# Novel Hybrid Statistical Learning Framework Coupled with Random Forest and Grasshopper Optimization Algorithm to Forecast Pesticide Use on Golf Courses

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Golf Course Database

#### 2.2. Theoretical Overview

#### 2.2.1. Random Forest

#### 2.2.2. Support Vector Machine (SVM)

_{i}, are defined, and the SVM optimization function is written as [20]:

_{i}and ${b}_{i}^{*}$ are obtained. Consequently, Equation (1) is rewritten as:

^{2}) is the RBF parameter.

#### 2.2.3. Grasshopper Optimization Algorithm (GOA)

_{i}) is defined as a function of wind advection (A

_{i}), gravity force (G

_{i}), and social interaction (S

_{i}) as follows [28]:

_{1}, r

_{2}, and r

_{3}are considered random through [0, 1].

_{ij}(= x

_{j}− x

_{i}) is the distance between two grasshoppers; and ${\stackrel{\u2322}{d}}_{ij}$ is a unit vector. The values ${\stackrel{\u2322}{d}}_{ij}$ and s are defined as:

_{s}is the attractive length scale.

_{d}and lb

_{d}are the upper and lower bounds in the dth dimension, respectively; s is a parameter defining the power of social forces Equation (11); ${\stackrel{\u2322}{T}}_{d}$ is the value of the dth dimension (i.e., the best solution obtained so far); and c is a parameter used to shrink the attraction, repulsion, and comfort zones.

_{min}and c

_{max}are the minimum and maximum values that Saremi et al. [26] recommended as 0.00001 and 1, respectively; k

_{l}and K denote the current iteration and the maximum number of iterations, respectively.

#### 2.2.4. Developed Hybrid RF-SVM-GOA

#### 2.3. Performance Evaluation Criteria

_{i}and A

_{i}are the predicted and actual (respectively) ith sample values, respectively.

## 3. Results and Discussion

#### 3.1. Tree-Based Methods in AIT Estimating

#### 3.2. Non-Tree-Based Methods in AIT Estimating

#### 3.3. AIT Estimating Using Hybrid Methods

#### 3.4. Comparison of the Individual and Hybrid Methods in AIT Estimating

#### 3.5. Evaluation of the Importance of Each of the Input Parameters in AIT Estimating

#### 3.6. Sensitivity of the Developed Models on the Input Variables

## 4. Advantages, Limitations, and Future Improvements

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Box plots of the independent input and dependent output variables: (

**a**) treated area (TA); (

**b**) active ingredient total (AIT); (

**c**) number of holes (NH).

**Figure 5.**Scatter plot of the tree-based techniques in AIT forecasting. Plots on the right are a scaled-up view of the region circled in red in the left plot.

**Figure 6.**Scatter plot of the non-tree-based techniques in AIT forecasting. Plots on the right are a scaled-up view of the region circled in red in the left plot.

**Figure 7.**Scatter plot of the hybrid techniques in AIT forecasting. Plots on the right are a scaled-up view of the region circled in red in the left plot.

**Figure 8.**Taylor graph comparing different developed techniques in AIT forecasting (black lines = standard deviation, blue lines = correlation coefficient, and green lines = root mean square error (RMSE, Equation (19))).

Method | Parameter | Setting |
---|---|---|

RF | Bag size percentage | 100 |

Batch size | 100 | |

Maximum depth of tree | 10, 5 | |

Number of decimal places | 2 | |

Number of execution slots | 1 | |

Number of features | 1 | |

Number of iterations | 100 | |

Seeds | 300, 10 | |

RT | Number of randomly chosen attributes | 0 |

Minimum total weights of instances in a leaf | 1 | |

Minimum proportion of the variance of all data that need to be present at a node for splitting to be performed in regression trees | 0.001 | |

Seed | 100 | |

Maximum depth of tree | 5 | |

REP Tree | Minimum total weights of instances in a leaf | 2 |

Minimum proportion of the variance of all data that need to be present at a node for splitting to be performed in regression trees | 0.001 | |

Seed | 100 | |

Maximum tree depth | 5 | |

M5P | Minimum number of instances to allow at a leaf node | 20 |

Number of decimal places to be used for output of numbers in model | 20 | |

GSGMDH | Maximum number of inputs for individual neurons | 3 |

Maximal number of neurons in a layer | 10 | |

Degree of polynomials in neurons | 3 | |

EPR | Number of terms | 50, 200 |

Maximum number of iterations | 50 | |

Population size | 50 | |

Crossover percentage | 0.35 | |

Mutation percentage | 0.04 | |

GOA | Maximum number of iterations | 1000 |

Number of search agents | 70 | |

c_{min} | 0.00001 | |

c_{max} | 1 |

**Table 2.**Effect of each independent input variable on AIT forecasting using developed hybrid technique.

AR | NH | GCI | Y | TA | Model No. | R^{2} | RMSE | NRMSE | MAE |
---|---|---|---|---|---|---|---|---|---|

• | • | • | • | • | 1 | 0.999 | 0.839 | 0.843 | 0.044 |

• | • | • | • | 2 | 0.003 | 303.782 | 480.594 | 25.072 | |

• | • | • | • | 3 | 0.011 | 73.952 | 261.179 | 13.625 | |

• | • | • | • | 4 | 0.020 | 54.141 | 204.369 | 10.661 | |

• | • | • | • | 5 | 0.522 | 2.563 | 49.765 | 2.596 | |

• | • | • | • | 6 | 0.522 | 2.563 | 49.766 | 2.596 |

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**MDPI and ACS Style**

Grégoire, G.; Fortin, J.; Ebtehaj, I.; Bonakdari, H.
Novel Hybrid Statistical Learning Framework Coupled with Random Forest and Grasshopper Optimization Algorithm to Forecast Pesticide Use on Golf Courses. *Agriculture* **2022**, *12*, 933.
https://doi.org/10.3390/agriculture12070933

**AMA Style**

Grégoire G, Fortin J, Ebtehaj I, Bonakdari H.
Novel Hybrid Statistical Learning Framework Coupled with Random Forest and Grasshopper Optimization Algorithm to Forecast Pesticide Use on Golf Courses. *Agriculture*. 2022; 12(7):933.
https://doi.org/10.3390/agriculture12070933

**Chicago/Turabian Style**

Grégoire, Guillaume, Josée Fortin, Isa Ebtehaj, and Hossein Bonakdari.
2022. "Novel Hybrid Statistical Learning Framework Coupled with Random Forest and Grasshopper Optimization Algorithm to Forecast Pesticide Use on Golf Courses" *Agriculture* 12, no. 7: 933.
https://doi.org/10.3390/agriculture12070933