# Hybridizing Artificial Intelligence Algorithms for Forecasting of Sediment Load with Multi-Objective Optimization

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{9}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}or approximately 4.3% of India’s total land area [46]. Odisha receives 53% of the river’s basin area, while Chhattisgarh receives 46% and Maharashtra, Madhya Pradesh, and Jharkhand share the remaining 1% [46]. Until it enters the Bay of Bengal, the river flows for a total of 851 km. Thr MR was located between 19°20′ and 23°35′ north, and 80°30′ and 86°50′ east. The MR contains the Hirakud dam which is the world’s largest earthen dam. In terms of current sediment load, the MR is second among Indian peninsular rivers. Figure 1 shows the MR basin elevation map and the locations of all 11 hydro-climatological sites. The average annual RF was between 1200 and 1400 mm [47]. Approximately 90% of the yearly RF that the MR basin receives occurs during the monsoons. The MR basin has a dispersed pattern of RF strength. In the MR basin, the warmest months are April and May, with summer temperatures of 39 to 45 °C, and the coldest months are December and January, with winter temperatures of 4 to 12 °C [47]. The two largest bodies of water in the MR are Lake Chilka and the Hirakud Dam.

## 3. Methodology and Data

^{9}[24]. In the fifth section, the biases and weights of the connections of ANN models are shown. The length of the chromosome changes because the number of hidden neurons and the number of inputs change. The ANN-MOGA forecasting models are designed with GA parameters such as the number of generations, the size of the population, the rate of mutation, and the probability of a crossover. In this study, a uniform crossover with a high probability value (0.6) and a low probability of constant mutation (0.05) was used. The values of each chromosome’s fitness are estimated using the fitness function (RMSE) of the training dataset. The maximum generations (50) were considered as stopping criteria.

_{0}of size $N$ is produced by the mutation, selection, and crossover operators at iteration 0. The overall number of chromosomal solutions for any iteration t following the genetic operations is R

_{t}= P

_{t}∪ Q

_{t}becomes twice (2N). P and Q represent the parent and child populations, respectively. R represents the total number of chromosomal solutions after the genetic operations. The objective functions of each solution (R

_{t}) were determined by calculating, and the solutions have been ranked using the previously discussed Non-Dominated Sorting criteria and crowding distance. The rest solutions were eliminated from the solution space, and the top $N$ solutions determined by their whole rank were chosen (referred to as elitism) for the following generation. The maximum number of individuals permitted from the i

^{th}non-dominated front as shown in Equation (5) is provided diversity in the new population, based on the geometric distribution [36].

_{i}($i$ = 0, 1, 2,....., $n$) represents the regression model’s coefficients. The MAR was designed using training datasets and the linear combination of the Autoregressive of multiple variables (WD, T, RF, and SL and spatial variables (R, CA, and RT). The MAR formula is shown below

_{i}, b

_{i}, c

_{i}, d

_{i}, e, f, and g (i = 1,2, 3,…, n) represent the coefficients of the MAR model. The a

_{i}, b

_{i}, c

_{i,}and d

_{i}represent the coefficients of WD, RF, T and SL, respectively. The coefficients of the RT, R, and CA are represented by the values e, f, and g, respectively. The maximum lag (n) in AR and MAR model for the SL forecasting is 12, after which the cyclicity begins due to seasonal behaviour of the data. There are four temporal variables: WD, SL, RF, and T. The RT, CA and R are the spatial variables.

## 4. Results and Discussion

#### 4.1. Data Analysis

#### 4.2. ANN-MOGA Forecasting Model

^{°}line, except for the four gauging stations that were mentioned earlier (Figure 8). The scatter plots and hydrographs show that the magnitudes and medium, high, and low SL forecasted values generated by the best ANN-MOGA-51 forecasting model are also fairly close to the corresponding actual SL values. The ANN-MOGA-51 model displayed a positive value SL at each of the 11 gauge stations, although the SL output was either 0 or very near zero (Figure 7 and Figure 8). Based on these findings, it was determined that the application of ANN in conjunction with GA is the method that yields the most accurate results for calculating SL in the MR basin system. The forecasting model provides the highest level of accuracy at the Tikarapara gauging station compared to any other station gauging station. This may be due to the location of Tikarapara, which is at the most downstream portion of the MR basin and possesses the highest WD, CA, RF, and SL of any of the gauging stations [24,47].

#### 4.3. AR Forecasting Model

#### 4.4. The Multivariate Autoregressive (MAR) Forecasting Model

#### 4.5. Comparison Results of Forecasting Models

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Frémion, F.; Bordas, F.; Mourier, B.; Lenain, J.; Kestens, T.; Courtin-Nomade, A. Influence of dams on sediment continuity: A study case of a natural metallic contamination. Sci. Total Environ.
**2016**, 547, 282–294. [Google Scholar] [CrossRef] [PubMed] - Xia, X.; Dong, J.; Wang, M.; Xie, H.; Xia, N.; Li, H.; Zhang, X.; Mou, X.; Wen, J.; Bao, Y. Effect of water-sediment regulation of the Xiaolangdi reservoir on the concentrations, characteristics, and fluxes of suspended sediment and organic carbon in the Yellow River. Sci. Total Environ.
**2016**, 571, 487–497. [Google Scholar] [CrossRef] [PubMed][Green Version] - Honorato, A.G.D.S.M.; Silva, G.B.L.D.; Guimarães Santos, C.A. Monthly streamflow forecasting using neuro-wavelet techniques and input analysis. Hydrol. Sci. J.
**2018**, 63, 2060–2075. [Google Scholar] [CrossRef][Green Version] - Dutta, S. Soil erosion, sediment yield and sedimentation of reservoir: A review. Model. Earth Syst. Environ.
**2016**, 2, 123. [Google Scholar] [CrossRef][Green Version] - Jansson, M.B. Land Erosion by Water in Different Climates; UNGI Report No. 57; Department of Physical Geography, University of Uppsala: Uppsala, Sweden, 1982. [Google Scholar]
- Syvitski, J.P.M.; Peckham, S.D.; Hilberman, R.; Mulder, T. Predicting the Terrestrial Flux of Sediment to the Global Ocean: A Planetary Perspective. Sediment. Geol.
**2003**, 162, 5–24. [Google Scholar] [CrossRef] - Gupta, H.; Chakrapani, G.J. Temporal and spatial variations in water flow and sediment load in Narmada River Basin, India: Natural and man-made factors. Environ. Geol.
**2005**, 48, 579–589. [Google Scholar] [CrossRef] - Ramesh, R.; Subramanian, V. Temporal, spatial and size variation in the sediment transport in the Krishna River basin, India. J. Hydrol.
**1988**, 98, 53–65. [Google Scholar] [CrossRef] - Bastia, F.; Equeenuddin, S.M. Spatio-temporal variation of water flow and sediment discharge in the Mahanadi River, India. Glob. Planet. Chang.
**2016**, 144, 51–66. [Google Scholar] [CrossRef] - Thodsen, H.; Hasholt, B.; Kjarsgaard, J.H. The influence of climate change on suspended sediment transport in Danish rivers. Hydrol. Process.
**2008**, 22, 764–774. [Google Scholar] [CrossRef] - Merritt, W.S.; Letcher, R.A.; Jakeman, A.J. A review of erosion and sediment transport models. Environ. Model. Softw.
**2003**, 18, 761–799. [Google Scholar] [CrossRef] - Salas, J.D.; Delleur, J.W.; Yevjevich, V.; Lane, W.L. Applied Modeling of Hydrologic Time Series; Water Resources Publications: Littleton, CO, USA, 1980; 484p. [Google Scholar]
- Adamowski, J.; Chan, H.F.; Prasher, S.O.; Ozga-Zielinski, B.; Sliusarieva, A. Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Wat. Resour. Res.
**2012**, 48, W01528. [Google Scholar] [CrossRef] - Pektas, A.O.; Cigizoglu, H.K. Long-range forecasting of suspended sediment. Hydrol. Sci. J.
**2017**, 62, 2415–2425. [Google Scholar] [CrossRef] - Partal, T.; Cigizoglu, H.K. Estimation and forecasting of daily suspended sediment data using wavelet-neural networks. J. Hydrol.
**2008**, 358, 317–331. [Google Scholar] [CrossRef] - Nourani, V.; Alizadeh, F.; Roushangar, K. Evaluation of a two-stage SVM and spatial statistics methods for modeling monthly river suspended sediment load. Water Resour. Manag.
**2016**, 30, 393–407. [Google Scholar] [CrossRef] - Meshram, S.G.; Ghorbani, M.A.; Deo, R.C.; Kashani, M.H.; Meshram, C.; Karimi, V. New approach for sediment yield forecasting with a two-phase feedforward neuron network-particle swarm optimization model integrated with the gravitational search algorithm. Water Resour. Manag.
**2019**, 33, 2335–2356. [Google Scholar] [CrossRef] - ASCE. Task Committee on Application of Artificial Neural Networks in Hydrology Artificial neural networks in hydrology. I: Preliminary concepts. J. Hydrol. Eng.
**2000**, 5, 115–123. [Google Scholar] [CrossRef] - Reddy, P.V.B. Modelling and Optimization of Wire Electrical Discharge Machining of Cr-Mo-V Special Alloy Steel Using Neuro Genetic Approach. Ph.D. Thesis, Jawaharlal Nehru Technological University, Anantapur, India, 2014. [Google Scholar]
- Tokar, A.S.; Johnson, P.A. Rainfall-Runoff Modelling using Artificial Neural Networks. J. Hydrol. Eng.
**1999**, 4, 232–239. [Google Scholar] [CrossRef] - Dawson, C.W.; Harpham, C.; Wilby, R.L.; Chen, Y. An evaluation of artificial neural network techniques for flow forecasting in the river Yangtze, China. Hydrol. Earth Syst. Sci.
**2002**, 6, 619–626. [Google Scholar] [CrossRef] - Kar, A.K.; Lohani, A.K.; Goel, N.K.; Roy, G.P. Development of Flood Forecasting System Using Statistical and ANN Techniques in the Downstream Catchment of Mahanadi Basin, India. J. Water Resour. Prot.
**2010**, 2, 880–887. [Google Scholar] - Bishop, M. Neural Networks for Pattern Recognition; Clarendon Press: Oxford, UK, 1998. [Google Scholar]
- Yadav, A.; Chatterjee, S.; Equeenuddin, S.M. Suspended Sediment Yield Estimation using Genetic Algorithm-based Artificial Intelligence Models in Mahanadi River. Hydrol. Sci. J.
**2018**, 63, 1162–1182. [Google Scholar] [CrossRef] - Holland, J. Adaptation in Natural and Artificial Systems; The University of Michigan Press: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Hosseini, S.A.; Abbaszadeh Shahri, A.; Asheghi, R. Prediction of bedload transport rate using a block combined network structure. Hydrol. Sci. J.
**2022**, 67, 117–128. [Google Scholar] [CrossRef] - Chatterjee, S.; Bandopadhyay, S. Reliability estimation using a genetic algorithm-based artificial neural network: An application to a load-haul-dump machine. Expert Syst. Appl.
**2012**, 39, 10943–10951. [Google Scholar] [CrossRef] - Asheghi, R.; Hosseini, S.A.; Saneie, M.; Shahri, A.A. Updating the neural network sediment load models using different sensitivity analysis methods: A regional application. J. Hydroinformatics
**2020**, 22, 562–577. [Google Scholar] [CrossRef][Green Version] - Adib, A.; Mahmoodi, A. Prediction of Suspended Sediment Load using ANN GA Conjunction Model with Markov Chain Approach at Flood Conditions. KSCE J. Civ. Eng.
**2016**, 1, 447–457. [Google Scholar] [CrossRef] - Chatterjee, S.; Bandopadhyay, S. Goodnews Bay Platinum Resource Estimation Using Least Squares Support Vector Regression with Selection of Input Space Dimension and Hyperparameters. Nat. Resour. Res.
**2016**, 20, 117–129. [Google Scholar] [CrossRef] - Samarasinghe, S. Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition; CRC Press: Boca Raton, FL, USA, 2016; p. 555. [Google Scholar]
- Geman, S.; Bienenstock, E.; Doursat, R. Neural networks and the bias/variance dilemma. Neural Comput.
**1992**, 4, 1–58. [Google Scholar] [CrossRef] - Rosales-Perez, A.; Escalante, H.J.; Gonzalez, J.A.; Reyes-Garcia, C.A. Bias and variance optimization for SVMs model selection. In Proceedings of the Twenty-Sixth International FLAIRS Conference, St. Pete Beach, FL, USA, 22–24 May 2013. [Google Scholar]
- Kulasiri, D.; Verwoerd, V. Stochastic Dynamics: Modeling Solute Transport in Porous Media; North Holland Series in Applied Mathematics and Mechanics; Elsevier: Amsterdam, The Netherlands, 2002; p. 44. [Google Scholar]
- Levin, S.A. Population dynamics in models in heterogeneous environments. Annu. Rev. Ecol. Syst.
**1976**, 7, 287. [Google Scholar] [CrossRef] - Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput.
**2002**, 6, 181–197. [Google Scholar] [CrossRef][Green Version] - Bharti, P.S.; Maheshwari, S.; Sharma, C. Multi-objective optimization of electric-discharge machining process using controlled elitist NSGA-II. J. Mech. Sci. Technol.
**2012**, 26, 1875–1883. [Google Scholar] [CrossRef] - Behzadian, K.; Kapelan, Z.; Savic, D.; Ardeshir, A. Stochastic sampling design using multi-objective genetic algorithm and adaptive neural network. Environ. Model. Softw.
**2009**, 24, 530–541. [Google Scholar] [CrossRef][Green Version] - Zhou, C.C.; Yin, G.F.; Hu, X.B. Multi-objective optimization of material selection for sustainable products: Artificial neural networks and genetic algorithm approach. Mater. Des.
**2009**, 30, 1209–1215. [Google Scholar] [CrossRef] - Yadav, A.; Chatterjee, S.; Equeenuddin, S.M. Suspended sediment yield modeling in Mahanadi River, India by multi-objective optimization hybridizing artificial intelligence algorithms. Int. J. Sediment Res.
**2021**, 36, 76–91. [Google Scholar] [CrossRef] - Sakai, K.; Osawa, K.; Yoshinaga, A. Development of suspended sediment concentration analysis model and its application with multi-objective optimization. Paddy Water Environ.
**2005**, 3, 201–209. [Google Scholar] [CrossRef] - Peng, Y.; Ji, C.; Gu, R. Multiobjective optimization model for coordinatec regulation of water flow and sediment in cascade reservoirs. Water Resour. Manag.
**2014**, 28, 4019–4033. [Google Scholar] [CrossRef] - Cigizoglu, H.K.; Kisi, O. Methods to improve the neural network performance in suspended sediment estimation. J. Hydrol.
**2006**, 317, 221–238. [Google Scholar] [CrossRef] - Cigizoglu, H.K.; Alp, M. Generalized regression neural network in modelling river sediment yield. Adv. Eng. Softw.
**2006**, 37, 63–68. [Google Scholar] [CrossRef] - Piotrowski, A.P.; Napiorkowski, M.J.; Napiorkowski, J.J.; Osuch, M. Comparing various artificial neural network types for water temperature prediction in rivers. J. Hydrol.
**2015**, 529, 302–315. [Google Scholar] [CrossRef] - Kant, A.; Suman, P.K.; Giri, B.K.; Tiwari, M.K.; Chatterjee, C.; Nayak, P.C.; Kumar, S. Comparison of multi-objective evolutionary neural network, adaptive neuro-inference system and bootstrap-based neural network for flood forecasting. Neural Comput. Appl.
**2013**, 23, S231–S246. [Google Scholar] [CrossRef] - India-WRIS. Water Resources Information System of India. Available online: http://india-wris.nrsc.gov.in/wrpinfo/index.php?title=Mahanadi (accessed on 8 August 2016).
- Yadav, A.; Chatterjee, S.; Equeenuddin, S.M. Prediction of Suspended Sediment Yield by Artificial Neural Network and Traditional Mathematical Model in Mahanadi River Basin, India. J. Sustain. Water Resour. Manag.
**2017**, 4, 745–759. [Google Scholar] [CrossRef] - Rojas, R. Neural Network: A Systematic Introduction; Springer: Berlin, Germany, 1996; pp. 151–184. [Google Scholar]
- Hagan, M.T.; Menhaj, M.B. Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Netw.
**1994**, 5, 989–993. [Google Scholar] [CrossRef] - Ebtehaj, I.; Bonakdari, H.; Safari, M.J.S.; Gharabaghi, B.; Zaji, A.H.; Madavar, H.R.; Khozani, Z.S.; Es-haghi, M.S.; Shishegaran, A.; Mehr, A.D. Combination of sensitivity and uncertainty analyses for sediment transport modeling in sewer pipes. Int. J. Sediment Res.
**2020**, 35, 157–170. [Google Scholar] [CrossRef] - Riahi-Madvar, H.; Gharabaghi, B. Pre-processing and Input Vector Selection Techniques in Computational Soft Computing Models of Water Engineering. In Computational Intelligence for Water and Environmental Sciences; Springer: Singapore, 2022; pp. 429–447. [Google Scholar]
- Dehghani, M.; Seifi, A.; Riahi-Madvar, H. Novel forecasting models for immediate-short-term to long-term influent flow prediction by combining ANFIS and grey wolf optimization. J. Hydrol.
**2019**, 576, 698–725. [Google Scholar] [CrossRef] - Riahi-Madvar, H.; Dehghani, M.; Memarzadeh, R.; Gharabaghi, B. Short to long-term forecasting of river flows by heuristic optimization algorithms hybridized with ANFIS. Water Resour. Manag.
**2021**, 35, 1149–1166. [Google Scholar] [CrossRef] - Riahi-Madvar, H.; Seifi, A. Uncertainty analysis in bed load transport prediction of gravel-bed rivers by ANN and ANFIS. Arab. J. Geosci.
**2018**, 11, 1–20. [Google Scholar] [CrossRef] - Gowda, C.C.; Mayya, S.G. Comparison of back propagation neural network and genetic algorithm neural network for stream flow prediction. J. Comput. Environ. Sci.
**2014**, 290127. [Google Scholar] [CrossRef][Green Version] - Senthil Kumar, A.R.; Sudheer, K.P.; Jain, S.K.; Agarwal, P.K. Rainfall-runoff modelling using artificial neural networks: Comparison of network types. Hydrol. Process. Int. J.
**2005**, 19, 1277–1291. [Google Scholar] [CrossRef] - Ghosh, A.; Das, M.K. Non-dominated rank-based sorting genetic algorithms. Fundam. Inform.
**2008**, 83, 231–252. [Google Scholar] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef]

**Figure 1.**The elevation map of the Mahanadi River basin with the geographical location of 11 gauging stations [48].

**Figure 3.**Spatial variation of monthly average hydro-climatic and geomorphological data such as water discharge (cms) (m

^{3}/s), temperature (°C), rainfall (mm) and sediment load (t/ month), relief (m), and catchment area (km

^{2}).

**Figure 4.**Comparative analysis of long-term variation over the past two decades of (

**a**) WD, (

**b**) RF, (

**c**) SL, and (

**d**) T.

**Figure 5.**The autocorrelation function (ACF) for monthly hydro-climatical data (

**a**) SL, (

**b**) WD, (

**c**) RF, (

**d**) T.

**Figure 6.**(

**a**) Dilemma between the bias and variance objectives. (

**b**) Variation of individuals and distance. (

**c**) Variation of individuals and corresponding ranking. (

**d**) Generation-wise variation of average spreads of Pareto.

**Figure 7.**Comparison of the actual and forecasted SL during the testing phase of the ANN-MOGA-51 forecasting model (

**a**–

**k**).

**Figure 8.**Scatter plot of the actual and forecasted SL of the ANN-MOGA-51 forecasting model during the testing phase (

**a**–

**k**).

**Figure 9.**Comparison of the actual and forecasted SL during the testing phase of the AR forecasting model (

**a**–

**k**).

**Figure 10.**Scatter plot of the actual and forecasted SL of the AR forecasting model during the testing phase (

**a**–

**k**).

**Figure 11.**Comparison of the actual and forecasted SL during the testing phase of the MAR forecasting model (

**a**–

**k**).

**Figure 12.**Scatter plot of the actual and forecasted SL of the MAR forecasting model during the testing phase (

**a**–

**k**).

**Table 1.**Spearman rank correlation coefficient

^{®}of hydro-climatolic data from eleven stations for the MR.

Stations | r1 (WD-SL) | r2 (SL-RF) | r3 (SL-T) |
---|---|---|---|

Tikarapara | 0.891951579 | 0.667566099 | 0.167164223 |

Sundargarh | 0.933162643 | 0.719490012 | 0.083275757 |

Simga | 0.912171157 | 0.669144968 | 0.016117111 |

Jondhara | 0.953615062 | 0.634788084 | 0.024002708 |

Andhiyarakhore | 0.930440984 | 0.679483679 | 0.172300271 |

Kurubhata | 0.914790531 | 0.739541786 | 0.09457768 |

Bamnidih | 0.792975574 | 0.673800075 | 0.19294038 |

Rajim | 0.933515452 | 0.652771319 | −0.053703323 |

Kantamal | 0.784858255 | 0.653582343 | 0.045884228 |

Baronda | 0.896128553 | 0.718865603 | 0.170015607 |

Basantpur | 0.900261237 | 0.717722236 | 0.120971863 |

Models | Number of Initial Inputs | Input Parameters |
---|---|---|

ANN-MOGA-51 | 51 | SL, WD, RF, T, RT, R and CA |

ANN-MOGA-48 | 48 | SL, WD, RF and T |

ANN-MOGA-15 | 15 | SL, RT, R and CA |

ANN-MOGA-12 | 12 | SL |

**Table 3.**Performance comparison of the hybrid multi-objective GA-based ANN forecasting models in the testing phase.

Models | RMSE | Initially Inputs No. | MSE | MAE | VAR | r |
---|---|---|---|---|---|---|

ANN-MOGA-51 | 0.011639 | 51 | 0.000135 | 0.003802 | 0.000136 | 0.643313 |

ANN-MOGA-48 | 0.013343 | 48 | 0.000178 | 0.00381194 | 0.0001783 | 0.5674853 |

ANN-MOGA-15 | 0.013637 | 15 | 0.000186 | 0.0044 | 0.000186 | 0.513217 |

ANN-MOGA-12 | 0.01181 | 12 | 0.000139 | 0.003626 | 0.00014 | 0.623344 |

Models | Transfer Function | Neurons | Inputs | µ |
---|---|---|---|---|

ANN-MOGA-51 | Log-sigmoid, pure linear | 29 | 22 | 2 |

ANN-MOGA-48 | Tan-sigmoid, pure linear | 19 | 21 | 9 |

ANN-MOGA-15 | Pure linear, tan-sigmoid | 15 | 10 | 10 |

ANN-MOGA-12 | Tan-sigmoid, pure linear | 4 | 6 | 6 |

**Table 5.**Error statistics of ANN-MOGA-51 forecasting model during validation, testing, and training phase.

ANN-MOGA-51 | MSE | RMSE | r | Error Variance | MAE |
---|---|---|---|---|---|

Training | 0.000241 | 0.015526 | 0.668938 | 0.000241 | 0.004677 |

Validation | 5.25 × 10^{−5} | 0.007243 | 0.7730 | 5.26 × 10^{−5} | 0.002867 |

Testing | 0.000135 | 0.011639 | 0.643313 | 0.000136 | 0.003802 |

Tikarapara | 0.000396 | 0.019905 | 0.731051 | 0.000407 | 0.010517 |

Simga | 1.17 × 10^{−5} | 0.003422 | 0.5930 | 9.81 × 10^{−6} | 0.001707 |

Andhiyarakhore | 1.10 × 10^{−5} | 0.003319 | 0.4001 | 9.06 × 10^{−5} | 0.001749 |

Sundargarh | 2.60 × 10^{−5} | 0.005097 | 0.635 | 2.67 × 10^{−5} | 0.002466 |

Bamnidih | 3.33 × 10^{−5} | 0.005769 | 0.695 | 3.27 × 10^{−5} | 0.002765 |

Jondhara | 3.02 × 10^{−5} | 0.005499 | 0.737 | 2.91 × 10^{−5} | 0.002534 |

Kurubhata | 2.06 × 10^{−5} | 0.001434 | 0.914 | 1.97 × 10^{−6} | 0.000865 |

Basantpur | 0.000229 | 0.015121 | 0.478143 | 0.000222 | 0.006185 |

Baronda | 5.66 × 10^{−6} | 0.002379 | 0.495 | 5.23 × 10^{−6} | 0.001319 |

Rajim | 2.10 × 10^{−6} | 0.001448 | 0.669 | 2.15 × 10^{−6} | 0.000722 |

Kantamal | 0.000806 | 0.028395 | 0.659518 | 0.000801 | 0.01198 |

**Table 6.**Error statistics of the autoregressive (AR) forecasting model at different gauging stations.

AR | RMSE | MSE | MAE | VAR | r |
---|---|---|---|---|---|

Training | 0.01640 | 0.00027 | 0.00473 | 0.00027 | 0.61268 |

Testing | 0.01335 | 0.00018 | 0.00365 | 0.00018 | 0.49670 |

Tikarapara | 0.02576 | 0.00066 | 0.01119 | 0.00066 | 0.51087 |

Simga | 0.00185 | 3.42 × 10^{−6} | 0.00069 | 3.49 × 10^{−06} | 0.19322 |

Andhiyarakhore | 0.00020 | 4.07 × 10^{−8} | 9.30×10^{−5} | 4.15 × 10^{−08} | 0.40166 |

Sundargarh | 0.00555 | 3.08 × 10^{−5} | 0.00303 | 3.02 × 10^{−05} | 0.44791 |

Bamnidih | 0.00024 | 5.56 × 10^{−8} | 0.00012 | 5.46 × 10^{−08} | 0.58226 |

Jondhara | 0.00668 | 4.46 × 10^{−5} | 0.00323 | 4.48 × 10^{−05} | 0.48917 |

Kurubhata | 0.00222 | 4.92 × 10^{−6} | 0.00103 | 4.72 × 10^{−06} | 0.74650 |

Basantpur | 0.01059 | 0.00011 | 0.00411 | 0.00011 | 0.32857 |

Baronda | 0.00187 | 3.49 × 10^{−6} | 0.00073 | 3.56 × 10^{−6} | 0.25906 |

Rajim | 0.00177 | 3.14 × 10^{−6} | 0.00079 | 3.18 × 10^{−6} | 0.37205 |

Kantamal | 0.03386 | 0.00115 | 0.01481 | 0.00116 | 0.36473 |

MAR | MAE | VAR | r | MSE | RMSE |
---|---|---|---|---|---|

Training | 0.00640 | 0.00023 | 0.68010 | 0.00023 | 0.01516 |

Testing | 0.00562 | 0.00017 | 0.55620 | 0.00017 | 0.01296 |

Tikarapara | 0.01306 | 0.00054 | 0.62380 | 0.00052 | 0.02284 |

Simga | 0.00395 | 2.65×10^{−5} | 0.49380 | 2.99×10^{−5} | 0.00547 |

Andhiyarakhore | 0.00260 | 1.20×10^{−5} | 0.39130 | 1.16×10^{−5} | 0.00341 |

Sundargarh | 0.00486 | 4.91×10^{−5} | 0.45670 | 4.79×10^{−5} | 0.00692 |

Bamnidih | 0.00272 | 1.53×10^{−5} | 0.61440 | 1.66×10^{−5} | 0.00407 |

Jondhara | 0.00458 | 5.44×10^{−5} | 0.63700 | 5.36×10^{−5} | 0.00732 |

Kurubhata | 0.00228 | 1.01×10^{−5} | 0.74210 | 9.80×10^{−6} | 0.00313 |

Basantpur | 0.00610 | 0.00010 | 0.62500 | 0.00011 | 0.01025 |

Baronda | 0.00306 | 1.75×10^{−5} | 0.44590 | 1.70×10^{−5} | 0.00412 |

Rajim | 0.00309 | 1.64×10^{−5} | 0.43390 | 1.59×10^{−5} | 0.00398 |

Kantamal | 0.01652 | 0.00111 | 0.39780 | 0.00108 | 0.03292 |

**Table 8.**Statistical performance evaluation of ANN-MOGA-51, AR, and MAR models along with all gauging stations in a testing phase.

Models | ANN-MOGA-51 | MAR | AR | |||
---|---|---|---|---|---|---|

Statistics | RMSE | r | RMSE | r | RMSE | r |

Testing | 0.01164 | 0.6433 | 0.01296 | 0.5562 | 0.01335 | 0.4967 |

Tikarapara | 0.01991 | 0.7311 | 0.02284 | 0.6238 | 0.02576 | 0.5109 |

Simga | 0.00342 | 0.5930 | 0.00547 | 0.4938 | 0.00185 | 0.1932 |

Andhiyarakhore | 0.00332 | 0.4001 | 0.00341 | 0.3913 | 0.00020 | 0.4017 |

Sundargarh | 0.00510 | 0.6350 | 0.00692 | 0.4567 | 0.00555 | 0.4479 |

Bamnidih | 0.00577 | 0.6950 | 0.00407 | 0.6144 | 0.00024 | 0.5821 |

Jondhara | 0.00550 | 0.7370 | 0.00732 | 0.6370 | 0.00668 | 0.4892 |

Kurubhata | 0.00143 | 0.9140 | 0.00313 | 0.7421 | 0.00222 | 0.7465 |

Basantpur | 0.01512 | 0.4781 | 0.01025 | 0.6250 | 0.01059 | 0.3286 |

Baronda | 0.00238 | 0.4950 | 0.00412 | 0.4459 | 0.00187 | 0.2591 |

Rajim | 0.00145 | 0.6690 | 0.00398 | 0.4339 | 0.00177 | 0.3721 |

Kantamal | 0.02840 | 0.6595 | 0.03292 | 0.3978 | 0.03386 | 0.3647 |

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**

Yadav, A.; Ali Albahar, M.; Chithaluru, P.; Singh, A.; Alammari, A.; Kumar, G.V.; Miro, Y.
Hybridizing Artificial Intelligence Algorithms for Forecasting of Sediment Load with Multi-Objective Optimization. *Water* **2023**, *15*, 522.
https://doi.org/10.3390/w15030522

**AMA Style**

Yadav A, Ali Albahar M, Chithaluru P, Singh A, Alammari A, Kumar GV, Miro Y.
Hybridizing Artificial Intelligence Algorithms for Forecasting of Sediment Load with Multi-Objective Optimization. *Water*. 2023; 15(3):522.
https://doi.org/10.3390/w15030522

**Chicago/Turabian Style**

Yadav, Arvind, Marwan Ali Albahar, Premkumar Chithaluru, Aman Singh, Abdullah Alammari, Gogulamudi Vijay Kumar, and Yini Miro.
2023. "Hybridizing Artificial Intelligence Algorithms for Forecasting of Sediment Load with Multi-Objective Optimization" *Water* 15, no. 3: 522.
https://doi.org/10.3390/w15030522