# Multi-Objective Optimal Scheduling of Generalized Water Resources Based on an Inter-Basin Water Transfer Project

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}and 827.9 million m

^{3}under the dry condition, respectively, and the water losses are reduced by 145.1 million m

^{3}and 141.1 million m

^{3}under the extremely dry condition, respectively. These findings could not only provide J-SNWT Project managers with guidelines for water allocation under normal, dry, and extremely dry conditions but also demonstrate that the G model could achieve better water-allocation benefits than the C model for inter-basin water transfer projects.

## 1. Introduction

## 2. Methods

#### 2.1. Optimal Allocation Model of Generalized Water Resources

#### 2.1.1. Objective Functions

- (1)
- Minimizing total water shortage

_{1}(m

^{3}) is the total amount of water shortage for each user’s agricultural, industrial, domestic, ecological environment, and shipping in the water resources system throughout the dispatch period, and T is the total number of months in the scheduling period. M is the total number of allocation units of the water resources system, W

^{D}

_{i}

_{,}

_{t}(m

^{3}) is the water demand of unit i at month t of the water resource system, l

_{j}is the total number of water sources (surface water, soil water, etc.) supplied by the water resource system to the j user, and W

^{S}

_{i}

_{,}

_{t}

_{,}k

_{j}(m

^{3}) is the water supply from the k

_{j}source of the water resource system to unit i at the month t.

- (2)
- Minimizing water loss in water resources systems

_{2}(m

^{3}) is the total water loss of the water resources system during the dispatch period; I is the total number of river cells; W

^{L}

_{i}

_{,}

_{t}and W

^{S}

_{i}

_{,}

_{t}(m

^{3})are the water loss by seepage and water disposal in month t for river cell i, respectively; J is the total number of lake cells; and W

^{E}

_{j}

_{,}

_{t}and W

^{S}

_{j}

_{,}

_{t}(m

^{3}) are the evaporation and disposal of water from the lake j unit in month t, respectively.

^{E}in Equation (3) is as follows.

^{E}(m

^{3}) is the monthly water surface evaporation volume, E

_{w}(mm) is the monthly water surface evaporation, and F (km

^{3}) is the monthly average water surface area.

^{L}is calculated by the Kostiakov formula [36], and the key formula is shown as follows.

^{L}(m

^{3}/s/km) is the leakage loss per unit canal length, Q

_{0}(m

^{3}/s) is the average channel traffic, and A and m are the soil permeability parameters.

#### 2.1.2. Constraints

- (1)
- Water balance constraint

_{i}

_{,}

_{t}

_{+1}and V

_{i}

_{,}

_{t}(m

^{3}) are the water storage of lake i at time t and time t + 1, respectively; Q

_{i}

_{,}

_{t}(m

^{3}/s) is the natural runoff of lake i at time t; DJ

_{i}

_{,}

_{t}and DC

_{i}

_{,}

_{t}(m

^{3}) are the inflow and outflow of lake i at time t, respectively; and P

_{i}

_{+1,t}(m

^{3}) is the amount of water released into lake i + 1 and at time t.

- (2)
- Soil water depth constraint

_{max}is the maximum depth of soil water.

- (3)
- Lake storage constraint

_{i}

_{,}

_{t}

_{,}

_{min}and V

_{i}

_{,}

_{t}

_{,}

_{max}(m

^{3}) are the minimizing and maximizing the water storage capacity of lake i at time t, respectively.

- (4)
- Pumping capacity constraint

_{i}

_{,}

_{t}

_{,}

_{max}and DC

_{i}

_{,}

_{t}

_{,}

_{max}(m

^{3}) are the maximizing pumping capacity of the pumping station of lake i at time t, respectively.

- (5)
- Sluice capacity constraint

^{S}

_{i}

_{,}

_{t}

_{,}

_{min}and W

^{S}

_{i}

_{,}

_{t}

_{,}

_{max}(m

^{3}) are the minimizing and maximizing overflow capacity of gate i at time t, respectively.

- (6)
- Minimizing water transfer level

- (7)
- Non-negative constraint

#### 2.2. Improved Multi-Objective Optimization Algorithm

_{a}, and (2) by introducing the population variation mechanism, the quality of the initial solution in the evolutionary algorithm will affect the convergence speed as well as the final optimization goal during the algorithm’s evolution. The optimal individuals of the multi-objective cuckoo optimization algorithm are mutated for each generation to further improve the quality of the population.

#### 2.2.1. Dynamic Discovery Probability

_{a}, the nest is updated randomly once, and then the best nest location is retained. A larger P

_{a}is used at the early stage of the algorithm operation to find the optimal solution quickly, and a smaller P

_{a}is used at the later stage of the operation to obtain the optimal convergence result, which is used to improve the accuracy of the algorithm for finding the optimal solution. Thus, the cosine strategy is used to achieve the dynamic change of P

_{a}so that P

_{a}decreases gradually as the algorithm proceeds [37].

_{i}(t + 1) is the new egg produced by the ith cuckoo at generation t + 1; α is the step control amount, α = α

_{0}(x

_{j}(t) − x

_{i}(t)), where α

_{0}is a constant; ⊕ is point-to-point multiplication; and L(β) is the search step length and obeys the Lévy distribution, i.e., L(β)~u = t

^{−1−}

^{β}, 0 < β ≤ 2.

_{a},

_{max}, and P

_{a},

_{min}are the control parameters of P

_{a}, both located in the range of 0~1; T is the current evolutionary generation; and T

_{max}is the maximum evolutionary generation.

#### 2.2.2. Mechanisms of Population Variation

_{t},

_{b}

_{2}and x

_{t},

_{b}

_{1}are the nest locations before and after the mutation; a

_{1}is the control parameter; ε is a 1 × d vector, obeying the standard normal distribution; and d is the dimension of the optimization problem.

#### 2.3. Evaluation of Non-Inferior Solutions for Scheduling of Water Resources

#### 2.3.1. Index System for Evaluating Water Resources Optimization Allocation

#### 2.3.2. Index Weight Quantification and Evaluation Methods

_{1}, v

_{2}, …, v

_{m})

^{T}is the basis vector, v

_{i}∈[0, 1], ∑v

_{i}

^{2}= 1; H = (h

_{1}, h

_{2}, …, h

_{n}) is the weight vector, h

_{j}∈[0, +∞), and a larger h

_{j}indicates a better water allocation effect of solution j; and z

_{ij}is the normalized value of solution j corresponding to index i.

#### 2.3.3. Determination of the Optimal Allocation Schemes of Water Resources

#### 2.3.4. Evaluation of the Optimal Allocation Schemes and Technology Road Map of the Study

## 3. Study Area and Data

#### 3.1. Study Area

#### 3.2. Data

#### 3.2.1. Surface Water

#### 3.2.2. Soil Water

## 4. Results

#### 4.1. Multi-Objective Optimal Allocation of Water Resources Based on the J-SNWT Project

#### 4.1.1. Pareto Frontiers of the G and C Models

^{3}, [1765.3, 8275.4] million m

^{3}, and [9704.5, 21,450.3] million m

^{3}, and the target values of system water loss range [12,779.3, 13,190.7] million m

^{3}, [6040.0, 8959.7] million m

^{3}, and [1414.7, 5938.5] million m

^{3}under the normal, dry and extremely dry conditions, respectively. As shown in Figure 5a–c, the distribution of the total water shortage in the water-receiving area of the C model ranges [135.9, 743.0] million m

^{3}, [2068.8, 9038.9] million m

^{3}, and [10,615.3, 22,380.1] million m

^{3}. The distribution of system water loss target values ranged [11,779.8, 12,063.0] million m

^{3}, [5999.2, 9608.5] million m

^{3}, and [1501.0, 6024.8] million m

^{3}.

#### 4.1.2. Pareto Optimal Solutions Box Diagram of G and C Models

^{3}compared to the C model. This indicates that the G model is more efficient for water resource utilization than the C model. As shown in Figure 6b, the G model reduces the water loss by 86.3 million m

^{3}compared to the C model under extremely dry conditions. The C model produces more general Pareto optimal solutions than the G model under dry conditions, but these solutions are dominated by the Pareto optimal solutions of the G model.

#### 4.2. Optimal Allocation Scheme Set of Water Resources Based on the J-SNWT Project

#### 4.2.1. Filtering Pareto Optimal Solutions of G (C) Model

#### 4.2.2. Quantification of the Index Weights for the G (C) Scheme Set

#### 4.3. The Best Scheme of Water Resources Based on the J-SNWT Project

#### 4.3.1. Evaluation of the Best G Scheme

^{3}, drainage volume is 1281.0 million m

^{3}, abandoned water is 7915.9 million m

^{3}, water loss is 13,139.0 million m

^{3}, and total pumping is 23,170.1 million m

^{3}under normal conditions. The total water shortage is 1865.2 million m

^{3}, drainage volume is 8843.1 million m

^{3}, abandoned water is 3359.5 million m

^{3}, water loss is 8863.8 million m

^{3}, and total pumping is 29,869.1 million m

^{3}under dry conditions. The total water shortage is 9792.4 million m

^{3}, drainage volume is 13,646.2 million m

^{3}, abandoned water is 0 million m

^{3}, water loss is 5766.0 million m

^{3}, and total pumping is 37,352.1 million m

^{3}under extremely dry conditions.

#### 4.3.2. Evaluation of the Best C Scheme

^{3}, drainage volume is 1389.3 million m

^{3}, abandoned water is 6874.2 million m

^{3}, water loss is 12,021.7 million m

^{3}, and total pumping is 23,196.1 million m

^{3}. In the dry conditions, the total water shortage is 2119.4 million m

^{3}, drainage volume is 9616.6 million m

^{3}, abandoned water is 3303.9 million m

^{3}, water loss is 9008.9 million m

^{3}, and total pumping is 31,329.2 million m

^{3}. In extremely dry conditions, the total water shortage is 10,620.3 million m

^{3}, drainage volume is 14,088.3 million m

^{3}, abandoned water is 0 million m

^{3}, water loss is 5907.1 million m

^{3}, and total pumping is 38,411.4 million m

^{3}.

#### 4.3.3. Comparison of the Best G Scheme and the Best C Scheme

^{3}, 254.2 million m

^{3}, and 827.9 million m

^{3}, respectively, compared with the best C scheme. In terms of operating costs, the drainage volume of the best G scheme under normal, dry, and extremely dry conditions is 108.3 million m

^{3}, 773.5 million m

^{3}, and 442.1 million m

^{3}less than the best C scheme, and the total pumped water volume is 26.0 million m

^{3}, 1460.1 million m

^{3}, and 1059.3 million m

^{3}lower than the best C scheme, respectively. In terms of water loss, the abandoned water and water loss of the best G scheme are 1041.7 million m

^{3}and 1117.3 million m

^{3}greater than the best C scheme under normal conditions. The abandoned water of the best G scheme is 55.6 million m

^{3}more than the best C scheme, and the water loss is 145.1 million m

^{3}lower than the best C scheme under dry conditions. The water loss of the best G scheme is 141.1 million m

^{3}less than the best C scheme under extremely dry conditions.

## 5. Discussion

#### 5.1. Effectiveness and Excellence of the G Model

#### 5.2. Optimized Allocation Scheme of J-SNWT

## 6. Conclusions

^{3}and 827.9 million m

^{3}, respectively, and the water losses are reduced by 145.1 million m

^{3}and 141.1 million m

^{3}, respectively. The G model shows significant improvements in terms of water shortage and the cost of water supply.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

IBWT | Inter-basin water transfer projects. |

SNWT | The South–North Water Transfer project. |

J-SNWT | The Jiangsu section of the South-to-North Water Transfer. |

G model | Optimal allocation model of generalized water resources. |

C model | Optimal allocation model of conventional water resources. |

IMOCS | Improved multi-objective cuckoo optimization algorithm. |

AHP | Analytic hierarchy process. |

CRITIC | Criteria importance through inter-criteria correlation. |

G scheme | The optimal allocation scheme of generalized water resources. |

C scheme | The optimal allocation scheme of conventional water resources. |

## References

- Cosgrove, W.J.; Loucks, D.P. Water management: Current and future challenges and research directions. Water Resour. Res.
**2015**, 51, 4823–4839. [Google Scholar] [CrossRef] - Dong, C.; Schoups, G.; Giesen, N.V.D. Scenario development for water resource planning and management: A review. Technol. Forecast. Soc. Chang.
**2013**, 80, 749–761. [Google Scholar] [CrossRef] - Li, Y.; Cui, Q.; Li, C.; Wang, X.; Cai, Y.; Cui, G.; Yang, Z. An improved multi-objective optimization model for supporting reservoir operation of China’s South-to-North Water Diversion Project. Sci. Total Environ.
**2017**, 575, 970–981. [Google Scholar] [CrossRef] - Akron, A.; Ghermandi, A.; Dayan, T.; Hershkovitz, Y. Interbasin water transfer for the rehabilitation of a transboundary Mediterranean stream: An economic analysis. J. Environ. Manag.
**2017**, 202, 276–286. [Google Scholar] [CrossRef] - Dou, X. China’s inter-basin water management in the context of regional water shortage. Sustain. Water Resour. Manag.
**2018**, 4, 519–526. [Google Scholar] [CrossRef] - Yan, B.; Chen, L. Coincidence probability of precipitation for the middle route of South-to-North water transfer project in China. J. Hydrol.
**2013**, 499, 19–26. [Google Scholar] [CrossRef] - Lopez, J.C. Interbasin water transfers and the size of regions: An economic geography example. Water Resour. Econ.
**2018**, 21, 40–54. [Google Scholar] [CrossRef] - Pohlner, H. Institutional change and the political economy of water megaprojects: China’s south-north water transfer. Glob. Environ. Chang.
**2016**, 38, 205–216. [Google Scholar] [CrossRef] - Davijani, M.H.; Banihabib, M.E.; Anvar, A.N.; Hashemi, S.R. Optimization model for the allocation of water resources based on the maximization of employment in the agriculture and industry sectors. J. Hydrol.
**2016**, 533, 430–438. [Google Scholar] [CrossRef] - Tian, J.; Guo, S.; Deng, L.; Yin, J.; Pan, Z.; He, S.; Li, Q. Adaptive optimal allocation of water resources response to future water availability and water demand in the Han River basin, China. Sci. Rep.
**2021**, 11, 7879. [Google Scholar] [CrossRef] - Zhang, C.; Wang, G.; Peng, Y.; Tang, G.; Liang, G. A Negotiation-Based Multi-Objective, Multi-Party Decision-Making Model for Inter-Basin Water Transfer Scheme Optimization. Water Resour. Manag.
**2012**, 26, 4029–4038. [Google Scholar] [CrossRef] - Guan, H.; Chen, L.; Huang, S.; Yan, C.; Wang, Y. Multi-objective optimal allocation of water resources based on ‘three red lines’ in Qinzhou, China. Water Policy
**2020**, 22, 541–560. [Google Scholar] [CrossRef] - Zhuang, X.; Li, Y.; Huang, G.; Zeng, X. An inexact joint-probabilistic programming method for risk assessment in water resources allocation. Stoch. Environ. Res. Risk Assess.
**2015**, 29, 1287–1301. [Google Scholar] [CrossRef] - Jafarzadegan, K.; Abed-Elmdoust, A.; Kerachian, R. A stochastic model for optimal operation of inter-basin water allocation systems: A case study. Stoch. Environ. Res. Risk Assess.
**2014**, 28, 1343–1358. [Google Scholar] [CrossRef] - Zhou, Y.; Guo, S.; Hong, X.; Chang, F. Systematic impact assessment on inter-basin water transfer projects of the Hanjiang River Basin in China. J. Hydrol.
**2017**, 553, 584–595. [Google Scholar] [CrossRef] - Zeng, C.; Ma, J.; Cao, M.; Xu, C.; Qi, W.; Wang, L. Modeling Water Allocation under Extreme Drought of South-to-North Water Diversion Project in Jiangsu Province, Eastern China. Front. Earth Sci.
**2020**, 8, 541664. [Google Scholar] [CrossRef] - Gonzalez, J.F.; Decker, C.A.; Hall, J.W. A Linear Programming Approach to Water Allocation during a Drought. Water
**2018**, 10, 363. [Google Scholar] [CrossRef] - Ahmad, A.; El-Shafie, A.; Razali, S.F.M.; Mohamad, Z.S. Reservoir optimization in water resources: A review. Water Resour. Manag.
**2014**, 28, 3391–3405. [Google Scholar] [CrossRef] - Eum, H.; Kim, Y.; Palmer, N.R. Optimal Drought Management Using Sampling Stochastic Dynamic Programming with a Hedging Rule. J. Water Resour. Plan. Manag.
**2011**, 137, 113–122. [Google Scholar] [CrossRef] - Tian, J.; Liu, D.; Guo, S.; Pan, Z.; Hong, X. Impacts of Inter-Basin Water Transfer Projects on Optimal Water Resources Allocation in the Hanjiang River Basin, China. Sustainability
**2019**, 11, 2044. [Google Scholar] [CrossRef] - Wu, X.; Wang, Z. Multi-objective optimal allocation of regional water resources based on slime mould algorithm. J. Supercomput.
**2022**, 78, 18288–18317. [Google Scholar] [CrossRef] - Wang, Z.; Tian, J.; Feng, K. Optimal allocation of regional water resources based on simulated annealing particle swarm optimization algorithm. Energy Rep.
**2022**, 8, 9119–9126. [Google Scholar] [CrossRef] - Li, Y.; Han, Y.; Liu, B.; Li, B.; Li, H.; Du, X.; Wang, Q.; Wang, X.; Zhu, X. Construction and application of a refined model for the optimal allocation of water resources-Taking Guantao County, China as an example. Ecol. Indic.
**2023**, 146, 109929. [Google Scholar] [CrossRef] - Yang, X.S.; Deb, S. Engineering optimization by cuckoo search. Int. J. Math. Model. Numer. Optim.
**2010**, 1, 330–343. [Google Scholar] - Yang, X.; Deb, S. Multi-objective cuckoo search for design optimization. Comput. Oper. Res.
**2013**, 40, 1616–1624. [Google Scholar] [CrossRef] - Sun, S.; Fu, G.; Bao, C.; Fang, C. Identifying hydro-climatic and socioeconomic forces of water scarcity through structural decomposition analysis: A case study of Beijing city. Sci. Total Environ.
**2019**, 687, 590–600. [Google Scholar] [CrossRef] [PubMed] - Ouyang, S.; Qin, H.; Shao, J.; Lu, J.; Bing, J.; Wang, X.; Zhang, R. Multi-objective optimal water supply scheduling model for an inter-basin water transfer system: The South-to-North Water Diversion Middle Route Project, China. Water Supply
**2020**, 20, 550–564. [Google Scholar] [CrossRef] - Fang, G.; Guo, Y.; Wen, X.; Fu, X.; Lei, X.; Tian, Y.; Wang, T. Multi-Objective Differential Evolution-Chaos Shuffled Frog Leaping Algorithm for Water Resources System Optimization. Water Resour. Manag.
**2018**, 32, 3835–3852. [Google Scholar] [CrossRef] - Guo, Y.; Tian, X.; Fang, G.; Xu, Y. Many-objective optimization with improved shuffled frog leaping algorithm for inter-basin water transfers. Adv. Water Resour.
**2020**, 138, 103531. [Google Scholar] [CrossRef] - Yan, B.; Jiang, H.; Zou, Y.; Liu, Y.; Mu, R.; Wang, H. An integrated model for optimal water resources allocation under “3 Redlines” water policy of the upper Hanjiang river basin. J. Hydrol. Reg. Stud.
**2022**, 42, 101167. [Google Scholar] [CrossRef] - Jing, S.; Xiao, W.; Wang, J.; Zhen, Y.; Wang, W.; Liu, Q.; Zhang, Z.; Hu, C. Evaporation variability and its control factors of Lake Taihu from 1958 to 2017. J. Lake Sci.
**2022**, 34, 1697–1711, (Chinese with English Abstract). [Google Scholar] - Ma, Y.; Li, X.; Wilson, M.; Wu, X.; Smith, A.; Wu, J. Water loss by evaporation from China’s South-North Water Transfer Project. Ecol. Eng.
**2016**, 95, 206–215. [Google Scholar] [CrossRef] - Pei, Y.; Zhang, J. The Conceptual Framework for Rational Allocation of Water Resources. Resour. Sci.
**2006**, 4, 166–171, (Chinese with English Abstract). [Google Scholar] - Veettil, A.V.; Mishra, A.K. Water security assessment using blue and green water footprint concepts. J. Hydrol.
**2016**, 542, 589–602. [Google Scholar] [CrossRef] - Wang, H.; You, J. Progress of water resource allocation during the past 30 years in China. J. Hydraul. Eng.
**2016**, 47, 265–271, (Chinese with English Abstract). [Google Scholar] - Parhi, P.K.; Mishra, S.K.; Singh, R. A Modification to Kostiakov and Modified Kostiakov Infiltration Models. Water Resour. Manag.
**2007**, 21, 1973–1989. [Google Scholar] [CrossRef] - Ming, B.; Huang, Q.; Wang, Y.; Liu, D.; Bai, T. Cascade reservoir operation optimization based-on improved Cuckoo Search. J. Hydraul. Eng.
**2015**, 46, 341–349, (Chinese with English Abstract). [Google Scholar] - Mosadeghi, R.; Warnken, J.; Tomlinson, R.; Mirfenderesk, H. Comparison of Fuzzy-AHP and AHP in a spatial multi-criteria decision-making model for urban land-use planning. Comput. Environ. Urban Syst.
**2015**, 49, 54–65. [Google Scholar] [CrossRef] - Abdel-Basset, M.; Mohamed, R. A novel plithogenic TOPSIS-CRITIC model for sustainable supply chain risk management. J. Clean. Prod.
**2020**, 247, 119586. [Google Scholar] [CrossRef] - Li, Y.; Li, Q.; Jiao, S. River health evaluation based on improved analytic hierarchy process, CRITIC method and compound fuzzy matter-element VIKOR model. Chin. J. Ecol.
**2022**, 41, 822–832. [Google Scholar] - Xie, Y.; Huang, Q.; Li, X.; Liu, S.; Wang, Y. Method for optimal selection of schemes based on the non-negative matrix factorization principle and its applications. J. Xi’an Univ. Technol.
**2017**, 33, 138–144, (Chinese with English Abstract). [Google Scholar] - Tangdamrongsub, N.; Ditmar, P.G.; Steele-Dunne, S.C.; Gunter, B.C.; Sutanudjaja, E.H. Assessing total water storage and identifying flood events over Tonlé Sap basin in Cambodia using GRACE and MODIS satellite observations combined with hydrological models. Remote Sens. Environ.
**2016**, 181, 162–173. [Google Scholar] [CrossRef] - GB/T 51051-2014; Code for Water Resources Planning. Planning Publishing House: Beijing, China, 2014.
- Yan, Z.; Sha, J.; Liu, B.; Tian, W.; Lu, J. An Ameliorative Whale Optimization Algorithm for Multi-Objective Optimal Allocation of Water Resources in Handan, China. Water
**2020**, 10, 87. [Google Scholar] [CrossRef] - Yu, F.; Fang, G.; Wang, W.; Wu, X.; Wen, X. Optimized dispatching of the lake group system along the South-to-North Water Diversion Route based on the multi-objective genetic algorithm. J. Irrig. Drain.
**2016**, 35, 78–85, (Chinese with English Abstract). [Google Scholar] - Wen, X.; Wang, Z.; Fang, G.; Guo, Y.; Zhou, L. Study on optimal operation of Jiangsu section of eastern route of South-to-North Water Diversion Project based on improved multi-objective particle swarm optimization algorithm. J. Water Resour. Water Eng.
**2017**, 28, 110–116, (Chinese with English Abstract). [Google Scholar]

**Figure 3.**The generalized system diagram of the J-SNWT Project (Note: YR-HZ Users represents Yangtze River–Hongze Lake Users, HZ Users represents Hongze Lake Users, HZ-LM Users represents Hongze Lake–Luoma Lake Users, LM Users represents Luoma Lake Users, LM-NS Users represents Luoma Lake–Nansi Lake Users, NS Users represents Nansi Lake Users, SD Users represents Shandong Users, and N represents the north direction).

**Figure 4.**Annual water demand per water user in 2030 under the (

**a**) normal, (

**b**) dry, and (

**c**) extremely dry conditions.

**Figure 5.**Pareto frontiers of the G and C models under (

**a**) normal, (

**b**) dry, and (

**c**) extremely dry conditions.

**Figure 6.**Box plots of Pareto solutions for the G and C models under normal, dry, and extremely dry conditions: (

**a**) minimizing total water shortage and (

**b**) minimizing water loss.

**Figure 9.**Comparison of the best G scheme and the best C scheme under (

**a**) normal, (

**b**) dry, and (

**c**) extremely dry conditions.

Evaluation Criteria | Index |
---|---|

Water use efficiency (million m^{3}) | total water shortage (f_{1}) |

drainage volume (f_{2}) | |

abandoned water (f_{3}) | |

water loss (f_{4}) | |

Water system costs (million m^{3}) | total pumped water (f_{5}) |

Lake | Dead Water Level (m) | Normal Water Level (m) | July–August | September–November | November–March | April–June | |
---|---|---|---|---|---|---|---|

Flood Season | Non-Flood Season | ||||||

Hongze Lake | 11.3 | 12.5 | 13.5 | 12.0 | 12.0~11.9 | 12.0~12.5 | 12.5~12.0 |

Luoma Lake | 20.5 | 22.5 | 23 | 22.2~22.1 | 22.1~22.2 | 22.1~23.0 | 23.0~22.5 |

Nansi Lake | 31.5 | 32.5 | 33 | 31.8 | 31.5~31.9 | 31.9~32.8 | 32.3~31.8 |

Section | Pumping Station Group | Pumping Station | Capacity (m^{3}/s) |
---|---|---|---|

YR-HZ | Drainage volume | Baoying | 100 |

Jiangdu | 400 | ||

Into Hongze lake | Hongze | 150 | |

Huaiyin | 300 | ||

HZ-LM | Out of Hongze lake | Sihong | 120 |

Siyang | 230 | ||

Into Luoma lake | Pizhou | 100 | |

Zaohe | 175 | ||

LM-NS | Out of Luoma lake | Taierzhuang | 125 |

Liushan | 125 | ||

Into Nansi lake | Hanzhuang | 125 | |

Linjiaba | 75 |

**Table 4.**Representative years under the normal, dry, and extremely dry conditions of two water sources.

Water Source | Conditions | Water Users | |||||
---|---|---|---|---|---|---|---|

Hongze Lake | Luoma Lke | Nansi Lake | |||||

Surface water | Normal | 1971.7~1972.6 | 1975.7~1976.6 | 1988.7~1989.6 | 1971.7~1972.6 | 1975.7~1976.6 | 1988.7~1989.6 |

Dry | 1958.7~1959.6 | 1969.7~1970.6 | 1967.7~1968.6 | 1958.7~1959.6 | 1969.7~1970.6 | 1967.7~1968.6 | |

Extremely dry | 1959.7~1960.7 | 1959.7~1960.6 | 1966.7~1967.6 | 1959.7~1960.7 | 1959.7~1960.6 | 1966.7~1967.6 | |

YR-HZ User | HZ User | HZ-LM User | LM User | LM-NS User | NS User | ||

Soil water | Normal | 2007.7~2008.6 | 2012.7~2013.6 | 2006.7~2007.6 | 2006.7~2007.6 | 2016.7~2017.6 | 2016.7~2017.7 |

Dry | 2014.7~2015.6 | 2014.7~2015.6 | 2012.7~2013.6 | 2012.7~2013.6 | 2015.7~2016.6 | 2015.7~2016.6 | |

Extremely dry | 2004.7~2005.6 | 2019.7~2020.6 | 2011.7~2012.6 | 2011.7~2012.6 | 2011.7~2012.6 | 2011.7~2012.6 |

**Table 5.**The index weights of the G (C) scheme set under the normal, dry, and extremely dry conditions.

Model | Weights | Normal | Dry | Extremely Dry | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

f_{1} | f_{2} | f_{3} | f_{4} | f_{5} | f_{1} | f_{2} | f_{3} | f_{4} | f_{5} | f_{1} | f_{2} | f_{3} | f_{4} | f_{5} | ||

G model | W^{1} | 0.18 | 0.15 | 0.15 | 0.36 | 0.16 | 0.21 | 0.10 | 0.21 | 0.34 | 0.14 | 0.24 | 0.16 | 0.18 | 0.30 | 0.12 |

W^{2} | 0.52 | 0.14 | 0.11 | 0.11 | 0.11 | 0.45 | 0.15 | 0.14 | 0.12 | 0.15 | 0.47 | 0.13 | 0.13 | 0.13 | 0.13 | |

W | 0.35 | 0.15 | 0.13 | 0.23 | 0.14 | 0.33 | 0.12 | 0.17 | 0.23 | 0.14 | 0.36 | 0.15 | 0.15 | 0.21 | 0.13 | |

C model | W^{1} | 0.18 | 0.15 | 0.15 | 0.36 | 0.16 | 0.21 | 0.10 | 0.21 | 0.34 | 0.14 | 0.24 | 0.16 | 0.18 | 0.30 | 0.12 |

W^{2} | 0.40 | 0.17 | 0.14 | 0.16 | 0.13 | 0.51 | 0.13 | 0.13 | 0.11 | 0.12 | 0.50 | 0.12 | 0.13 | 0.13 | 0.12 | |

W | 0.29 | 0.16 | 0.15 | 0.26 | 0.14 | 0.36 | 0.11 | 0.17 | 0.23 | 0.13 | 0.34 | 0.14 | 0.19 | 0.21 | 0.12 |

_{1}represents total water shortage (million m

^{3}), f

_{2}represents drainage volume (million m

^{3}), f

_{3}represents abandoned water (million m

^{3}), f

_{4}represents water loss (million m

^{3}), and f

_{5}represents total pumped water (million m

^{3}). W

^{1}represents the subjective weights, W

^{2}represents the objective weights, and W represents the combined weights.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xi, H.; Xie, Y.; Liu, S.; Mao, Q.; Shen, T.; Zhang, Q.
Multi-Objective Optimal Scheduling of Generalized Water Resources Based on an Inter-Basin Water Transfer Project. *Water* **2023**, *15*, 3195.
https://doi.org/10.3390/w15183195

**AMA Style**

Xi H, Xie Y, Liu S, Mao Q, Shen T, Zhang Q.
Multi-Objective Optimal Scheduling of Generalized Water Resources Based on an Inter-Basin Water Transfer Project. *Water*. 2023; 15(18):3195.
https://doi.org/10.3390/w15183195

**Chicago/Turabian Style**

Xi, Haichao, Yangyang Xie, Saiyan Liu, Qing Mao, Teng Shen, and Qin Zhang.
2023. "Multi-Objective Optimal Scheduling of Generalized Water Resources Based on an Inter-Basin Water Transfer Project" *Water* 15, no. 18: 3195.
https://doi.org/10.3390/w15183195