# Multilayer Perceptron and Their Comparison with Two Nature-Inspired Hybrid Techniques of Biogeography-Based Optimization (BBO) and Backtracking Search Algorithm (BSA) for Assessment of Landslide Susceptibility

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## Abstract

**:**

## 1. Introduction

## 2. Review of Case Study

## 3. Methodology

#### 3.1. Artificial Neural Network

#### 3.2. Hybrid Model Development

- (a)
- Determining the ideal structure of the ANN model: we are aware that the structure of the ANN has a significant impact on the accuracy of its predictions [41]. As the model’s backbone, it should be optimized in hybrid models [39]. The network with several processors in the intermediate layer and a Tansig activation function is the optimal solution, as determined by a trial-and-error procedure applied to various tested configurations.
- (b)
- Specify the problem function and use the BBO-MLP and BSA-MLP models.
- (c)
- Specify precise parameters such as population size, number of iterations, and goal function.
- (d)
- Minimizing inaccuracy by modifying the ANN’s weights and biases
- (e)
- Storing the optimum solution when a termination condition is met.

_{iobserved}, and S

_{ipredicted}display the expected and actual production figures. U also represents the quantity of samples.

#### 3.2.1. Biogeography-Based Optimization (BBO)

- (1)
- BBO parameters require configuration, which consists of emanating a representative method for habitats, that is concerned with hanging and initializing the highest migration rate, transformation rate, and elitism parameter.
- (2)
- Create a random set of habitats based on the possible solution sets and initialize them.
- (3)
- Each habitat’s migration and emigration rates can be determined by utilizing its HSI.
- (4)
- Migrate in a random fashion to change the environment of each special habitat. The HSIs were then computed again.
- (5)
- Each habitat should be assigned a mutation rate based on the number of species present.
- (6)
- Random mutations should be applied to every non-light habitat. It was then recalculated for each individual HSI.
- (7)
- To begin the next iteration, go to step one (3). Repeat for as many generations as necessary till you have come up with the right answer.

#### 3.2.2. Backtracking Search Algorithm (BSA)

**A. Initialization:**BSA’s initial population (P) consists of D variables and N individuals, which are generated at random. Equivalently, Equation (3) states it this way:

**B. Selection-I:**Pre- and post-selection are handled by the selection-I and selection-II operators, respectively, in BSA. Using the pre-selection operator, the historical population (${P}^{old}$) is acquired, and this data is used to decide the search’s direction. To find out what (${P}^{old}$) is valued, you must perform the following three steps:

**C. Mutation.**The mutation is applied to the first trial population (mutant) by BSA as described in Equation (7).

^{ald-p}).

**D. Crossover.**As a result of BSA’s crossover, the final trial population (T) is formed. Two steps are involved:

**E. Selection-II.**BSA greedy selection is the name given to selection-II. The trail population T is replaced if its fitness values outperform those of the population P. Whichever individual with the highest fitness value yields the most effective global solution.

**F. Fitness evaluation**. In order to evaluate a group of individuals, the fitness evaluation is utilized. An individual’s level of fitness is the outcome of this algorithm.

#### 3.3. Landslide Inventory Map (LIM) and Landslide Conditioning Factors

## 4. Results and Discussion

^{2}indicators, the best network was created using a feed-forward back-propagation approach with six hidden units (i.e., the tansig function and six neurons in the hidden layer) (Table 2). Initial optimization results are used as a starting phase for different optimization methods. The best predictive network results from the model with the highest score (or least rank in Table 2). It is noteworthy that the scores came directly from the model prediction result accuracies. For instance, the lowest RMSE obtained results in a higher score for the specified model. However, for the R

^{2}, the higher R

^{2}will result in a higher score. Therefore, the next sections make use of the results of these networks. Figure 7 and Figure 8 further show how the MSE changes when the amount of each neuron per hidden layer increases or decreases. Table 2: A sensitivity study of forecasting landslide susceptibility mapping’s number on varying numbers of neurons.

_{swarm}) as the optimal solution based on these data.

#### Error Analysis

## 5. Conclusions

_{BBO-MLP and BSA-MLP}= 0.551 and 0.557). Additionally, despite the superiority of the BBO-MLP in learning landslide patterns, both ensembles presented a close prediction accuracy (AUC

_{BBO-MLP}= 0.842 and AUC

_{BSA-MLP}= 0.771). In general, this BBO-MLP is more effective in improving neural network performance in this paper.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Basic structure of neural network for landslide susceptibility analysis with optimization algorithms.

**Figure 5.**Methodological process of the applied model for measuring susceptibility landslides assessment.

**Figure 7.**The variation of mean squared error versus iterations obtained from the proposed BBOMLP structures in predicting landslide susceptibility mapping.

**Figure 8.**The variation of mean squared error as a function of iterations was acquired as from suggested BSAMLP architectures for forecasting flood vulnerability mapping.

**Figure 9.**The ROC curves plotted for the (i) training and (ii) testing datasets in BBOMLP algorithm.

**Figure 10.**The ROC curves plotted for the (i) training and (ii) testing datasets in BSAMLP algorithm.

Factor | Classes | GIS Data Type | Scale | Classification Method | |
---|---|---|---|---|---|

Profile | −25.21 | GRID | 30 m × 30 m | Natural breaks | |

−1.11 | |||||

0.34–21 | |||||

Plane | Convex | −16.58 | GRID | 30 m × 30 m | Natural breaks |

Flat | −0.62 | ||||

Concave | 0.22–15 | ||||

SPI (Stream Power Index) | −8.4 | GRID | 30 m × 30 m | Manual | |

−4.3 | |||||

−1.37 | |||||

0.28–2.2 | |||||

2.3–8.5 | |||||

TWI (Topographic Wetness Index) | 1.7–5.3 | GRID | 30 m × 30 m | Natural breaks | |

5.4–6.7 | |||||

6.8–8.4 | |||||

8.5–11 | |||||

20-Dec | |||||

Distance to River | 200 | Line | 30 m × 30 m | Natural breaks | |

400 | |||||

600 | |||||

800 | |||||

>800 | |||||

Rainfall | 400 | GRID | 30 m × 30 m | Natural breaks | |

500 | |||||

600 | |||||

700 | |||||

800 | |||||

NDVI (Normalized Difference Vegetation Index) | −1.04 | GRID | 30 m × 30 m | Natural breaks | |

0.041–0.13 | |||||

0.17–0.20 | |||||

0.24–0.32 | |||||

0.33–0.65 | |||||

Slope | <7 | GRID | 30 m × 30 m | Manual | |

15 | |||||

22 | |||||

32 | |||||

>80 | |||||

Aspect | a-Northwest, b-South, c-North, d-Southeast, e-East, f-West, g-Southwest, e-Northeast, j-North k-Flat, | GRID | 30 m × 30 m | Azimuth | |

classification | |||||

Land use | Sliding influential factors | Polygon | 1:25,000 | Natural breaks | |

Geology | Qt^{1} | Polygon | 1:100,100 | Natural breaks | |

OMI, OMm^{1}, OMI, | |||||

Jkb2, Ksfsh, kussh, K1m, | |||||

Pr | |||||

Qiib, Oibv | |||||

hmet | |||||

Urm | |||||

PEf | |||||

TRI (Terrain Ruggedness Index) | 0.11–0.38 | GRID | 30 m × 30 m | Natural breaks | |

0.39–0.46 | |||||

0.47–0.52 | |||||

0.53–0.6 | |||||

0.61–0.89 | |||||

STI (Sediment transport index) | 0–0.45 | GRID | 30 m × 30 m | Natural breaks | |

0.45–7.44 | |||||

7.45–28.2 | |||||

28.3–52.7 | |||||

52.8–82.6 | |||||

Distance from Road | 100 | Line | 1:25,000 | Manual | |

200 | |||||

300 | |||||

400 | |||||

>500 | |||||

Distance from Fault | 100 | Line | 1:100,100 | Manual | |

200 | |||||

300 | |||||

400 | |||||

>500 | |||||

Elevation | <1000 | GRID | 30 m × 30 m | Natural breaks | |

1500 | |||||

2000 | |||||

2500 | |||||

>3000 |

**Table 2.**Change in neuronal density as a predictor for landslide susceptibility mapping: sensitivity analysis.

Model ID | Number of Neurons | RMSE Training | RMSE Testing | RMSE Total | Scoring | Total Score | RANK | ||
---|---|---|---|---|---|---|---|---|---|

Train | Test | Total Data | |||||||

ANN_1 | 1 | 1.214 | 1.230 | 1.222 | 1 | 1 | 1 | 3 | 10 |

ANN_2 | 2 | 0.873 | 0.891 | 0.875 | 2 | 2 | 2 | 6 | 9 |

ANN_3 | 3 | 0.629 | 0.655 | 0.635 | 5 | 4 | 5 | 14 | 6 |

ANN_4 | 4 | 0.649 | 0.624 | 0.641 | 4 | 5 | 4 | 13 | 7 |

ANN_5 | 5 | 0.560 | 0.553 | 0.561 | 8 | 9 | 8 | 25 | 3 |

ANN_6 | 6 | 0.721 | 0.717 | 0.722 | 3 | 3 | 3 | 9 | 8 |

ANN_7 | 7 | 0.570 | 0.573 | 0.579 | 7 | 7 | 7 | 21 | 4 |

ANN_8 | 8 | 0.554 | 0.557 | 0.550 | 10 | 10 | 10 | 30 | 1 |

ANN_9 | 9 | 0.549 | 0.551 | 0.555 | 9 | 8 | 9 | 26 | 2 |

ANN_10 | 10 | 0.582 | 0.578 | 0.584 | 6 | 6 | 6 | 18 | 5 |

**Table 3.**The Results of AUC for different BBOMLP proposed structure in predicting the landslide susceptibility mapping.

Population Size | Network AUC Results | Scoring | Total Score | RANK | ||
---|---|---|---|---|---|---|

Training | Testing | Training | Testing | |||

50 | 0.906 | 0.773 | 8 | 2 | 10 | 6 |

100 | 0.899 | 0.788 | 4 | 3 | 7 | 9 |

150 | 0.914 | 0.842 | 10 | 10 | 20 | 1 |

200 | 0.896 | 0.804 | 2 | 7 | 9 | 7 |

250 | 0.905 | 0.801 | 6 | 6 | 12 | 5 |

300 | 0.903 | 0.834 | 5 | 9 | 14 | 3 |

350 | 0.883 | 0.743 | 1 | 1 | 2 | 10 |

400 | 0.909 | 0.792 | 9 | 4 | 13 | 4 |

450 | 0.896 | 0.798 | 3 | 5 | 8 | 8 |

500 | 0.906 | 0.809 | 7 | 8 | 15 | 2 |

**Table 4.**The Results of AUC for different BSAMLP proposed structure in predicting the landslide susceptibility mapping.

Population Size | Network AUC Results | Scoring | Total Score | RANK | ||
---|---|---|---|---|---|---|

Training | Testing | Training | Testing | |||

50 | 0.789 | 0.702 | 1 | 3 | 4 | 9 |

100 | 0.789 | 0.694 | 2 | 2 | 4 | 9 |

150 | 0.795 | 0.710 | 4 | 5 | 9 | 6 |

200 | 0.799 | 0.727 | 5 | 7 | 12 | 4 |

250 | 0.813 | 0.756 | 10 | 8 | 18 | 2 |

300 | 0.803 | 0.689 | 7 | 1 | 8 | 7 |

350 | 0.794 | 0.706 | 3 | 4 | 7 | 8 |

400 | 0.805 | 0.771 | 9 | 10 | 19 | 1 |

450 | 0.804 | 0.758 | 8 | 9 | 17 | 3 |

500 | 0.799 | 0.715 | 6 | 6 | 12 | 4 |

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## Share and Cite

**MDPI and ACS Style**

Moayedi, H.; Canatalay, P.J.; Ahmadi Dehrashid, A.; Cifci, M.A.; Salari, M.; Le, B.N.
Multilayer Perceptron and Their Comparison with Two Nature-Inspired Hybrid Techniques of Biogeography-Based Optimization (BBO) and Backtracking Search Algorithm (BSA) for Assessment of Landslide Susceptibility. *Land* **2023**, *12*, 242.
https://doi.org/10.3390/land12010242

**AMA Style**

Moayedi H, Canatalay PJ, Ahmadi Dehrashid A, Cifci MA, Salari M, Le BN.
Multilayer Perceptron and Their Comparison with Two Nature-Inspired Hybrid Techniques of Biogeography-Based Optimization (BBO) and Backtracking Search Algorithm (BSA) for Assessment of Landslide Susceptibility. *Land*. 2023; 12(1):242.
https://doi.org/10.3390/land12010242

**Chicago/Turabian Style**

Moayedi, Hossein, Peren Jerfi Canatalay, Atefeh Ahmadi Dehrashid, Mehmet Akif Cifci, Marjan Salari, and Binh Nguyen Le.
2023. "Multilayer Perceptron and Their Comparison with Two Nature-Inspired Hybrid Techniques of Biogeography-Based Optimization (BBO) and Backtracking Search Algorithm (BSA) for Assessment of Landslide Susceptibility" *Land* 12, no. 1: 242.
https://doi.org/10.3390/land12010242