dim = 100) traditional benchmark functions as well. The improved algorithm (IPSOGSA) significantly enhances the performance of the traditional gravitational search algorithm and demonstrates competitiveness in solving single-objective optimization problems.

#### 2.3.2. Modern Benchmark Functions Set

## 3. Optimal Scheduling Model of Hydraulic Structures

#### 3.1. Mathematical Problem Formulation

#### 3.1.1. Economic Objective

#### 3.1.2. Water Quality Constraints

#### 3.1.3. Hydraulic Constraints

#### 3.2. Water Quality Prediction Model

## 4. Practical Application

#### 4.1. Case Study

^{2}, with 256 rivers and 52 hydraulic structures for flood control. Jiaxing City suffers from poor water quality in its rivers, owing to the stagnant water flow caused by flood control structures. Long-term practice has proved that water diversion through these structures can significantly improve the water quality of the river network. In order to maximize the economic benefit and environmental benefit, this study applied the improved gravitational search algorithm to solve the optimization problem of the joint management of sluices and pumps in water diversion projects. In this study, the IPSOGSA was applied as the optimizer. One is to optimize the weights and thresholds of the BPNN. The other is to solve the optimal dispatching problem of water diversion projects (Figure 4).

#### 4.2. Backpropagation Neural Network

_{Mn}), ammonia nitrogen (NH

_{3}-N), and total phosphorus (TP). The sample data of three models were consistent, which was divided into a training set (900) and a test set (100). The network structure was 13-12-3. The initial interval of weights and thresholds was [−3, 3]. The max iteration was 10 and the population size was 40.

^{2}) of the predicted results were taken as evaluation indices to reflect the fitting degree of the BPNN in practical engineering applications. The smaller RMSE and larger R

^{2}mean that the model has a higher fitting degree, accuracy, and prediction ability.

^{2}in both the training set and the test set. It is noteworthy that the R

^{2}values of the IGSA-BPNN model are all more than 0.95. Compared with the GA and GSA, the IGSA-BPNN model, respectively, achieved an average improvement of 1.5% and 0.9% in R

^{2}on the training set, and 1.1% and 1.5% on the test set. The IGSA-BPNN model led to a reduction of 18.6% and 13.1% in RMSE in the training set, and 13.3% and 19.7% in the test set. In addition, the IGSA-BPNN model does not suffer from overfitting or underfitting problems. These findings verified that the IGSA-BPNN model is the best model for water quality prediction.

#### 4.3. Optimal Operation Scheduling of Water Diversion Project

^{3}/s, 60 m

^{3}/s, and 36 m

^{3}/s, respectively (Figure 5). The maximum operation time of the pumps is 180 h. The operation height of the gate was [0.3, 1.5] (unit: meters). Five scenarios are depicted in Table 4. The initial target water quality in scenario 1 and scenario 2 is the same, and the upstream water quality in scenario 2 is better than that in scenario 1. The upstream water quality of scenario 2 and scenario 3 is the same, and the initial target water quality in scenario 3 is better than that in scenario 2. The target water quality in scenario 4 meets the Class III environmental quality standards for surface water. The target water quality in scenario 5 is better than the upstream water quality.

## 5. Conclusions

^{2}values. The optimal scheduling model provided the optimal and feasible operation scheme under various scenarios for the multi-objective regulation problem of the Jiaxing water diversion project. These results show that the established intelligent scheduling model has good reliability and application prospects. The intelligent scheduling model can be applied to assist decision-makers in selecting the most efficient operation plan. This method can be extended to similar areas and used to develop operation strategies of water diversion projects for regional water quality improvement.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Hosper, H.; Meyer, M.-L. Control of phosphorus loading and flushing as restoration methods for Lake Veluwe, The Netherlands. Hydrobiol. Bull.
**1986**, 20, 183–194. [Google Scholar] [CrossRef] - Welch, E.B.; Barbiero, R.P.; Bouchard, D.; Jones, C.A. Lake trophic state change and constant algal composition following dilution and diversion. Ecol. Eng.
**1992**, 1, 173–197. [Google Scholar] [CrossRef] - Bode, H.; Evers, P.; Albrecht, D.R. Integrated water resources management in the Ruhr River Basin, Germany. Water Sci. Technol.
**2003**, 47, 81–86. [Google Scholar] [CrossRef] [PubMed] - Lane, R.R.; Day, J.W.; Kemp, G.P.; Demcheck, D.K. The 1994 experimental opening of the Bonnet Carre Spillway to divert Mississippi River water into Lake Pontchartrain, Louisiana. Ecol. Eng.
**2001**, 17, 411–422. [Google Scholar] [CrossRef] - Yin, W.; Xin, X.K.; Jia, H.Y. Preliminary research on hydrodynamic dispatch method of algal blooms in Three Gorges Reservoir Bays. Appl. Mech. Mater.
**2014**, 675–677, 811–817. [Google Scholar] [CrossRef] - Gao, X.P.; Xu, L.P.; Zhang, C. Modelling the effect of water diversion projects on renewal capacity in an urban artificial lake in China. J. Hydroinformatics
**2015**, 17, 990–1002. [Google Scholar] [CrossRef] - Kumar, D.N.; Baliarsingh, F.; Raju, K.S. Optimal reservoir operation for flood control using folded dynamic programming. Water Resour. Manag.
**2010**, 24, 1045–1064. [Google Scholar] [CrossRef] - Chang, L.C. Guiding rational reservoir flood operation using penalty-type genetic algorithm. J. Hydrol.
**2008**, 354, 65–74. [Google Scholar] [CrossRef] - Chen, H.-t.; Wang, W.-c.; Chau, K.-w.; Xu, L.; He, J. Flood Control Operation of Reservoir Group Using Yin-Yang Firefly Algorithm. Water Resour. Manag.
**2021**, 35, 5325–5345. [Google Scholar] [CrossRef] - Li, Q.; Ouyang, S. Research on multi-objective joint optimal flood control model for cascade reservoirs in river basin system. Nat. Hazards
**2015**, 77, 2097–2115. [Google Scholar] [CrossRef] - Niu, W.-j.; Feng, Z.-k.; Liu, S. Multi-strategy gravitational search algorithm for constrained global optimization in coordinative operation of multiple hydropower reservoirs and solar photovoltaic power plants. Appl. Soft Comput.
**2021**, 107, 107315. [Google Scholar] [CrossRef] - Zhou, Y.L.; Guo, S.L.; Chang, F.J.; Liu, P.; Chen, A.B. Methodology that improves water utilization and hydropower generation without increasing flood risk in mega cascade reservoirs. Energy
**2018**, 143, 785–796. [Google Scholar] [CrossRef] - Xu, Z.; Mo, L.; Zhou, J.; Zhang, X. Optimal dispatching rules of hydropower reservoir in flood season considering flood resources utilization: A case study of Three Gorges Reservoir in China. J. Clean. Prod.
**2023**, 388, 135975. [Google Scholar] [CrossRef] - Moazeni, F.; Khazaei, J. Optimal design and operation of an islanded water-energy network including a combined electrodialysis-reverse osmosis desalination unit. Renew. Energy
**2021**, 167, 395–408. [Google Scholar] [CrossRef] - Yan, P.; Zhang, Z.; Lei, X.; Hou, Q.; Wang, H. A multi-objective optimal control model of cascade pumping stations considering both cost and safety. J. Clean. Prod.
**2022**, 345, 131171. [Google Scholar] [CrossRef] - Liu, Y.; Zheng, H.; Wan, W.; Zhao, J. Optimal operation toward energy efficiency of the long-distance water transfer project. J. Hydrol.
**2023**, 618, 129152. [Google Scholar] [CrossRef] - Zhu, Y.P.; Zhang, H.P.; Chen, L.; Zhao, J.F. Influence of the South–North Water Diversion Project and the Mitigation Projects on the water quality of Han River. Sci. Total Environ.
**2008**, 406, 57–68. [Google Scholar] [CrossRef] - Yang, H.; Wang, J.; Li, J.; Zhou, H.; Liu, Z. Modelling impacts of water diversion on water quality in an urban artificial lake. Environ. Pollut.
**2021**, 276, 116694. [Google Scholar] [CrossRef] - Zhou, H.P.; Shao, W.Y.; Jiang, L.J. Optimal model of hydrodynamic controlling on pumps and slice gates for water quality improvement. Appl. Mech. Mater.
**2013**, 316–317, 732–740. [Google Scholar] [CrossRef] - Emary, E.; Zawbaa, H.M.; Grosan, C. Experienced Gray Wolf Optimization Through Reinforcement Learning and Neural Networks. IEEE Trans. Neural Netw. Learn. Syst.
**2018**, 29, 681–694. [Google Scholar] [CrossRef] - Heidari, A.A.; Faris, H.; Aljarah, I.; Mirjalili, S. An efficient hybrid multilayer perceptron neural network with grasshopper optimization. Soft Comput.
**2019**, 23, 7941–7958. [Google Scholar] [CrossRef] - Khishe, M.; Mosavi, M.R. Improved whale trainer for sonar datasets classification using neural network. Appl. Acoust.
**2019**, 154, 176–192. [Google Scholar] [CrossRef] - Khishe, M.; Safari, A. Classification of Sonar Targets Using an MLP Neural Network Trained by Dragonfly Algorithm. Wirel. Pers. Commun.
**2019**, 108, 2241–2260. [Google Scholar] [CrossRef] - Zheng, X.; Nguyen, H. A novel artificial intelligent model for predicting water treatment efficiency of various biochar systems based on artificial neural network and queuing search algorithm. Chemosphere
**2022**, 287, 132251. [Google Scholar] [CrossRef] - Aarts, E.H.L.; van Laarhoven, P.J.M. Simulated annealing: An introduction. Stat. Neerl.
**1989**, 43, 31–52. [Google Scholar] [CrossRef] - Holland, J.H. Genetic Algorithms. Sci. Am.
**1992**, 267, 66–73. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the ICNN’95—International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995; Volume 4, pp. 1942–1948. [Google Scholar] [CrossRef]
- Rashedi, E.; Nezamabadi-pour, H.; Saryazdi, S. GSA: A Gravitational Search Algorithm. Inf. Sci.
**2009**, 179, 2232–2248. [Google Scholar] [CrossRef] - Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey Wolf Optimizer. Adv. Eng. Softw.
**2014**, 69, 46–61. [Google Scholar] [CrossRef] - Li, C.; Zhou, J. Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm. Energy Convers. Manag.
**2011**, 52, 374–381. [Google Scholar] [CrossRef] - Rashedi, E.; Nezamabadi-pour, H.; Saryazdi, S. Filter modeling using gravitational search algorithm. Eng. Appl. Artif. Intell.
**2011**, 24, 117–122. [Google Scholar] [CrossRef] - Zhang, X.; Zou, D.; Shen, X. A Simplified and Efficient Gravitational Search Algorithm for Unconstrained Optimization Problems. In Proceedings of the 2017 International Conference on Vision, Image and Signal Processing (ICVISP), Osaka, Japan, 22–24 September 2017; pp. 11–17. [Google Scholar] [CrossRef]
- Zhang, Y.; Wu, L.; Zhang, Y.; Wang, J. Immune Gravitation Inspired Optimization Algorithm. In Advanced Intelligent Computing; Huang, D.S., Gan, Y., Bevilacqua, V., Figueroa, J.C., Eds.; Springer: Berlin/Heidelberg, Germany, 2011; pp. 178–185. [Google Scholar] [CrossRef]
- Shaw, B.; Mukherjee, V.; Ghoshal, S.P. A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. Int. J. Electr. Power Energy Syst.
**2012**, 35, 21–33. [Google Scholar] [CrossRef] - Hatamlou, A.; Abdullah, S.; Othman, Z. Gravitational search algorithm with heuristic search for clustering problems. In Proceedings of the 2011 3rd Conference on Data Mining and Optimization (DMO), Putrajaya, Malaysia, 28–29 June 2011; pp. 190–193. [Google Scholar] [CrossRef]
- Darzi, S.; Sieh Kiong, T.; Tariqul Islam, M.; Rezai Soleymanpour, H.; Kibria, S. A memory-based gravitational search algorithm for enhancing minimum variance distortionless response beamforming. Appl. Soft Comput.
**2016**, 47, 103–118. [Google Scholar] [CrossRef] - Yin, B.; Guo, Z.; Liang, Z.; Yue, X. Improved gravitational search algorithm with crossover. Comput. Electr. Eng.
**2017**, 66, 505–516. [Google Scholar] [CrossRef] - Mirjalili, S.; Hashim, S.Z.M. A new hybrid PSOGSA algorithm for function optimization. In Proceedings of the 2010 International Conference on Computer and Information Application, Tianjin, China, 3–5 December 2010; pp. 374–377. [Google Scholar] [CrossRef]
- Duman, S.; Yorukeren, N.; Altas, I.H. A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect. Int. J. Electr. Power Energy Syst.
**2015**, 64, 121–135. [Google Scholar] [CrossRef] - Xiao, J.; Niu, Y.; Chen, P.; Leung, S.C.H.; Xing, F. An improved gravitational search algorithm for green partner selection in virtual enterprises. Neurocomputing
**2016**, 217, 103–109. [Google Scholar] [CrossRef] - Salajegheh, F.; Salajegheh, E.; Shojaee, S. An enhanced approach for optimizing mathematical and structural problems by combining PSO, GSA and gradient directions. Soft Comput.
**2022**, 26, 11891–11913. [Google Scholar] [CrossRef] - Tian, H.; Yuan, X.; Ji, B.; Chen, Z. Multi-objective optimization of short-term hydrothermal scheduling using non-dominated sorting gravitational search algorithm with chaotic mutation. Energy Convers. Manag.
**2014**, 81, 504–519. [Google Scholar] [CrossRef] - Duman, S.; Li, J.; Wu, L.; Guvenc, U. Optimal power flow with stochastic wind power and FACTS devices: A modified hybrid PSOGSA with chaotic maps approach. Neural Comput. Appl.
**2020**, 32, 8463–8492. [Google Scholar] [CrossRef] - Li, N.; Su, Z.; Jerbi, H.; Abbassi, R.; Latifi, M.; Furukawa, N. Energy management and optimized operation of renewable sources and electric vehicles based on microgrid using hybrid gravitational search and pattern search algorithm. Sustain. Cities Soc.
**2021**, 75, 103279. [Google Scholar] [CrossRef] - Hui, W.; Zhijian, W.; Shahryar, R.; Yong, L.; Mario, V. Enhancing particle swarm optimization using generalized opposition-based learning. Inf. Sci.
**2011**, 181, 4699–4714. [Google Scholar] [CrossRef] - Lou, Y.; Li, J.L.; Shi, Y.H.; Jin, L.P. Gravitational Co-evolution and Opposition-based Optimization Algorithm. Int. J. Comput. Intell. Syst.
**2013**, 6, 849–861. [Google Scholar] [CrossRef] - Xin, Y.; Yong, L.; Guangming, L. Evolutionary programming made faster. IEEE Trans. Evol. Comput.
**1999**, 3, 82–102. [Google Scholar] [CrossRef] - Joshi, S.K. Chaos embedded opposition based learning for gravitational search algorithm. Appl. Intell.
**2023**, 53, 5567–5586. [Google Scholar] [CrossRef] - Khishe, M.; Mosavi, M.R. Chimp optimization algorithm. Expert Syst. Appl.
**2020**, 149, 113338. [Google Scholar] [CrossRef] - Dhiman, G. SSC: A hybrid nature-inspired meta-heuristic optimization algorithm for engineering applications. Knowl. -Based Syst.
**2021**, 222, 106926. [Google Scholar] [CrossRef] - Dhiman, G. ESA: A hybrid bio-inspired metaheuristic optimization approach for engineering problems. Eng. Comput.
**2021**, 37, 323–353. [Google Scholar] [CrossRef] - Aydilek, İ.B. A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Appl. Soft Comput.
**2018**, 66, 232–249. [Google Scholar] [CrossRef] - Askarzadeh, A. A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm. Comput. Struct.
**2016**, 169, 1–12. [Google Scholar] [CrossRef] - Civicioglu, P. Backtracking Search Optimization Algorithm for numerical optimization problems. Appl. Math. Comput.
**2013**, 219, 8121–8144. [Google Scholar] [CrossRef] - Mirjalili, S. SCA: A Sine Cosine Algorithm for solving optimization problems. Knowl.-Based Syst.
**2016**, 96, 120–133. [Google Scholar] [CrossRef] - Salajegheh, F.; Salajegheh, E. PSOG: Enhanced particle swarm optimization by a unit vector of first and second order gradient directions. Swarm Evol. Comput.
**2019**, 46, 28–51. [Google Scholar] [CrossRef]

**Figure 2.**Boxplot graphs of optimal solutions on unimodal benchmark functions (Dim = 30/50/100, A: GSA, B: PSOGSA, C: IPSOGSA).

**Figure 3.**Boxplot graphs of optimal solutions on multimodal benchmark functions (Dim = 30/50/100, A: GSA, B: PSOGSA, C: IPSOGSA).

Algorithm | ${\mathit{G}}_{0}$ | α | ${\mathit{m}}_{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{m}}_{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{T}}_{0}$ | rate | ${\mathit{T}}_{\mathit{e}\mathit{n}\mathit{d}}$ |
---|---|---|---|---|---|---|---|

GSA | 100 | 20 | - | - | - | - | - |

PSOGSA | 100 | 20 | - | - | - | - | - |

IPSOGSA | 100 | 20 | 0.1 | 0.2 | 1000 | 0.96 | 0.01 |

Dimension | IPSOGSA vs. | w (+) | t (=) | l$(-$) |
---|---|---|---|---|

30 | GSA | 12 | 0 | 1 |

PSOGSA | 11 | 1 | 1 | |

50 | GSA | 12 | 0 | 1 |

PSOGSA | 11 | 0 | 2 | |

100 | GSA | 13 | 0 | 0 |

PSOGSA | 13 | 0 | 0 |

Phase | Indicators | GA | GSA | IGSA | |||
---|---|---|---|---|---|---|---|

RMSE | R^{2} | RMSE | R^{2} | RMSE | R^{2} | ||

Training phase | COD_{Mn} | 0.591 | 0.961 | 0.582 | 0.962 | 0.472 | 0.975 |

NH_{3}-N | 0.075 | 0.969 | 0.073 | 0.971 | 0.058 | 0.981 | |

TP | 0.023 | 0.933 | 0.020 | 0.946 | 0.020 | 0.950 | |

Test phase | COD_{Mn} | 0.496 | 0.971 | 0.572 | 0.962 | 0.463 | 0.975 |

NH_{3}-N | 0.080 | 0.966 | 0.087 | 0.960 | 0.066 | 0.976 | |

TP | 0.019 | 0.950 | 0.019 | 0.954 | 0.016 | 0.967 |

Scenario Number | Description: Water Quality (mg/L) |
---|---|

S1 | Upstream: COD_{Mn}:5; NH_{3}-N:0.75; TP:0.15Initial: COD _{Mn}:15; NH_{3}-N:2.0; TP:0.4 |

S2 | Upstream: COD_{Mn}:4; NH_{3}-N:0.5; TP:0.1Initial: COD _{Mn}:15; NH_{3}-N:2.0; TP:0.4 |

S3 | Upstream: COD_{Mn}:4; NH_{3}-N:0.5; TP:0.1Initial: COD _{Mn}:10; NH_{3}-N:1.5; TP:0.3 |

S4 | Upstream: COD_{Mn}:4; NH_{3}-N:0.5; TP:0.1Initial: COD _{Mn}:6; NH_{3}-N:1.0; TP:0.2 |

S5 | Upstream: COD_{Mn}:6; NH_{3}-N:1.3; TP:0.25Initial: COD _{Mn}:6; NH_{3}-N:1.2; TP:0.25 |

Scenario Number | Algorithm | Height of Gate (m) | Flow (m^{3}/s) | Run Time (h) | Economic Cost $\left({\sum}_{\mathit{i}=1}^{\mathit{P}}{\mathit{Q}}_{\mathit{i}}{\mathit{t}}_{\mathit{i}}\right)$ | ||||
---|---|---|---|---|---|---|---|---|---|

P1 | P2 | P3 | P1 | P2 | P3 | ||||

S1 | GSA | 1.4 | 0 | 36 | 24 | 0 | 170 | 34 | 2.50 × 10^{7} |

IPSOGSA | 1.4 | 12 | 12 | 24 | 5 | 173 | 1 | 7.78 × 10^{6} | |

S2 | GSA | 0.7 | 72 | 12 | 12 | 45 | 177 | 53 | 2.16 × 10^{7} |

IPSOGSA | 1.4 | 12 | 12 | 0 | 3 | 167 | 0 | 7.34 × 10^{6} | |

S3 | GSA | 1.2 | 12 | 0 | 12 | 104 | 0 | 145 | 1.08 × 10^{7} |

IPSOGSA | 1.2 | 0 | 12 | 12 | 0 | 132 | 4 | 5.88 × 10^{6} | |

S4 | No scheduling required | ||||||||

S5 | No scheduling required |

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## Share and Cite

**MDPI and ACS Style**

Huang, F.; Zhang, H.; Wu, Q.; Chi, S.; Yang, M.
An Optimal Model and Application of Hydraulic Structure Regulation to Improve Water Quality in Plain River Networks. *Water* **2023**, *15*, 4297.
https://doi.org/10.3390/w15244297

**AMA Style**

Huang F, Zhang H, Wu Q, Chi S, Yang M.
An Optimal Model and Application of Hydraulic Structure Regulation to Improve Water Quality in Plain River Networks. *Water*. 2023; 15(24):4297.
https://doi.org/10.3390/w15244297

**Chicago/Turabian Style**

Huang, Fan, Haiping Zhang, Qiaofeng Wu, Shanqing Chi, and Mingqing Yang.
2023. "An Optimal Model and Application of Hydraulic Structure Regulation to Improve Water Quality in Plain River Networks" *Water* 15, no. 24: 4297.
https://doi.org/10.3390/w15244297