# Binary Coati Optimization Algorithm- Multi- Kernel Least Square Support Vector Machine-Extreme Learning Machine Model (BCOA-MKLSSVM-ELM): A New Hybrid Machine Learning Model for Predicting Reservoir Water Level

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## Abstract

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## 1. Introduction

- The MKLSSVM model is introduced to predict the water level of a reservoir in Malaysia.
- The LLSVM and MKLSSVM model is coupled with the extreme learning machine (ELM) model to predict water level fluctuations. In addition, the hybrid model boosts the learning ability of the LLSVM and MKLSSVM models.
- This study introduces a novel binary optimization algorithm for choosing input data.

## 2. Materials and Methods

#### 2.1. Structure of the LLSVM Model

#### 2.2. Structure of the Multi-Kernel Least Square Support Vector Machine Model (MKLSSVM)

- Radial basis function (LSSVM-RBF)

- Linear Kernel Function (LSSVM-LKF)

- Polynomial Kernel Function (LSSVM-PKF)$$K\left({q}_{i},{q}_{j}\right)={\left(\frac{{q}_{i}^{T}.{q}_{j}}{c}+1\right)}^{d}$$$$K{\left({q}_{i},{q}_{j}\right)}_{final}={\delta}_{1}{K}_{RBF}+{\delta}_{2}{K}_{LKF}+{\delta}_{3}{K}_{PKF}$$
_{i}: ith input q_{j}: jth: input ${\delta}_{1}$, ${\delta}_{2}$, and ${\delta}_{3}$: Weight coefficients, ${K}_{RBF}$, ${K}_{LKF}$, and ${K}_{PKF}$: RBF, LKF, and PKF. Since there is no priority, we assign equal weights to the kernel functions. Kernel parameters are set using an optimization algorithm.

#### 2.3. Structure of Extreme Learning Machine (ELM)

_{j}: input data. The input weight matrix and bias are randomly initialized. Equation (10) can be rewritten as follows:

#### 2.4. Optimization Algorithm

_{i}: Objective function value of the ith coati. The location of Iguana shows the best location. When predators attack coatis, they escape from their locations. Equations (17) and (18) simulate this behavior:

#### 2.5. Structure of Coati Optimization Algorithm—ELM-MKLSSVM

## 3. Case Study

^{3}/s (Spillway and outlet). Decision makers need to predict the reservoir’s water level for flood control. A humid climate prevails in the basin. Figure 1a,b show the location of the case study and the data points.

- 1
- Root mean square error (RMSE)$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{\left(W{L}_{es}-W{L}_{ob}\right)}^{2}}}$$

- 2
- Mean absolute error (MAE)$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\left|W{L}_{ob}-W{L}_{es}\right|}$$

- 3
- Nash–Sutcliff efficiency (NSE)$$NSE=1-\frac{{\displaystyle \sum _{i=1}^{n}{\left(W{L}_{ob}-W{L}_{es}\right)}^{2}}}{{\displaystyle \sum _{i=1}^{n}\left(W{L}_{ob}-W{\overline{L}}_{ob}\right)}}$$

- 4
- Willmott index$$WI=1-\frac{{{\displaystyle \sum _{i=1}^{n}\left(W{L}_{es}-W{L}_{ob}\right)}}^{2}}{{\displaystyle \sum _{i=1}^{n}{\left(\left|W{L}_{es}-W{\overline{L}}_{ob}\right|+\left|W{L}_{es}-W{\overline{L}}_{ob}\right|\right)}^{2}}}$$

## 4. Results and Discussion

#### 4.1. Determination of Optimal Input Scenario

^{20}-1. Manually determining the optimal input scenario is time-consuming and complex. In this study, the COA automatically determine the best input combination. The name of the input variables was defined as binary variables. The names of the input variables were considered decision variables. Locations of coatis show input combinations. The operators of the COA were used to update the input combinations at each iteration. Table 2 shows the first-best to third-best input combinations.

#### 4.2. Determination of Random Parameters

#### 4.3. Evaluation of the Accuracy of LSSVM Models

#### 4.4. Evaluation of the Accuracy of Hybrid Models

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Parameter | Maximum | Average | Minimum |
---|---|---|---|

Water Level (m) | 104.46 | 99.23 | 93.11 |

Rainfall (mm) | 50.5 | 34.56 | 0.50 |

Input Combination | Components |
---|---|

First best input combination | rainfall (t−1), rainfall (t−2), water level (t−1), water level (t−2), water level (t−3) |

Second best input combination | rainfall (t−1), rainfall (t−2), water level (t−1), water level (t−2), water level (t−3), rainfall (t−4) |

Third-best input combination | rainfall (t−1), rainfall (t−2), water level (t−1), water level (t−2), water level (t−3), rainfall (t−3), water level (t−5) |

Model | MAE (Training) | MAE (Testing) | RMSE (Training) | RMSE (Testing) | NSE (Training) | NSE (Testing) | WI (Training) | WI (Testing) |
---|---|---|---|---|---|---|---|---|

MKLSSVM | 0.96 | 0.99 | 1.67 | 1.78 | 0.79 | 0.78 | 0.80 | 0.79 |

LSSVM-PKF | 1.02 | 1.12 | 1.97 | 1.98 | 0.77 | 0.77 | 0.78 | 0.76 |

LSSVM-RBF | 1.14 | 1.23 | 1.99 | 2.01 | 0.76 | 0.74 | 0.75 | 0.74 |

LSSVM-LKF | 1.18 | 1.28 | 2.12 | 2.24 | 0.73 | 0.72 | 0.73 | 0.71 |

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**MDPI and ACS Style**

Sammen, S.S.; Ehteram, M.; Sheikh Khozani, Z.; Sidek, L.M.
Binary Coati Optimization Algorithm- Multi- Kernel Least Square Support Vector Machine-Extreme Learning Machine Model (BCOA-MKLSSVM-ELM): A New Hybrid Machine Learning Model for Predicting Reservoir Water Level. *Water* **2023**, *15*, 1593.
https://doi.org/10.3390/w15081593

**AMA Style**

Sammen SS, Ehteram M, Sheikh Khozani Z, Sidek LM.
Binary Coati Optimization Algorithm- Multi- Kernel Least Square Support Vector Machine-Extreme Learning Machine Model (BCOA-MKLSSVM-ELM): A New Hybrid Machine Learning Model for Predicting Reservoir Water Level. *Water*. 2023; 15(8):1593.
https://doi.org/10.3390/w15081593

**Chicago/Turabian Style**

Sammen, Saad Sh., Mohammad Ehteram, Zohreh Sheikh Khozani, and Lariyah Mohd Sidek.
2023. "Binary Coati Optimization Algorithm- Multi- Kernel Least Square Support Vector Machine-Extreme Learning Machine Model (BCOA-MKLSSVM-ELM): A New Hybrid Machine Learning Model for Predicting Reservoir Water Level" *Water* 15, no. 8: 1593.
https://doi.org/10.3390/w15081593