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

Issue

Authors’ answer

Revisions

Many thanks for the valuable and constructive comments of the reviewers. An attempt was made to accurately apply all comments to the text of the article. Revisions made to the text of the article include:

Responses to the First Reviewer

1

This paper focused on the landslide susceptibility zoning with Machine learning, which is a hot topic in nowadays. The authors select some factors of the geo-environments with new idea, like topographic wetness index, sediment transport index. Anyway, the authors emphsis on the optimization of ML algorithm, and did not give why choose these factors and its effect.

Although the machine learning is popular, it still can not give good explaination of some algorithm. The BBO and BSA is some kind a ecology model, part of this model related with its inner species' selection, maybe different to the non-life rock and soil. Perhaps there are some work can be done here.

Thanks for your comments. The answer to this comment point to point is presented in the text and in the section as follows:

This paper focused on the landslide susceptibility zoning with Machine learning, which is a hot topic in nowadays. The authors select some factors of the geo-environments with new idea, like topographic wetness index, sediment transport index. Anyway, the authors emphsis on the optimization of ML algorithm, and did not give why choose these factors and its effect.

Many studies have been conducted in the field of landslide susceptibility zoning in different regions of the world. But most of them have ignored these two TWI & STI indicators. These two indicators are especially effective in mountainous areas that have a high potential for landslides. The area studied in this research is also mountainous, so it was necessary to consider these two indicators as well. It should also be mentioned that in landslide zoning studies, the more the number of indicators to identify risky areas, the higher the accuracy of the study. Since the mechanism of occurrence of this hazard in different regions with different geographical conditions on a micro to macro scale; it is different, so the researchers should use the indicators to identify and zone this hazard with the knowledge of the geographical conditions and spatial and social constructions of that place. Therefore, in this study, these two indicators were also considered.

Although the machine learning is popular, it still can not give good explaination of some algorithm. The BBO and BSA is some kind a ecology model, part of this model related with its inner species' selection, maybe different to the non-life rock and soil. Perhaps there are some work can be done here

Today, artificial intelligence techniques have many applications in various sciences, especially biological sciences, engineering, medicine, earth sciences, etc. Although this model is simulated from the human neural network, it is used in various fields in a practical and research way. Neural network algorithms have no restrictions on its application in different fields, in any problem that has a network nature and in which a range of factors are systematically related and have backward/forward relationships and It can be used if it has a role in the occurrence of a problem or risk. This model requires the use of optimization algorithms in order to be used in different fields due to some problems and limitations in it. In fact, BBO & BSO algorithms, by simulating the problem in the real world and converting it into mathematical equations, use the same strategy of living organisms to provide the optimal solution among the existing solutions. In fact, all living organisms use biological and optimal strategies for survival and even in the face of dangers, the mechanism of these algorithms is to convert these biological strategies into mathematical equations to solve the problems of human societies in the face of natural or human dangers. In the case that these strategies are used to solve neural network problems to face natural hazards, optimization algorithms can solve complex problems intelligently and in accordance with mathematical equations, and the accuracy and accuracy of neural network operations in identifying and increasing risk assessment.

Please see the whole manuscript

2

As the authors mentioned, the swarm population affected the training effect, and this population is lack of explaination, why the swarm size 150 and 400 are the best performance? The final suceptibility level is also different with traditional one, they are four map and even some isolated point is obvious. the result need more explain or adjustment.

Thanks to the valuable comments of the reviewer, the result was corrected and revised in the text of the article were made as follows:

Conditioning factors were evaluated based on factors, including; elevation, slope aspect, slope angle, NDVI, distance to fault, plan curvature, profile curvature, rainfall, distance from the river, distance to road, SPI, STI, TRI, TWI, land use, and geology. There were 1072 sites in the landslide inventory database, separated into two groups for training and testing the model, each comprising 536 landslides. The results showed AUC values; the Optimized metaheuristic algorithm was calculated to be 0.842 in swarm size 150 for BBO-MLP and BSA-MLP, it was obtained in swarm size 400. The landslide susceptibility map was created based on the best-fit hybrid model specified as an optimized category with a higher AUC. The real inspiration for using BBO & BSA algorithms in the current study was the widespread use of conventional optimization for landslide susceptibility mapping. The algorithm's computational parameters were effectively optimized via a synthetic neural network. That model's ideal structure was ultimately discovered after significant trial and error. There are fourteen landslide conditioning factors in the spatial database in different ecological, geographical, and structural dimensions. By random selection, the proposed models are trained on seventy percent of the identified landslides using an accidental sampling method, and their precision is evaluated on the residual thirty percent. To evaluate the accuracy of the forecasting models, the area under the curve (AUC) criterion was used. The precision indicator of the area underneath the receiving operating characteristic curve (AUROC) demonstrated that the maps created by the BBO-ANN (with an AUROC value of 0.842) are more precise compared to those generated by the BSA-ANN (with an AUROC value of 0.771). Also, the corresponding estimated AUCs in this regard were for BBO-MLP 0.842, 0.834, 0.809, 0.804, 0.801, 0.798, 0.792, 0.788, 0.773, and 0.743 and BSA-MLP 0.813, 0.805, 0.804, 0.803, 0.799, 0.799, 0.794, 0.795, 0.789, and 0.789, respectively. A 150-person swarm size characterizes the best-fit hybrid model for predicting landslide susceptibility mapping, and it belongs to the BBO-MLP model. According to the findings, these algorithms functioned well to enhance the MLP's learning potential. Additionally, adding metaheuristic algorithms such as BBO may significantly enhance the performance of the ANN with a drop in prediction MSE of 1.230 to 0.551 percent. Three well-known accuracy criteria—MSE, RMSE, and AUROC—were employed to create a rating system that compared the practicality of the utilized model. The result of this part showed that effectively the BBO & BSA algorithms increase the MLP's capacity for learning.

Please see page 27 -28

Issue

Authors’ answer

Revisions

Many thanks for the valuable and constructive comments of the reviewers. An attempt was made to accurately apply all comments to the text of the article. Revisions made to the text of the article include:

1

In introduction chapter, the content introduced is landslide displacement prediction, which does not match the title

Thank you very much for your comments. It was a typo mistake during the proofreading that used this keyword. We normally use “landslide susceptibility mapping/maps/assessment/analysis/ evaluation/ zonation/ zoning”.

Please kindly be informed that some sections of the introduction are changed and we believe that the revised version is in much better form that the initial submission version.

In this regard, researchers are now using meta-heuristic strategies to improve efficiency due to the limitations of current models, including local minimum and dimension dangers [35]. In this respect, all of these meta-heuristic approaches have a great capacity to resolve optimization issues, and for such reason, they have indeed been implemented in several scientific disciplines. The algorithms have several characteristics, and the majority are population-based techniques. Throughout the calculations, we could perhaps find the best design for each of them. It might be beneficial to create a novel technique that enhances the process or outcomes of optimization.

These techniques are used to find high-quality solutions that are based on the best possible computing structure(Tian, Wang, Chen, Zhang, & Qin, 2021). Several advanced strategies (including parallel computation, multi-agent systems, and decomposition of the search space)(Jun Li et al., 2017) are often used in hybrid metaheuristic algorithms. The problems are solved collaboratively by a proactive search agents group acting individually and with parallel computation. They solved many large-scale distributed and dynamic systems with successful results(Reza Naji, Shadravan, Mousa Jafarabadi, & Momeni, 2022).

Previous studies have shown that not estimating the participation of each parameter in the classification by the optimized ANN model is one of the primary challenges of neural network model optimization algorithms. It also has some limitations and drawbacks, including high computational power requirements and a significant computation time for determining the final result. In cases where immediate results are required, both weaknesses can be problematic(Chen, Chen, Tsangaratos, Ilia, & Wang, 2020).

Please see pages 3-4

2

In 3.2 chapter, The format of Siobserved and Sipredicted is different.

Thanks much for your comments. I think you mean equation 1.

I have double-checked and the format is corrected. Kindly double-check and see if it is correctly revised.

Please see page 8 

3

The introduction and use of the content is confusing. Formula 1 explains MSE, Figure 3 introduces RMSE, MAE, R2 and MSE, and the following text uses RMSE.

Thank you very much for your comment. The mentioned comments are corrected based on the respected reviewer's comments.

The below text is used accordingly.

In order to find the minimum error (e.g. finding the best predictive network) during the new model evaluation, we used the term mean square error (here abbreviated as MSE) as the objective function. It indicates the quality of each iteration's resulting solution. In Equation 1, the MSE is given as a formula.

Please see page 8 and the whole manuscript

4

The formula introduction is not uniform, using sequence number (1) and Equation 2.

The mathematical expressions and equations were revised in the article.

Please see pages 8-12

5

The formula is not used uniformly, using Equation 1 and Eq. (2).

The mathematical expressions and equations were revised in the article.

Please see pages 8-12

6

Simulation environment Settings, model parameters need to be described in detail.

Thank you for your comments. We need to first bring your attention to Figure 3 where all the model descriptions are discussed. Similarly Figures 4 and 5 is also described the methods individually. Thereafter in Figure 6, we have shown 16 different data layer inputs that we have employed and that is the most useful spatial distribution basis method that is available in such landslide susceptibility mapping studies. All the input layers are shown and legends are used based on the influential factors that impact the landslide occurrence in the study area. This issue is also well described in section 3.3.

Please see page 27 -28

7

Lack of detailed comparisons between MLP and BBOMLP and BSAMLP. The ability of BBO and BSA to enhance MLP is not stated.

Thanks to the valuable comments of the reviewer, comparisons between MLP and BBOMLP and BSAMLP and ability them for enhancing ANN-MLP revised in the text of the article were made as follows:

Conditioning factors were evaluated based on factors, including; elevation, slope aspect, slope angle, NDVI, distance to fault, plan curvature, profile curvature, rainfall, distance from the river, distance to road, SPI, STI, TRI, TWI, land use, and geology. There were 1072 sites in the landslide inventory database, separated into two groups for training and testing the model, each comprising 536 landslides. The results showed AUC values; the Optimized metaheuristic algorithm was calculated to be 0.842 in swarm size 150 for BBO-MLP and BSA-MLP, it was obtained in swarm size 400. The landslide susceptibility map was created based on the best-fit hybrid model specified as an optimized category with a higher AUC. The real inspiration for using BBO & BSA algorithms in the current study was the widespread use of conventional optimization for landslide susceptibility mapping. The algorithm's computational parameters were effectively optimized via a synthetic neural network. That model's ideal structure was ultimately discovered after significant trial and error. There are fourteen landslide conditioning factors in the spatial database in different ecological, geographical, and structural dimensions. By random selection, the proposed models are trained on seventy percent of the identified landslides using an accidental sampling method, and their precision is evaluated on the residual thirty percent. To evaluate the accuracy of the forecasting models, the area under the curve (AUC) criterion was used. The precision indicator of the area underneath the receiving operating characteristic curve (AUROC) demonstrated that the maps created by the BBO-ANN (with an AUROC value of 0.842) are more precise compared to those generated by the BSA-ANN (with an AUROC value of 0.771). Also, the corresponding estimated AUCs in this regard were for BBO-MLP 0.842, 0.834, 0.809, 0.804, 0.801, 0.798, 0.792, 0.788, 0.773, and 0.743 and BSA-MLP 0.813, 0.805, 0.804, 0.803, 0.799, 0.799, 0.794, 0.795, 0.789, and 0.789, respectively. A 150-person swarm size characterizes the best-fit hybrid model for predicting landslide susceptibility mapping, and it belongs to the BBO-MLP model. According to the findings, these algorithms functioned well to enhance the MLP's learning potential. Additionally, adding metaheuristic algorithms such as BBO may significantly enhance the performance of the ANN with a drop in prediction MSE of 1.230 to 0.551 percent. Three well-known accuracy criteria—MSE, RMSE, and AUROC—were employed to create a rating system that compared the practicality of the utilized model. The result of this part showed that effectively the BBO & BSA algorithms increase the MLP's capacity for learning.

8

The Scoring system needs to be explained in detail.

Thank you for your valuable comments. Kindly be noted that below text are added to the section 4 in order to provide more illustrations for the used scoring system. This systems are used in many other literature review too but we also believed that is the best to be discussed here too.

“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 R², the higher R² will result in a higher score. Therefore, the next sections make use of the results of these networks. Figures 7 and 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.

Issue

Authors’ answer

Revisions

Many thanks for the valuable and constructive comments of the reviewers. An attempt was made to accurately apply all comments to the text of the article. Revisions made to the text of the article include:

1

In introduction chapter, the content introduced is landslide displacement prediction, which does not match the title

Thank you very much for your comments. It was a typo mistake during the proofreading that used this keyword. We normally use “landslide susceptibility mapping/maps/assessment/analysis/ evaluation/ zonation/ zoning”.

Please kindly be informed that some sections of the introduction are changed and we believe that the revised version is in much better form that the initial submission version.

In this regard, researchers are now using meta-heuristic strategies to improve efficiency due to the limitations of current models, including local minimum and dimension dangers [35]. In this respect, all of these meta-heuristic approaches have a great capacity to resolve optimization issues, and for such reason, they have indeed been implemented in several scientific disciplines. The algorithms have several characteristics, and the majority are population-based techniques. Throughout the calculations, we could perhaps find the best design for each of them. It might be beneficial to create a novel technique that enhances the process or outcomes of optimization.

These techniques are used to find high-quality solutions that are based on the best possible computing structure(Tian, Wang, Chen, Zhang, & Qin, 2021). Several advanced strategies (including parallel computation, multi-agent systems, and decomposition of the search space)(Jun Li et al., 2017) are often used in hybrid metaheuristic algorithms. The problems are solved collaboratively by a proactive search agents group acting individually and with parallel computation. They solved many large-scale distributed and dynamic systems with successful results(Reza Naji, Shadravan, Mousa Jafarabadi, & Momeni, 2022).

Previous studies have shown that not estimating the participation of each parameter in the classification by the optimized ANN model is one of the primary challenges of neural network model optimization algorithms. It also has some limitations and drawbacks, including high computational power requirements and a significant computation time for determining the final result. In cases where immediate results are required, both weaknesses can be problematic(Chen, Chen, Tsangaratos, Ilia, & Wang, 2020).

Please see pages 3-4

2

In 3.2 chapter, The format of Siobserved and Sipredicted is different.

Thanks much for your comments. I think you mean equation 1.

I have double-checked and the format is corrected. Kindly double-check and see if it is correctly revised.

Please see page 8 

3

The introduction and use of the content is confusing. Formula 1 explains MSE, Figure 3 introduces RMSE, MAE, R2 and MSE, and the following text uses RMSE.

Thank you very much for your comment. The mentioned comments are corrected based on the respected reviewer's comments.

The below text is used accordingly.

In order to find the minimum error (e.g. finding the best predictive network) during the new model evaluation, we used the term mean square error (here abbreviated as MSE) as the objective function. It indicates the quality of each iteration's resulting solution. In Equation 1, the MSE is given as a formula.

Please see page 8 and the whole manuscript

4

The formula introduction is not uniform, using sequence number (1) and Equation 2.

The mathematical expressions and equations were revised in the article.

Please see pages 8-12

5

The formula is not used uniformly, using Equation 1 and Eq. (2).

The mathematical expressions and equations were revised in the article.

Please see pages 8-12

6

Simulation environment Settings, model parameters need to be described in detail.

Thank you for your comments. We need to first bring your attention to Figure 3 where all the model descriptions are discussed. Similarly Figures 4 and 5 is also described the methods individually. Thereafter in Figure 6, we have shown 16 different data layer inputs that we have employed and that is the most useful spatial distribution basis method that is available in such landslide susceptibility mapping studies. All the input layers are shown and legends are used based on the influential factors that impact the landslide occurrence in the study area. This issue is also well described in section 3.3.

Please see page 27 -28

7

Lack of detailed comparisons between MLP and BBOMLP and BSAMLP. The ability of BBO and BSA to enhance MLP is not stated.

Thanks to the valuable comments of the reviewer, comparisons between MLP and BBOMLP and BSAMLP and ability them for enhancing ANN-MLP revised in the text of the article were made as follows:

Conditioning factors were evaluated based on factors, including; elevation, slope aspect, slope angle, NDVI, distance to fault, plan curvature, profile curvature, rainfall, distance from the river, distance to road, SPI, STI, TRI, TWI, land use, and geology. There were 1072 sites in the landslide inventory database, separated into two groups for training and testing the model, each comprising 536 landslides. The results showed AUC values; the Optimized metaheuristic algorithm was calculated to be 0.842 in swarm size 150 for BBO-MLP and BSA-MLP, it was obtained in swarm size 400. The landslide susceptibility map was created based on the best-fit hybrid model specified as an optimized category with a higher AUC. The real inspiration for using BBO & BSA algorithms in the current study was the widespread use of conventional optimization for landslide susceptibility mapping. The algorithm's computational parameters were effectively optimized via a synthetic neural network. That model's ideal structure was ultimately discovered after significant trial and error. There are fourteen landslide conditioning factors in the spatial database in different ecological, geographical, and structural dimensions. By random selection, the proposed models are trained on seventy percent of the identified landslides using an accidental sampling method, and their precision is evaluated on the residual thirty percent. To evaluate the accuracy of the forecasting models, the area under the curve (AUC) criterion was used. The precision indicator of the area underneath the receiving operating characteristic curve (AUROC) demonstrated that the maps created by the BBO-ANN (with an AUROC value of 0.842) are more precise compared to those generated by the BSA-ANN (with an AUROC value of 0.771). Also, the corresponding estimated AUCs in this regard were for BBO-MLP 0.842, 0.834, 0.809, 0.804, 0.801, 0.798, 0.792, 0.788, 0.773, and 0.743 and BSA-MLP 0.813, 0.805, 0.804, 0.803, 0.799, 0.799, 0.794, 0.795, 0.789, and 0.789, respectively. A 150-person swarm size characterizes the best-fit hybrid model for predicting landslide susceptibility mapping, and it belongs to the BBO-MLP model. According to the findings, these algorithms functioned well to enhance the MLP's learning potential. Additionally, adding metaheuristic algorithms such as BBO may significantly enhance the performance of the ANN with a drop in prediction MSE of 1.230 to 0.551 percent. Three well-known accuracy criteria—MSE, RMSE, and AUROC—were employed to create a rating system that compared the practicality of the utilized model. The result of this part showed that effectively the BBO & BSA algorithms increase the MLP's capacity for learning.

8

The Scoring system needs to be explained in detail.

Thank you for your valuable comments. Kindly be noted that below text are added to the section 4 in order to provide more illustrations for the used scoring system. This systems are used in many other literature review too but we also believed that is the best to be discussed here too.

“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 R², the higher R² will result in a higher score. Therefore, the next sections make use of the results of these networks. Figures 7 and 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.