# Multi-Objective Lower Irrigation Limit Simulation and Optimization Model for Lycium Barbarum Based on NSGA-III and ANN

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview of the Study Area

#### 2.2. Lycium Barbarum’s Active Root Layer Water Balance Model

_{i}is the rainfall on day i (mm). I

_{i}is the irrigation volume (mm) on day i; ${K}_{c}$ is soil moisture coefficient; $E{T}_{0}$ is the reference crop exfoliation (mm), the Penman–Monteith model recommended by the Food and Agriculture Organization of the United Nations (FAO) used to calculate the reference crop exfoliation in this study; ${Q}_{i}$ is the sum of groundwater leakage and recharge in the active root layer (mm).

#### 2.3. Water Production Function of Lycium barbarum

#### 2.4. ADF-50 Artificial Neural Network Model

_{ih}, W

_{hh,}and W

_{ho}of each layer were set as 0.5, the learning rate was 0.1, the initial thresholds a and b for the hidden and output layers was 0.3, and the sigmoid function was selected as the activation function. The expression is shown in Equation (4).

_{ih}, W

_{hj,}and the threshold a

_{i}. The calculation formulas are shown in Equations (5) and (6).

_{2j}, the connection weights W

_{jo}and the threshold, the output value P

_{ADF-50}was calculated. The calculation formula is shown in Equation (7).

#### 2.5. Multi-Objective Genetic Algorithm Optimization Model NSGA-III

#### 2.5.1. Decision Variable

#### 2.5.2. Objective Function

#### 2.5.3. Constraint

#### 2.6. Construction of the Coupling Model

## 3. Results

#### 3.1. Simulation Models Validation

#### 3.2. Optimization Results of Irrigation Drip Lower Irrigation Limit for Lycium barbarum

^{3}/hm

^{2}; S2 were 25 and 2628.06 m

^{3}/hm

^{2}; S3 were 13 and 1648.10 m

^{3}/hm

^{2}; original scheme were 22 and 2405.34 m

^{3}/hm

^{2}. In 2019, the irrigation time and quantity of S1 were 23 and 2152.93 m

^{3}/hm

^{2}; S2 were 28 and 2910.16 m

^{3}/hm

^{2}; S3 were 14 and 1781.73 m

^{3}/hm

^{2}; original scheme were 25 and 2687.45 m

^{3}/hm

^{2}. Based on the analysis of the lower limit of irrigation water in Table 1, it could be seen that the irrigation times and the total quantity of irrigation water were positively correlated with the lower limit of irrigation water. In addition, within the constraint range, the yield and ADF-50 showed an increasing trend with the increase of the total irrigation quantity, indicating that increasing the lower limit of irrigation water and increasing the irrigation water could improve the yield but reduce the quality of Lycium barbarum. It is worth noting that the larger the ADF-50, the worse the quality. Compared with the original lower limit scheme of drip irrigation, the S1 scheme with compromise consideration of the two objectives could increase the yield by 10.7% while reducing the ADF-50 by 8.8% and improving the quality of Lycium barbarum while increasing the yield. The S2 increased yield by 32.5% at the cost of increasing ADF-50 by 4.6%. In contrast, the S3 decreased ADF-50 by 26.8% at the cost of decreasing yield by 8.0%.

## 4. Discussion

^{3}/hm

^{2}total irrigation quantity (61.5%) in the two years. Li got the same conclusion when studying the effect of irrigation limits on the water production efficiency of tomatoes [34]. And it is similar to the viewpoint that the frequency of drip irrigation is positively correlated with the lower irrigation limit, which was found by Hou when he was studying the water and heat distribution of Lycium barbarum orchard’s soil [35]. By observing the yield and ADF-50 value of different schemes, the yield and ADF-50 increased along with the increase of total irrigation water. Similar conclusions were also obtained in other studies on Lycium barbarum in the same area [36]. Compared with S3, S2 increased yield by 44.2% and ADF-50 by 43.9% (The smaller ADF-50, the better quality of Lycium barbarum), further verifying the competitive relationship between yield and ADF-50 objectives. It can be seen that the simulation–optimization model selected the scheme which tended to yield objectives with higher irrigation lower limits so as to increase the irrigation quantity and yield; When selecting the scheme which tended to the quality of Lycium barbarum, the scheme with lower irrigation limit was a priority, which reduced the total irrigation quantity, yield, and value of ADF-50. When the simulation–optimization model selected a scheme that tended to one objective, it also considered this scheme’s performance of the other objective. Compared with the original scheme, the scheme which tended to yield objective increased the yield by 32.6% on average during the two years of the simulation experiment but only increased the ADF-50 by 4.6%, and the quality of Lycium barbarum was only slightly reduced. The scheme which tended to the ADF-50 objective reduced the yield by 8.1% while reducing ADF-50 by 26.8%. The results show that NSGA-III can deal with the relationship between multiple competing objectives well. Liu and Hou also get the same conclusion when using NSGA-III to solve the multi-objective optimization problem [37,38]. S1 was a compromise scheme, which meant a compromise between the two objectives. Therefore, the lower limits of irrigation of this scheme were between S2 and S3, which were 65%, 50%, and 65% of field capacity at T1, T2, and T3. This is similar to the Lycium barbarum’s lower irrigation limit scheme, which Xu selected by manual comparison (65%, 65%, and 55% of field capacity for the three stages) [39]. Irrigation times, the total amount of irrigation water, yield, and ADF-50 of S1 are all between S2 and S3. Compared with the original scheme, the yield of S1 increased by 10.7%, and ADF-50 decreased by 8.8%, which indicates that the simulation–optimization model can effectively improve the yield and quality of crops. Numerous scholars reached a similar conclusion when they used the simulation–optimization model to optimize the allocation of irrigation water [40,41,42].

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, G.Z. Research on Wolfberry Irrigation and Mulching Measures. Master’s Thesis, Gansu Agricultural University, Lanzhou, China, 2009. [Google Scholar]
- Peng, J.; Wang, L.; Wang, M.; Du, R.; Qin, S.; Jin, C.Y.; Wei, Y. Yeast Synthetic Biology for the Production of Lycium barbarum Polysaccharides. Molecules
**2021**, 26, 1641. [Google Scholar] [CrossRef] - Cui, F.; Shi, C.L.; Zhou, X.J.; Wen, W.; Gao, X.P.; Wang, L.Y.; He, B.; Yin, M.; Zhao, J.Q. Lycium barbarum Polysaccharide Extracted from Lycium barbarum Leaves Ameliorates Asthma in Mice by Reducing Inflammation and Modulating Gut Microbiota. J. Med. Food
**2020**, 23, 699–710. [Google Scholar] [CrossRef] [PubMed] - Zheng, G.Q.; Zhang, L.; Zheng, G.B. Effects of irrigation amount on leaf structure photosynthetic physiology and fruit yield of Lycium barbarum in arid area. Chin. J. Appl. Ecol.
**2010**, 21, 2806–2813. [Google Scholar] [CrossRef] - Zhou, Q. Effects of Different Water and Nitrogen Coupling and Mulching on the Growth, Yield and Nutrient Uptake of Lycium barbarum. Master’s Thesis, Northwest A&F University, Yangling, China, 2014. [Google Scholar]
- Zhou, Y.Q.; Gao, X.D.; Wang, J.X.; Brett, H.R.; Zhao, X.N. Water-use patterns of Chinese wolfberry (Lycium barbarum L.) on the Tibetan Plateau. Agric. Water Manag.
**2021**, 255, 107010. [Google Scholar] [CrossRef] - Zeng, X.C. Irrigation and Overbearing of the Effects of the Growth and Water Utilization Efficiency of Goji Berries. Master’s Thesis, Gansu Agricultural University, Lanzhou, China, 2013. [Google Scholar]
- Zhang, T.B.; Kang, Y.H.; Liu, S.H.; Liu, S.P. Alkaline phosphatase activity and its relationship to soil properties in a saline–sodic soil reclaimed by cropping wolfberry (Lycium barbarum L.) with drip irrigation. Paddy Water Environ.
**2014**, 12, 309–317. [Google Scholar] [CrossRef] - Earl, V.; Stevens, W.; Matthew, R.; Zachary, S. Investigating irrigation scheduling for rice using variable rate irrigation. Agric. Water Manag.
**2017**, 179, 314–323. [Google Scholar] [CrossRef] - Zhao, Y.; Li, F.W.; Jiang, R.G. Irrigation schedule optimization based on the combination of an economic irrigation quota and the AquaCrop model. Irrig. Drain.
**2021**, 70, 773–785. [Google Scholar] [CrossRef] - Albo-Salih, H.; Mays, L. Testing of an Optimization-Simulation Model for Real-Time Flood Operation of River Reservoir Systems. Water
**2021**, 13, 1207. [Google Scholar] [CrossRef] - Jamshid Mousavi, S.; Anzab, N.R.; Asl-Rousta, B. Multi-Objective Optimization-Simulation for Reliability-Based Inter-Basin Water Allocation. Water Resour. Manag.
**2017**, 31, 3445–3464. [Google Scholar] [CrossRef] - Wang, Y.M.; Yang, J.; Chang, J.X. Development of a coupled quantity-quality-environment water allocation model applying the optimization-simulation method. J. Clean. Prod.
**2019**, 213, 944–955. [Google Scholar] [CrossRef] - Kim, Y.G.; Jo, M.B.; Kim, P. Effective Optimization-Simulation Model for Flood Control of Cascade Barrage Network. Water Resour. Manag.
**2021**, 35, 135–157. [Google Scholar] [CrossRef] - Aspelund, A.; Gundersen, T.; Myklebust, J.; Nowak, M.P.; Tomasgard, A. An optimization-simulation model for a simple LNG process. Comput. Chem. Eng.
**2010**, 34, 1606–1617. [Google Scholar] [CrossRef] - Sedki, A.; Ouazar, D. Simulation-Optimization Modeling for Sustainable Groundwater Development: A Moroccan Coastal Aquifer Case Study. Water Resour. Manag.
**2011**, 25, 2855–2875. [Google Scholar] [CrossRef] - Yao, J.; Xu, X.; Huang, Q.Z.; Huo, Z.L.; Huang, G.H. Optimizing regional irrigation water use by integrating a two-level optimization model and an agro-hydrological model. Agric. Water Manag.
**2016**, 178, 76–88. [Google Scholar] [CrossRef] [Green Version] - Liu, X.; Yang, D.W. Irrigation schedule analysis and optimization under the different combination of P and ET0 using a spatially distributed crop model. Agric. Water Manag.
**2021**, 256, 107084. [Google Scholar] [CrossRef] - Cobo, M.T.C.; Poyato, E.C.; Montesinos, P.; Díaz, J.A.R. New model for sustainable management of pressurized irrigation networks. Application to Bembézar MD irrigation district (Spain). Sci. Total Environ.
**2014**, 473, 1–8. [Google Scholar] [CrossRef] [PubMed] - Liu, J.; Hu, Y.Q.; Chen, H.R. Conjunctive use of surface water and groundwater in irrigation districts in China. Irrig. Drain.
**2020**, 69, 135–141. [Google Scholar] [CrossRef] - Jia, S.; Long, Q.; Wang, R.Y. On the Inapplicability of the Cobb-Douglas Production Function for Estimating the Benefit of Water Use and the Value of Water Resources. Water Resour. Manag.
**2016**, 30, 3645–3650. [Google Scholar] [CrossRef] - Li, F.; Zhang, H.; Li, X.; Deng, H.; Chen, X.; Liu, L. Modelling and Evaluation of Potato Water Production Functions in a Cold and Arid Environment. Water
**2022**, 14, 2044. [Google Scholar] [CrossRef] - Holzapfel, E.; Merino, R.; Mariño, M. Water production functions in kiwi. Irrig. Sci.
**2000**, 19, 73–79. [Google Scholar] [CrossRef] - Kasiviswanathan, K.S.; Sudheer, K.P.; Soundharajan, B.S. Implications of uncertainty in inflow forecasting on reservoir operation for irrigation. Paddy Water Environ.
**2021**, 19, 99–111. [Google Scholar] [CrossRef] - Kouadri, S.; Pande, C.B.; Panneerselvam, B. Prediction of irrigation groundwater quality parameters using ANN, LSTM, and MLR models. Environ. Sci. Pollut. Res.
**2022**, 29, 21067–21091. [Google Scholar] [CrossRef] [PubMed] - Shao, W.Y.; Guan, Q.Y.; Tan, Z.; Luo, H.P.; Li, H.C.; Sun, Y.F.; Ma, Y.R. Application of BP-ANN model in evaluation of soil quality in the arid area, northwest China. Soil Tillage Res.
**2021**, 208, 104907. [Google Scholar] [CrossRef] - Deng, Y.; Zhou, X.L.; Shen, J.; Xiao, G.; Hong, H.C.; Lin, H.J.; Wu, F.Y.; Liao, B.Q. New methods based on back propagation (BP) and radial basis function (RBF) artificial neural networks (ANNs) for predicting the occurrence of haloketones in tap water. Sci. Total Environ.
**2021**, 772, 145534. [Google Scholar] [CrossRef] - Zhang, J.L. Effects of deficit irrigation on water use efficiency and fruit quality of Lycium barbarum. Res. Agric. Sci.
**2015**, 36, 29–34. [Google Scholar] - Zheng, G.B.; Zhang, Y.P.; Zhu, J.X.; Zhou, L.; Kong, D.J.; Wang, Y.P. Study on water effect and water production function of Lycium barbarum in different growth stages. Water Sav. Irrig.
**2012**, 11, 22–24. (In Chinese). [Google Scholar] - Bi, S.; Xiong, W. Small sample expansion method based on the data distribution and application. J. Control. Eng.
**2019**, 26, 1431–1436. [Google Scholar] [CrossRef] - Fernández Jaramillo, J.M.; Mayerle, R. Sample selection via angular distance in the space of the arguments of an artificial neural network. Comput. Geosci.
**2018**, 114, 98–106. [Google Scholar] [CrossRef] - Ai, X.; Sun, B.; Chen, X. Construction of small sample seismic landslide susceptibility evaluation model based on Transfer Learning: A case study of Jiuzhaigou earthquake. Bull. Eng. Geol. Environ.
**2022**, 81, 116. [Google Scholar] [CrossRef] - Zhang, Z.; Wang, H.; Wang, N. Sample extraction and expansion method with feature reconstruction and deformation information. Appl. Intell.
**2022**, 52, 15916–15928. [Google Scholar] [CrossRef] - Li, B.; Bao, Z.R.; Yao, M.Z.; Li, C.X.; Sun, X.L. Effects of irrigation lower limit and straw returning amount on yield, quality and water use efficiency of greenhouse tomato. Chin. J. Appl. Ecol.
**2020**, 31, 493–500. [Google Scholar] [CrossRef] - Hou, J.; Nan, X.; Kang, C. Effects of drip irrigation frequency and quota on soil water and heat distribution and yield in Lycium barbarum orchard. Econ. For. Res.
**2019**, 37, 58–66. [Google Scholar] - Bo, M.A.; Tian, J. Advance in Research on Water and Fertilizer Effect on Yield and Quality of Lycium Barbarum L. Water Sav. Irrig.
**2020**, 11, 6–11. [Google Scholar] - Liu, Q.; Liu, X.; Wu, J.; Li, Y. An Improved NSGA-III Algorithm Using Genetic K-Means Clustering Algorithm. IEEE Access
**2019**, 7, 185239–185249. [Google Scholar] [CrossRef] - Hou, Y.; Wu, N.Q.; Li, Z.W.; Zhang, Y.X.; Qu, T.; Zhu, Q.H. Many-objective optimization for scheduling of crude oil operations based on NSGA-III with consideration of energy efficiency. Swarm Evol. Comput.
**2020**, 57, 100714. [Google Scholar] [CrossRef] - Xu, L.G.; Wang, H.B.; Bao, Z.Y.; Li, J.Z. Experimental study on soil moisture lower limit-based drip irrigation schedule for Lycium barbarum in Ningxia arid area. J. Drain. Irrig. Mach. Eng.
**2020**, 38, 523–529. [Google Scholar] - Li, J.; Shang, S.H.; Jiang, H.Z.; Song, J.; Rahman, K.U.; Adeloye, A.J. Simulation-based optimization for spatiotemporal allocation of irrigation water in arid region. Agric. Water Manag.
**2021**, 254, 106952. [Google Scholar] [CrossRef] - Kuo, S.F.; Liu, C.W. Simulation and optimization model for irrigation planning and management. Hydrol. Process.
**2003**, 17, 3141–3159. [Google Scholar] [CrossRef] - Pan, Y.X.; Yuan, C.F.; Jing, S.Y. Simulation and optimization of irrigation schedule for summer maize based on SWAP model in saline region. Int. J. Agric. Biol. Eng.
**2020**, 13, 117–122. [Google Scholar] [CrossRef] - Bedekar, V.; Scantlebury, L.; Panday, S. Axisymmetric Modeling Using MODFLOW-USG. Groundwater
**2019**, 57, 772–777. [Google Scholar] [CrossRef] [PubMed]

**Figure 6.**Scatterplot of relationship between lower irrigation limit and score at different growth stages (LIL means lower irrigation limit).

**Figure 7.**Scatterplot of relationship between lower irrigation limit and yield at different growth stages.

**Figure 8.**Scatterplot of relationship between lower irrigation limit and ADF-50 at different growth stages.

Scheme | Lower Irrigation Limits (Percentage of Field Capacity) | Yield (kg/hm^{2}) | ADF-50 | ||||
---|---|---|---|---|---|---|---|

T1 | T2 | T3 | 2018 | 2019 | 2018 | 2019 | |

S1 | 65% | 50% | 65% | 1655.21 | 1473.34 | 312 | 306 |

S2 | 70% | 50% | 70% | 1983.69 | 1757.82 | 357 | 352 |

S3 | 60% | 50% | 65% | 1322.95 | 1271.46 | 247 | 249 |

Original | 50% | 60% | 65% | 1473.76 | 1348.87 | 342 | 336 |

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**

Zhao, J.; Yu, Y.; Lei, J.; Liu, J.
Multi-Objective Lower Irrigation Limit Simulation and Optimization Model for *Lycium Barbarum* Based on NSGA-III and ANN. *Water* **2023**, *15*, 783.
https://doi.org/10.3390/w15040783

**AMA Style**

Zhao J, Yu Y, Lei J, Liu J.
Multi-Objective Lower Irrigation Limit Simulation and Optimization Model for *Lycium Barbarum* Based on NSGA-III and ANN. *Water*. 2023; 15(4):783.
https://doi.org/10.3390/w15040783

**Chicago/Turabian Style**

Zhao, Jinpeng, Yingduo Yu, Jinyang Lei, and Jun Liu.
2023. "Multi-Objective Lower Irrigation Limit Simulation and Optimization Model for *Lycium Barbarum* Based on NSGA-III and ANN" *Water* 15, no. 4: 783.
https://doi.org/10.3390/w15040783