# Examination of Single- and Hybrid-Based Metaheuristic Algorithms in ANN Reference Evapotranspiration Estimating

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## Abstract

**:**

## 1. Introduction

#### 1.1. Research Background

#### 1.2. Applied Machine Learning Methods for ETo Forecasting

#### 1.3. Research Significance and Motivation

#### 1.4. Research Objectives

- Employ a pre-processing technique, namely singular spectrum analysis (SSA), to enhance the quality of the raw data and the mutual information (MI) technique to select the optimum model input (lags) scenario.
- Suggest a novel combined technique by coupling the ANN model with the hybrid-based PSOGWO algorithm to estimate monthly ETo based on multiple lags.
- Compare forecast accuracy and computational efficiency of the proposed PSOGWO-ANN model with other hybrid ML models, e.g., CPSOCGSA-ANN (hybrid-based), and single-based (i.e., MPA-ANN, SMA-ANN and MPSO-ANN).
- Examine how the novel HPOH technique simulates monthly ETo, depending on several lags.

## 2. Materials

#### 2.1. Area of Study and Dataset

^{2}/day). The meteorological parameters are described statistically in Table 1.

#### 2.2. FAO-56 PM Approach

^{−2}day

^{−1}), G the soil heat flux (MJm

^{−2}day

^{−1}), Tave the average monthly temperature (°C), es the mean saturation vapour pressure (kPa), ea the actual vapour pressure (kPa), Δ the slope of vapour pressure function (kPa/°C) and γ the psychometric constant (kPa/°C). The FAO Irrigation and Drainage Paper No. 56 fully explains the method of calculation and ETo principles [51].

## 3. Methodology

#### 3.1. Data Pre-Processing Techniques

#### 3.2. Hybrid Particle Swarm Optimisation–Grey Wolf Optimiser Algorithm (PSOGWO)

_{p}is the location of the prey, X is the location of the grey wolves and A and C are the vector coefficients. The coefficients for A and C are as follows:

_{(t}

_{+1)}is the position for the next iteration.

_{1}and r

_{2}, represent random numbers between 0 and 1. ω is the inertia weight parameter, where its value is given as 0.5+rand/2, C

_{1}and C

_{2}are set to be 0.5, x the position, v the velocity and p

^{i}the best position information that the i particle has attained. p

^{g}represents the best position information accessible in the swarm, the coefficients C

_{1}and C

_{2}indicating the optimisation parameters. The new position and velocity of the particles with smaller possibilities are disregarded in favour of a random position inside the search space in order to prevent local minima. The procedure continues until the ideal outcome is achieved or the exhaustion of the predetermined maximum number of iterations.

Algorithm 1. Hybrid PSOGWO | |

The user-specified: maximum number of iterations (MAXi), number of population sizes (PS), small possibility rate (prob), | |

Small population size = psizesmall, Possibility rate = prob. | |

1 | Initialise population |

2 | For Iteration = 1 to Max. Iteration do |

3 | for iteration count do |

4 | for population size do |

5 | r1 = rand; r2 = rand; |

6 | Update a, A and C vectors |

7 | Update alfa, beta and delta |

8 | Call PSO routine |

9 | Update PSO position |

10 | end |

11 | end |

12 | end |

13 | end |

#### 3.3. Artificial Neural Network (ANN)

#### 3.4. ANN-Based MHAs

#### 3.5. Model Performance Assessment

^{2}). The model’s precision and the quality of fit increases as the R

^{2}number gets closer to 1 [65]. However, R

^{2}only examines linear relationships between simulated and computed ETo values [81,82]. Therefore, further statistical metrics are required to assess the accuracy of the modelling. RMSE illustrates the average magnitude of error by weighting significant errors more heavily [83]. It also shows the deviation between calculated and predicted values [84]. Model deviance decreases as RMSE decreases [85]. The Scatter Index (SI) compares model performance qualitatively: excellent, good, fair or poor. The model’s accuracy is excellent when SI is less than 10%, good when it is between 10% and 20%, fair when it is between 20% and 30%, and poor when it is greater than 30% [13]. Finally, NSE compares the ratios of model errors and observed data variance to the ideal value of unity. The NSE index has been developed and used in many hydrological investigations [86]. Its value, as established by Pan et al. [87], ranges from 1 to −∞, NSE is a good indicator of model performance when it is close to 1. The following are the formulas required, defined in Equations (15)–(18):

## 4. Results

#### 4.1. Data Pre-Processing Analysis

#### 4.2. ANN Technique Configuration

#### 4.3. Performance Evaluation

^{2}evaluate the linear dependence between measured and simulated ETo data, while RMSE and SI evaluate the nonlinear dependence. As stated in the Section 3.5, ANN models provide good to excellent accuracy. Nevertheless, ANN combined with the PSOGWO algorithm slightly outperforms the other models, which have the lowest RMSE and SI and the highest NSE and R

^{2}.

^{2}values for all the suggested hybrid models. The results of all models demonstrate good simulation levels for the ETo time series based on R

^{2}, according to Dawson et al. [90]. R

^{2}values offer information about the linear relationship between the measured ETo value (i.e., computed by FAO56-PM, target) and predicted ETo value (output), for all models. The graphs demonstrate excellent levels of consistency between measured and forecast data, and the absence of any irregular data or distinct pattern trends.

## 5. Discussion

^{2}of 0.99899, 0.99896, 0.99888, 0.99895 and 0.99894 for PSOGWO-ANN, CPSOCGSA-ANN, MPA-ANN, SMA-ANN and MPOS-ANN, respectively. PSOGWO-ANN is better at determining the optimal hyperparameters (Lr, N1 and N2) of the ANN technique and also saves time. These results reflect those of Adnan et al. [40] and Khalilpourazari and Khalilpourazary [91], who also found that hybrid MHAs outperform single MHAs. This finding may assist in better understanding and regulation of water balance processes. Further work could consider if the learning process can be improved by examining alternative tuning parameters for optimisers, and also applying training strategies, such as transfer learning and reinforcement learning.

## 6. Conclusions

- The data pre-processing procedures used in the present study, i.e., the use of SSA and MI, are essential for improving the quality of raw data and selecting the best lagged scenario, whereby the CC of Lag 1 increased from 0.83 to 0.99.
- ANN is an effective tool for predicting evapotranspiration. Integrating it with algorithms improves its performance and saves time by selecting the optimal Lr coefficient and N1 and N2 numbers.
- All the forecasting models gave a good and similar performance, but it has been demonstrated that PSOGWO-ANN slightly outperformed other hybrid models. The best model shows that the suggested methodology is an accurate strategy for predicting monthly ETo, with R
^{2}= 0.99, RMSE = 0.00151, SI = 0.08317 and NSE = 0.99896.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Nourani, V.; Elkiran, G.; Abdullahi, J. Multi-step ahead modeling of reference evapotranspiration using a multi-model approach. J. Hydrol.
**2020**, 581, 124434. [Google Scholar] [CrossRef] - Hussain, M.I.; Muscolo, A.; Farooq, M.; Ahmad, W. Sustainable use and management of non-conventional water resources for rehabilitation of marginal lands in arid and semiarid environments. Agric. Water Manag.
**2019**, 221, 462–476. [Google Scholar] [CrossRef] - Raza, A.; Hu, Y.; Shoaib, M.; Abd Elnabi, M.K.; Zubair, M.; Nauman, M.; Syed, N.R. A systematic review on estimation of reference evapotranspiration under prisma guidelines. Pol. J. Environ. Stud
**2021**, 30, 5413–5422. [Google Scholar] [CrossRef] - Krishnashetty, P.H.; Balasangameshwara, J.; Sreeman, S.; Desai, S.; Kantharaju, A.B. Cognitive computing models for estimation of reference evapotranspiration: A review. Cogn. Syst. Res.
**2021**, 70, 109–116. [Google Scholar] [CrossRef] - Roy, D.K. Long Short-Term Memory Networks to Predict One-Step Ahead Reference Evapotranspiration in a Subtropical Climatic Zone. Environ. Process.
**2021**, 8, 911–941. [Google Scholar] [CrossRef] - Sabziparvar, A.A.; Mirmasoudi, S.H.; Tabari, H.; Nazemosadat, M.J.; Maryanaji, Z. ENSO teleconnection impacts on reference evapotranspiration variability in some warm climates of Iran. Int. J. Climatol.
**2011**, 31, 1710–1723. [Google Scholar] [CrossRef] - Proias, G.; Gravalos, I.; Papageorgiou, E.; Poczęta, K.; Sakellariou-Makrantonaki, M. Forecasting Reference Evapotranspiration Using Time Lagged Recurrent Neural Network. Wseas Trans. Environ. Dev.
**2020**, 16, 699–707. [Google Scholar] [CrossRef] - Muhammad Adnan, R.; Chen, Z.; Yuan, X.; Kisi, O.; El-Shafie, A.; Kuriqi, A.; Ikram, M. Reference Evapotranspiration Modeling Using New Heuristic Methods. Entropy
**2020**, 22, 547. [Google Scholar] [CrossRef] - Alawsi, M.A.; Zubaidi, S.L.; Al-Ansari, N.; Al-Bugharbee, H.; Ridha, H.M. Tuning ANN Hyperparameters by CPSOCGSA, MPA, and SMA for Short-Term SPI Drought Forecasting. Atmosphere
**2022**, 13, 1436. [Google Scholar] [CrossRef] - Ethaib, S.; Zubaidi, S.L.; Al-Ansari, N. Evaluation water scarcity based on GIS estimation and climate-change effects: A case study of Thi-Qar Governorate, Iraq. Cogent Eng.
**2022**, 9, 2075301. [Google Scholar] [CrossRef] - IOM. Migration, Environment, and Climate Change in Iraq; International Organization for Migration (IOM): Baghdad, Iraq, 2022; pp. 1–32. [Google Scholar]
- Ferreira, L.B.; da Cunha, F.F. Multi-step ahead forecasting of daily reference evapotranspiration using deep learning. Comput. Electron. Agric.
**2020**, 178, 105728. [Google Scholar] [CrossRef] - Roy, D.K.; Barzegar, R.; Quilty, J.; Adamowski, J. Using ensembles of adaptive neuro-fuzzy inference system and optimization algorithms to predict reference evapotranspiration in subtropical climatic zones. J. Hydrol.
**2020**, 591, 125509. [Google Scholar] [CrossRef] - Naganna, S.R.; Beyaztas, B.H.; Bokde, N.; Armanuos, A.M. On the evaluation of the gradient tree boosting model for groundwater level forecasting. Knowl.-Based Eng.
**2020**, 1, 48–57. [Google Scholar] [CrossRef] - Sayyahi, F.; Farzin, S.; Karami, H.; Cai, N. Forecasting Daily and Monthly Reference Evapotranspiration in the Aidoghmoush Basin Using Multilayer Perceptron Coupled with Water Wave Optimization. Complexity
**2021**, 2021, 6683759. [Google Scholar] [CrossRef] - Yaghoubzadeh-Bavandpour, A.; Bozorg-Haddad, O.; Rajabi, M.; Zolghadr-Asli, B.; Chu, X. Application of swarm intelligence and evolutionary computation algorithms for optimal reservoir operation. Water Resour. Manag.
**2022**, 36, 2275–2292. [Google Scholar] [CrossRef] - Khairan, H.E.; Zubaidi, S.L.; Muhsen, Y.R.; Al-Ansari, N. Parameter Optimisation Based Hybrid Reference Evapotranspiration Prediction Models A Systematic Review of Current Implementations and Future Research Directions. Atmosphere
**2022**, 14, 77. [Google Scholar] [CrossRef] - Khudhair, Z.S.; Zubaidi, S.L.; Ortega-Martorell, S.; Al-Ansari, N.; Ethaib, S.; Hashim, K.J.E. A Review of Hybrid Soft Computing and Data Pre-Processing Techniques to Forecast Freshwater Quality’s Parameters: Current Trends and Future Directions. Environments
**2022**, 9, 85. [Google Scholar] [CrossRef] - Mohammed, S.J.; Zubaidi, S.L.; Ortega-Martorell, S.; Al-Ansari, N.; Ethaib, S.; Hashim, K.J.C.E. Application of hybrid machine learning models and data pre-processing to predict water level of watersheds: Recent trends and future perspective. Cogent Eng.
**2022**, 9, 2143051. [Google Scholar] [CrossRef] - Merchaoui, M.; Sakly, A.; Mimouni, M.F. Particle swarm optimisation with adaptive mutation strategy for photovoltaic solar cell/module parameter extraction. Energy Convers. Manag.
**2018**, 175, 151–163. [Google Scholar] [CrossRef] - Chen, H.; Jiao, S.; Wang, M.; Heidari, A.A.; Zhao, X. Parameters identification of photovoltaic cells and modules using diversification-enriched Harris hawks optimization with chaotic drifts. J. Clean. Prod.
**2020**, 244, 118778. [Google Scholar] [CrossRef] - Ridha, H.M. Parameters extraction of single and double diodes photovoltaic models using Marine Predators Algorithm and Lambert W function. Sol. Energy
**2020**, 209, 674–693. [Google Scholar] [CrossRef] - Wolpert, D.H.; Macready, W.G. No free lunch theorems for optimization. IEEE Trans. Evol. Comput.
**1997**, 1, 67–82. [Google Scholar] [CrossRef] - Adetunji, K.E.; Hofsajer, I.W.; Abu-Mahfouz, A.M.; Cheng, L. A Review of Metaheuristic Techniques for Optimal Integration of Electrical Units in Distribution Networks. IEEE Access
**2021**, 9, 5046–5068. [Google Scholar] [CrossRef] - Roy, D.K.; Lal, A.; Sarker, K.K.; Saha, K.K.; Datta, B. Optimization algorithms as training approaches for prediction of reference evapotranspiration using adaptive neuro fuzzy inference system. Agric. Water Manag.
**2021**, 255, 107003. [Google Scholar] [CrossRef] - Almubaidin, M.A.A.; Ahmed, A.N.; Sidek, L.B.M.; Elshafie, A. Using Metaheuristics Algorithms (MHAs) to Optimize Water Supply Operation in Reservoirs: A Review. Arch. Comput. Methods Eng.
**2022**, 29, 3677–3711. [Google Scholar] [CrossRef] - Lai, V.; Essam, Y.; Huang, Y.F.; Ahmed, A.N.; El-Shafie, A. Investigating dam reservoir operation optimization using metaheuristic algorithms. Appl. Water Sci.
**2022**, 12, 280. [Google Scholar] [CrossRef] - Li, S.; Chen, H.; Wang, M.; Heidari, A.A.; Mirjalili, S. Slime mould algorithm: A new method for stochastic optimization. Future Gener. Comput. Syst.
**2020**, 111, 300–323. [Google Scholar] [CrossRef] - ElSayed, S.K.; Elattar, E.E. Slime mold algorithm for optimal reactive power dispatch combining with renewable energy sources. Sustainability
**2021**, 13, 5831. [Google Scholar] [CrossRef] - Houssein, E.H.; Mahdy, M.A.; Blondin, M.J.; Shebl, D.; Mohamed, W.M. Hybrid slime mould algorithm with adaptive guided differential evolution algorithm for combinatorial and global optimization problems. Expert Syst. Appl.
**2021**, 174, 114689. [Google Scholar] [CrossRef] - Kumar, C.; Raj, T.D.; Premkumar, M.; Raj, T.D. A new stochastic slime mould optimization algorithm for the estimation of solar photovoltaic cell parameters. Optik
**2020**, 223, 165277. [Google Scholar] [CrossRef] - Faramarzi, A.; Heidarinejad, M.; Mirjalili, S.; Gandomi, A.H. Marine Predators Algorithm: A nature-inspired metaheuristic. Expert Syst. Appl.
**2020**, 152, 113377. [Google Scholar] [CrossRef] - Ghafil, H.N.; Jármai, K. Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications. Appl. Soft Comput.
**2020**, 93, 106392. [Google Scholar] [CrossRef] - Eid, A.; Kamel, S.; Abualigah, L. Marine predators algorithm for optimal allocation of active and reactive power resources in distribution networks. Neural Comput. Appl.
**2021**, 33, 14327–14355. [Google Scholar] [CrossRef] - Rather, S.A.; Bala, P.S. A hybrid constriction coefficient-based particle swarm optimization and gravitational search algorithm for training multi-layer perceptron. Int. J. Intell. Comput. Cybern.
**2020**, 13, 129–165. [Google Scholar] [CrossRef] - Ahmadi, F.; Mehdizadeh, S.; Mohammadi, B.; Pham, Q.B.; Doan, T.N.C.; Vo, N.D. Application of an artificial intelligence technique enhanced with intelligent water drops for monthly reference evapotranspiration estimation. Agric. Water Manag.
**2021**, 244, 106622. [Google Scholar] [CrossRef] - Tao, H.; Diop, L.; Bodian, A.; Djaman, K.; Ndiaye, P.M.; Yaseen, Z.M. Reference evapotranspiration prediction using hybridized fuzzy model with firefly algorithm: Regional case study in Burkina Faso. Agric. Water Manag.
**2018**, 208, 140–151. [Google Scholar] [CrossRef] - Maroufpoor, S.; Bozorg-Haddad, O.; Maroufpoor, E. Reference evapotranspiration estimating based on optimal input combination and hybrid artificial intelligent model: Hybridization of artificial neural network with grey wolf optimizer algorithm. J. Hydrol.
**2020**, 588, 125060. [Google Scholar] [CrossRef] - Chica, M.; Juan Pérez, A.A.; Cordon, O.; Kelton, D. Why simheuristics? Benefits, limitations, and best practices when combining metaheuristics with simulation. SORT
**2017**, 44, 311–334. [Google Scholar] [CrossRef] - Adnan, R.M.; Mostafa, R.R.; Islam, A.R.M.T.; Kisi, O.; Kuriqi, A.; Heddam, S. Estimating reference evapotranspiration using hybrid adaptive fuzzy inferencing coupled with heuristic algorithms. Comput. Electron. Agric.
**2021**, 191, 106541. [Google Scholar] [CrossRef] - Rather, S.A.; Bala, P.S. Hybridization of constriction coefficient-based particle swarm optimization and chaotic gravitational search algorithm for solving engineering design problems. Appl. Soft Comput. Commun. Netw. Proc. ACN
**2020**, 125, 95–115. [Google Scholar] - Črepinšek, M.; Liu, S.-H.; Mernik, M. Exploration and exploitation in evolutionary algorithms: A survey. ACM Comput. Surv.
**2013**, 45, 1–33. [Google Scholar] [CrossRef] - Eiben, A.E.; Schippers, C.A. On evolutionary exploration and exploitation. Fundam. Informaticae
**1998**, 35, 35–50. [Google Scholar] [CrossRef] - Şenel, F.A.; Gökçe, F.; Yüksel, A.S.; Yiğit, T. A novel hybrid PSO–GWO algorithm for optimization problems. Eng. Comput.
**2019**, 35, 1359–1373. [Google Scholar] [CrossRef] - Hajirahimi, Z.; Khashei, M. Hybridization of hybrid structures for time series forecasting: A review. Artif. Intell. Rev.
**2022**, 56, 1201–1261. [Google Scholar] [CrossRef] - Zubaidi, S.L.; Al-Bdairi, N.S.S.; Ortega-Martorell, S.; Ridha, H.M.; Al-Ansari, N.; Al-Bugharbee, H.; Hashim, K.; Gharghan, S.K. Assessing the Benefits of Nature-Inspired Algorithms for the Parameterization of ANN in the Prediction of Water Demand. J. Water Resour. Plan. Manag.
**2023**, 149, 1–10. [Google Scholar] [CrossRef] - Edan, M.H.; Maarouf, R.M.; Hasson, J. Predicting the impacts of land use/land cover change on land surface temperature using remote sensing approach in Al Kut, Iraq. Phys. Chem. Earth Parts A/B/C
**2021**, 123, 103012. [Google Scholar] [CrossRef] - Muter, S.A.; Nassif, W.G.; Al-Ramahy, Z.A.; Al-Taai, O.T. Analysis of seasonal and annual relative humidity using GIS for selected stations over Iraq during the period (1980–2017). J. Green Eng.
**2020**, 10, 9121–9135. [Google Scholar] - Al-Abadi, A.; Al-Aboodi, A.H.D. Optimum rain-gauges network design of some cities in Iraq. J. Babylon Univ./Eng. Sci.
**2014**, 22, 946–958. [Google Scholar] - Capt, T.; Mirchi, A.; Kumar, S.; Walker, W.S. Urban Water Demand: Statistical Optimization Approach to Modeling Daily Demand. J. Water Resour. Plan. Manag.
**2021**, 147, 1–10. [Google Scholar] [CrossRef] - Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. Crop Evapotranspiration-Guidelines for Computing Crop Water Requirements-FAO Irrigation and Drainage Paper 56; FAO: Rome, Italy, 1998; Volume 300, p. D05109. [Google Scholar]
- Yu, J.; Zheng, W.; Xu, L.; Zhangzhong, L.; Zhang, G.; Shan, F. A PSO-XGBoost Model for Estimating Daily Reference Evapotranspiration in the Solar Greenhouse. Intell. Autom. Soft Comput.
**2020**, 26, 989–1003. [Google Scholar] [CrossRef] - Behboudian, S.; Tabesh, M.; Falahnezhad, M.; Ghavanini, F.A. A long-term prediction of domestic water demand using preprocessing in artificial neural network. J. Water Supply Res. Technol.-Aqua
**2014**, 63, 31–42. [Google Scholar] [CrossRef] - Espinosa, F.; Bartolomé, A.B.; Hernández, P.V.; Rodriguez-Sanchez, M. Contribution of Singular Spectral Analysis to Forecasting and Anomalies Detection of Indoors Air Quality. Sensors
**2022**, 22, 3054. [Google Scholar] [CrossRef] [PubMed] - Al-Bugharbee, H.; Trendafilova, I. A fault diagnosis methodology for rolling element bearings based on advanced signal pretreatment and autoregressive modelling. J. Sound Vib.
**2016**, 369, 246–265. [Google Scholar] [CrossRef] - Bureneva, O.; Safyannikov, N.; Aleksanyan, Z. Singular Spectrum Analysis of Tremorograms for Human Neuromotor Reaction Estimation. Mathematics
**2022**, 10, 1794. [Google Scholar] [CrossRef] - Kilundu, B.; Chiementin, X.; Dehombreux, P. Singular spectrum analysis for bearing defect detection. J. Vib. Acoust.
**2011**, 133, 051007. [Google Scholar] [CrossRef] - Hassani, H. Singular spectrum analysis: Methodology and comparison. J. Data Sci.
**2007**, 5, 239–257. [Google Scholar] [CrossRef] [PubMed] - Pham, Q.B.; Yang, T.-C.; Kuo, C.-M.; Tseng, H.-W.; Yu, P.-S. Coupling singular spectrum analysis with least square support vector machine to improve accuracy of SPI drought forecasting. Water Resour. Manag.
**2021**, 35, 847–868. [Google Scholar] [CrossRef] - Ouyang, Q.; Lu, W. Monthly rainfall forecasting using echo state networks coupled with data preprocessing methods. Water Resour. Manag.
**2018**, 32, 659–674. [Google Scholar] [CrossRef] - Apaydin, H.; Sattari, M.T.; Falsafian, K.; Prasad, R. Artificial intelligence modelling integrated with Singular Spectral analysis and Seasonal-Trend decomposition using Loess approaches for streamflow predictions. J. Hydrol.
**2021**, 600, 126506. [Google Scholar] [CrossRef] - Danandeh Mehr, A.; Ghadimi, S.; Marttila, H.; Torabi Haghighi, A.; Climatology, A. A new evolutionary time series model for streamflow forecasting in boreal lake-river systems. Theor. Appl. Climatol.
**2022**, 148, 255–268. [Google Scholar] [CrossRef] - Ramírez-Rojas, A.; Cárdenas-Moreno, P.; Vargas, C. Mutual information analysis between NO
_{2}and O_{3}pollutants measured in Mexico City before and during 2020 COVID-19 pandemic year. J. Phys. Conf. Ser.**2022**, 2307, 012053. [Google Scholar] [CrossRef] - Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey wolf optimizer. Adv. Eng. Softw.
**2014**, 69, 46–61. [Google Scholar] [CrossRef] - Dong, J.; Liu, X.; Huang, G.; Fan, J.; Wu, L.; Wu, J. Comparison of four bio-inspired algorithms to optimize KNEA for predicting monthly reference evapotranspiration in different climate zones of China. Comput. Electron. Agric.
**2021**, 186, 106211. [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; pp. 1942–1948. [Google Scholar]
- Zhu, B.; Feng, Y.; Gong, D.; Jiang, S.; Zhao, L.; Cui, N. Hybrid particle swarm optimization with extreme learning machine for daily reference evapotranspiration prediction from limited climatic data. Comput. Electron. Agric.
**2020**, 173, 105430. [Google Scholar] [CrossRef] - Roy, D.K.; Saha, K.K.; Kamruzzaman, M.; Biswas, S.K.; Hossain, M.A. Hierarchical Fuzzy Systems Integrated with Particle Swarm Optimization for Daily Reference Evapotranspiration Prediction: A Novel Approach. Water Resour. Manag.
**2021**, 35, 5383–5407. [Google Scholar] [CrossRef] - Alizamir, M.; Kisi, O.; Muhammad Adnan, R.; Kuriqi, A. Modelling reference evapotranspiration by combining neuro-fuzzy and evolutionary strategies. Acta Geophys.
**2020**, 68, 1113–1126. [Google Scholar] [CrossRef] - Jawad, H.M.; Jawad, A.M.; Nordin, R.; Gharghan, S.K.; Abdullah, N.F.; Ismail, M.; Abu-AlShaeer, M.J. Accurate empirical path-loss model based on particle swarm optimization for wireless sensor networks in smart agriculture. IEEE Sens. J.
**2019**, 20, 552–561. [Google Scholar] [CrossRef] - Peng, T.; Zhou, J.; Zhang, C.; Fu, W. Streamflow forecasting using empirical wavelet transform and artificial neural networks. Water
**2017**, 9, 406. [Google Scholar] [CrossRef] - Nabipour, N.; Dehghani, M.; Mosavi, A.; Shamshirband, S. Short-term hydrological drought forecasting based on different nature-inspired optimization algorithms hybridized with artificial neural networks. IEEE Access
**2020**, 8, 15210–15222. [Google Scholar] [CrossRef] - Tikhamarine, Y.; Malik, A.; Kumar, A.; Souag-Gamane, D.; Kisi, O. Estimation of monthly reference evapotranspiration using novel hybrid machine learning approaches. Hydrol. Sci. J.
**2019**, 64, 1824–1842. [Google Scholar] [CrossRef] - Zhang, N.; Hwang, B.-G.; Lu, Y.; Ngo, J. A Behavior theory integrated ANN analytical approach for understanding households adoption decisions of residential photovoltaic (RPV) system. Technol. Soc.
**2022**, 70, 102062. [Google Scholar] [CrossRef] - Gocić, M.; Arab Amiri, M. Reference Evapotranspiration Prediction Using Neural Networks and Optimum Time Lags. Water Resour. Manag.
**2021**, 35, 1913–1926. [Google Scholar] [CrossRef] - Pourdarbani, R.; Sabzi, S.; Rohban, M.H.; Garcia-Mateos, G.; Paliwal, J.; Molina-Martinez, J.M. Using metaheuristic algorithms to improve the estimation of acidity in Fuji apples using NIR spectroscopy. Ain Shams Eng. J.
**2022**, 13, 101776. [Google Scholar] [CrossRef] - Kapanova, K.G.; Dimov, I.; Sellier, J.M. A genetic approach to automatic neural network architecture optimization. Neural Comput. Appl.
**2016**, 29, 1481–1492. [Google Scholar] [CrossRef] - Alemu, H.; Wu, W.; Zhao, J. Feedforward Neural Networks with a Hidden Layer Regularization Method. Symmetry
**2018**, 10, 525. [Google Scholar] [CrossRef] - Yahya-Khotbehsara, A.; Shahhoseini, A. A fast modeling of the double-diode model for PV modules using combined analytical and numerical approach. Sol. Energy
**2018**, 162, 403–409. [Google Scholar] [CrossRef] - Ahmed, A.N.; Van Lam, T.; Hung, N.D.; Van Thieu, N.; Kisi, O.; El-Shafie, A. A comprehensive comparison of recent developed meta-heuristic algorithms for streamflow time series forecasting problem. Appl. Soft Comput.
**2021**, 105, 107282. [Google Scholar] [CrossRef] - Legates, D.R.; McCabe Jr, G.J. Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef] - Hodges, G.; Eadsforth, C.; Bossuyt, B.; Bouvy, A.; Enrici, M.-H.; Geurts, M.; Kotthoff, M.; Michie, E.; Miller, D.; Müller, J.; et al. A comparison of log Kow (n-octanol–water partition coefficient) values for non-ionic, anionic, cationic and amphoteric surfactants determined using predictions and experimental methods. Environ. Sci. Eur.
**2019**, 31, 1. [Google Scholar] [CrossRef] - Shiri, J.; Zounemat-Kermani, M.; Kisi, O.; Mohsenzadeh Karimi, S. Comprehensive assessment of 12 soft computing approaches for modelling reference evapotranspiration in humid locations. Meteorol. Appl.
**2019**, 27, e1841. [Google Scholar] [CrossRef] - Wang, W.; Kong, W.; Shen, T.; Man, Z.; Zhu, W.; He, Y.; Liu, F. Quantitative analysis of cadmium in rice roots based on LIBS and chemometrics methods. Environ. Sci. Eur.
**2021**, 33, 37. [Google Scholar] [CrossRef] - Despotovic, M.; Nedic, V.; Despotovic, D.; Cvetanovic, S. Review and statistical analysis of different global solar radiation sunshine models. Renew. Sustain. Energy Rev.
**2015**, 52, 1869–1880. [Google Scholar] [CrossRef] - Jain, S.K.; Sudheer, K. Fitting of hydrologic models: A close look at the Nash–Sutcliffe index. J. Hydrol. Eng.
**2008**, 13, 981–986. [Google Scholar] [CrossRef] - Pan, M.; Zhou, H.; Cao, J.; Liu, Y.; Hao, J.; Li, S.; Chen, C.-H. Water level prediction model based on GRU and CNN. IEEE Access
**2020**, 8, 60090–60100. [Google Scholar] [CrossRef] - Stergiou, N. Nonlinear Analysis for Human Movement Variability; CRC Press: Boca Raton, FL, USA, 2018. [Google Scholar]
- Tabachnick, B.G.; Fidell, L.S.; Ullman, J.B. Using Multivariate Statistics; Pearson: Boston, MA, USA, 2013; Volume 6. [Google Scholar]
- Dawson, C.W.; Abrahart, R.J.; See, L.M. HydroTest: A web-based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environ. Model. Softw.
**2007**, 22, 1034–1052. [Google Scholar] [CrossRef] - Khalilpourazari, S.; Khalilpourazary, S. An efficient hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems. Soft Comput.
**2019**, 23, 1699–1722. [Google Scholar] [CrossRef]

**Figure 9.**Measured and simulated ETo data comparison for all suggested strategies in the validation phase.

Variable | Mean | Maximum | Minimum |
---|---|---|---|

U2 | 1.83 | 5.34 | 3.0497 |

RH | 10.18 | 70.60 | 33.8648 |

Tdew | 3.8761 | 12.05 | −3.66 |

Tmin | 17.9526 | 32.50 | 1.54 |

Tmax | 32.6396 | 48.93 | 32.6396 |

Rs | 19.3106 | 30.13 | 8.61 |

Hyperparameter | PSOGWO-ANN | CPSOCGSA-ANN | SMA-ANN | MPA-ANN | MPSO-ANN |
---|---|---|---|---|---|

N1 | 4 | 4 | 2 | 1 | 2 |

N2 | 3 | 5 | 1 | 19 | 5 |

LR | 0.0470 | 0.3219 | 0.8496 | 0.0558 | 0.781 |

Model | RMSE | SI | NSE | R^{2} |
---|---|---|---|---|

PSOGWO-ANN | 0.00151 | 0.08317 | 0.99896 | 0.99899 |

CPSOCGSA-ANN | 0.00153 | 0.0842 | 0.99893 | 0.99896 |

MPA-ANN | 0.00159 | 0.08769 | 0.99884 | 0.99888 |

SMA-ANN | 0.00154 | 0.08488 | 0.99892 | 0.99895 |

MPSO-ANN | 0.00152 | 0.8396 | 0.99896 | 0.99894 |

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**MDPI and ACS Style**

Khairan, H.E.; Zubaidi, S.L.; Raza, S.F.; Hameed, M.; Al-Ansari, N.; Ridha, H.M.
Examination of Single- and Hybrid-Based Metaheuristic Algorithms in ANN Reference Evapotranspiration Estimating. *Sustainability* **2023**, *15*, 14222.
https://doi.org/10.3390/su151914222

**AMA Style**

Khairan HE, Zubaidi SL, Raza SF, Hameed M, Al-Ansari N, Ridha HM.
Examination of Single- and Hybrid-Based Metaheuristic Algorithms in ANN Reference Evapotranspiration Estimating. *Sustainability*. 2023; 15(19):14222.
https://doi.org/10.3390/su151914222

**Chicago/Turabian Style**

Khairan, Hadeel E., Salah L. Zubaidi, Syed Fawad Raza, Maysoun Hameed, Nadhir Al-Ansari, and Hussein Mohammed Ridha.
2023. "Examination of Single- and Hybrid-Based Metaheuristic Algorithms in ANN Reference Evapotranspiration Estimating" *Sustainability* 15, no. 19: 14222.
https://doi.org/10.3390/su151914222