Indoor Genetic Algorithm-Based 5G Network Planning Using a Machine Learning Model for Path Loss Estimation

Round 1

Reviewer 1 Report

- The proposal is almost appealing and exciting, and the method warrants consideration. Nevertheless, the paper is almost well written and well organized.

- It would be useful that the authors give a frank account of the strengths and weaknesses of their proposed research method.

- In the introduction, the authors could include a sound literature survey to prove what is novel about their approach. In fact, it would be beneficial to present an explicit discussion on the current research versus the unique contribution of the paper. 

I suggest to analyze the following papers:

*** doi: 10.3390/s22010026
*** doi: 10.1109/ACES53325.2021.00053
*** doi: 10.1109/APCAP50217.2020.9246088
*** doi: 10.3390/data7030034 

- The contributions of the paper are based on realistic and referenced theories.

- The conclusions and potential impacts of the paper are made clear.

Author Response

*We have put an asterisk (*) before every response.

- It would be useful that the authors give a frank account of the strengths and weaknesses of their proposed research method.

*Thanks for your comments. This help to improve the quality of the manuscript. To address your comment, we improved the overview about the state-of-the-art of Machine Learning (ML) models to approximate complex path loss models (e.g., ray-tracing). Only three publications were found demonstrating that the Random Forest (adding bagging technique) algorithm can be used for estimating this kind of computationally expensive path loss models.  However, none of them used the resulting model to perform and evaluate wireless network planning.

The main contribution of this work is that network planning that builds on advanced, but computationally expensive path loss models (i.e., too expensive to perform sufficient evaluations of candidate planning solutions), is improved by approximating the complex PL model by a ML-based PL model, that is much more agile in evaluations. It is shown that the accuracy of the ML PL model is satisfactory and that a GA manages to find a better network planning solution, thanks to the ability to evaluate many more candidate solutions, thanks to the agility of the ML-based PL model. In the Related Work section, we added the research related to this topic.

“In [20], the authors proposed a path loss model for a Unmanned Aerial Vehicle (UAV) air-to-air (AA) scenario based on ML. Two ML algorithms (K nearest neighbors (kNN) and Random Forest) were used to build the models and the results were compared to the data generated by the ray-tracing software developed in [20]. Both ML models have better performance than the empirical models (COST231 and SUI model), the Random Forest algorithm even outperforms the kNN by 2 dB. The calculation times for Random Forest and kNN to make predictions are 8.71 s and 5.95 s, respectively. However, running the ray-tracing software took more than 10 minutes. In [21], the authors compared three ML algorithms: kNN, SVR, and Random Forest. In this case, to avoid time-consuming and expensive measurement campaigns, the PL values to train/validate the ML algorithms were generated with a 3D ray-tracing model in the city center of Tripoli, Greece. As results, they obtained estimations with a Mean Absolute Error (MAE) less than 3 dB for the three ML algorithms, which prove that ML can be both a fast and accurate approach to approximate complex PL models (e.g., ray-tracing). Looking for further improvements, we use in our research the Ensembles trees: the Bagging algorithm, which is a combination of Random Forest algorithm and the Bagging technique to reduce the standard deviation of the error (we refer the reader to Section 3.1.2). Further, we introduce the opportunities that such quick ML-based PL model brings: wireless network planning using (ML-approximated) advanced PL models is made possible, allowing for better results and more flexibility in the planning process.”

*The current approach is now only considered for the Indoor Dominant Path model (more accurate model in [12]). Future work consists of testing the approach for accurate wireless network planning using ray-tracing path loss models. We have referred to this future work in the conclusions section.

“Future work will consist of a time optimization for the features (inputs) calculation process, where the PL for all possible AP-grid point links is calculated to be used in the GA. A modification to the cost function in the GA will be added to target a minimal human exposure, and a higher SIR. Finally, this approach will be tested for accurate wireless network planning using ray-tracing path loss models.”

- In the introduction, the authors could include a sound literature survey to prove what is novel about their approach. In fact, it would be beneficial to present an explicit discussion on the current research versus the unique contribution of the paper.

I suggest to analyze the following papers:

*** doi: 10.3390/s22010026

*** doi: 10.1109/ACES53325.2021.00053

*** doi: 10.1109/APCAP50217.2020.9246088

*** doi: 10.3390/data7030034

* A discussion about this topic is valuable and helps to improve our work. In the introduction section, we added a brief discussion to better introduce the reader to our work. As a result, 9 new references were added. 

“Fifth Generation (5G) cellular networks are promising to be a real improvement compared to all the previous mobile generation networks [1]. It brings three main services for end-users i.e., Extreme Mobile Broadband (eMBB), Massive Machine Type Communications (eMTC), and Ultra-Reliable Low Latency Communication (URLLC) [1][2]. The 5G New Radio (5G-NR) operates over two frequencies ranges, Frequency Range 1 (FR1 includes sub-6 GHz), and Frequency Range 2 (FR2, which includes the millimeter-wave band, from 24.25 to 52.6 GHz). A significant number of commercial 5G networks are currently under deployment in the sub-6 GHz band, particularly in the 3.3-3.8 GHz (3.5 GHz band) portion, which offers a good trade-off between coverage and capacity [3]. Therefore, understanding signal propagation characteristics in the 3.5 GHz band is particularly important, especially in the 5G indoor scenarios where many applications are being developed.  

Some 5G use cases target indoor scenarios, such as smart building monitoring with different types of sensors, factory automation, object tracking inside a building, and automated vehicles (logistic applications) [4][5]. These indoor scenarios are likely to be addressed via an outdoor (outdoor-to-indoor, O2I) deployment of the 5G Base Station (BS) [6][7][8]. However, it was demonstrated in [9] that the PL for O2I increases by approximately 100 dB when the distance between the BS and the building is increased by 50 m, and the use of indoor-to-indoor (I2I) deployments can reduce the PL up to 60 dB compared to O2I deployments. This emphasizes the need for understanding propagation characteristics in indoor scenarios with I2I deployments.”

“In this research work, we propose a generic method based on the Decision Tree Ensembles (Bagging) algorithm for the estimation of the PL experienced by 5G signals at 3.5 GHz in indoor scenarios. Subsequently, the obtained model is used in a Genetic Algorithm (GA) [12] to perform 5G network planning. The novelty of this work is (i) to build a generic (applicable to other buildings) ML model able to accurately approximate an advanced PL model, (ii) use the ML estimation in a combination with a GA for wireless network planning, and (iii) obtain deployment solutions with a similar or better performance than existing heuristic tools (e.g., the one developed in [11]) but, in less time.

We show that an advanced, but computationally expensive path loss model, that builds on the physical properties of propagation, can be well approximated by a ML-based PL model that allows much faster PL estimations for a given link. Such quick, but still accurate PL model unlocks the possibility of a more thorough exploration of the optimization space to find the optimal network deployment (number and location of APs). It is shown that the proposed approach is accurate (i.e., is able to provide the required coverage according to the complex PL model), is 15 times faster than a heuristic optimization algorithm (and thus more flexible towards recalculations with adjusted optimization settings), finds a better solution (with fewer APs), and allows accounting for additional constraints such as striving for a maximal received power.”

[1]          R. Dangi, P. Lalwani, G. Choudhary, I. You, and G. Pau, “Study and Investigation on 5G Technology: A Systematic Review,” Sensors, vol. 22, no. 1. 2022. doi: 10.3390/s22010026.

[2]          U. Ali et al., “Large-Scale Dataset for the Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks,” Data, vol. 7, no. 3. 2022. doi: 10.3390/data7030034.

[3]          E. I. Adegoke, R. M. Edwards, W. G. Whittow, and A. Bindel, “Characterizing the Indoor Industrial Channel at 3.5GHz for 5G,” in 2019 Wireless Days (WD), 2019, pp. 1–4. doi: 10.1109/WD.2019.8734160.

[4]          M. Attaran, “The impact of 5G on the evolution of intelligent automation and industry digitization,” J. Ambient Intell. Humaniz. Comput., vol. 1, p. 3, 2021, doi: 10.1007/s12652-020-02521-x.

[5]          B. El Boudani et al., “Implementing Deep Learning Techniques in 5G IoT Networks for 3D Indoor Positioning: DELTA (DeEp Learning-Based Co-operaTive Architecture),” Sensors, vol. 20, no. 19. 2020. doi: 10.3390/s20195495.

[6]          M. U. Sheikh, L. Mela, N. Saba, K. Ruttik, and R. Jäntti, “Outdoor to Indoor Path Loss Measurement at 1.8GHz, 3.5GHz, 6.5GHz, and 26GHz Commercial Frequency Bands,” in 2021 24th International Symposium on Wireless Personal Multimedia Communications (WPMC), 2021, pp. 1–5. doi: 10.1109/WPMC52694.2021.9700427.

[7]          M. E. Diago-Mosquera, A. Aragón-Zavala, and M. Rodriguez, “Testing a 5G Communication System: Kriging-Aided O2I Path Loss Modeling Based on 3.5 GHz Measurement Analysis,” Sensors, vol. 21, no. 20. 2021. doi: 10.3390/s21206716.

[8]          M. A. Samad, F. D. Diba, Y.-J. Kim, and D.-Y. Choi, “Results of Large-Scale Propagation Models in Campus Corridor at 3.7 and 28 GHz,” Sensors, vol. 21, no. 22. 2021. doi: 10.3390/s21227747.

[9]          U. Ullah, U. R. Kamboh, F. Hossain, and M. Danish, “Outdoor-to-Indoor and Indoor-to-Indoor Propagation Path Loss Modeling Using Smart 3D Ray Tracing Algorithm at 28 GHz mmWave,” Arab. J. Sci. Eng., vol. 45, no. 12, pp. 10223–10232, 2020, doi: 10.1007/s13369-020-04661-w.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presents a network planning method based on machine learning and genetic algorithms, and the authors shows that more effective network planning is achieved through several experimental results. Unfortunately, I cannot recommend this paper for publication for the following concerns:

1. The novelty and originality of this paper is weak. The authors are just applying simple machine learning technique to finding the optimal combination of APs.
2. The authors do not well present the ML model and learning method they used. They need to provide the network model in more detail. More formal mathematical descriptions are also needed.
3. Using genetic algorithms generally suffers from long training time. I cannot understand the claim that the proposed scheme is 15 times faster than the legacy scheme.
4. Introduction is poorly written and at least not much informative. The motivation, contributions, basic approach and idea of this paper must be well presented in there.

Author Response

*We have put an asterisk (*) before every response.

Comments and Suggestions for Authors

This paper presents a network planning method based on machine learning and genetic algorithms, and the authors shows that more effective network planning is achieved through several experimental results. Unfortunately, I cannot recommend this paper for publication for the following concerns: 

1. The novelty and originality of this paper is weak. The authors are just applying simple machine learning technique to finding the optimal combination of APs.

*We try to better clarify the originality and novelty of our work. The use of machine learning techniques itself is not the main contribution of this work, but we rather show that (1) it is possible to well approximate complex PL models with ML-based PL models, so that (2) (unlike the original complex model,) we can use these models in an optimization algorithm, to finally (3) obtain a network deployment with better properties (better QoS, fewer APs).

To the best of our knowledge, no works have yet presented wireless network optimizations that are built on computationally expensive PL models, due to the inherent longer PL calculation time of these complex models, prohibiting a thorough scan of the solution space.

Please, also note that it is not the ML technique that is used to find the optimal combination of APs, but the Genetic Algorithm (cfr. your comment). The main contribution of this work is that network planning build on advanced, but computationally expensive path loss models (i.e., too expensive to perform sufficient evaluations of candidate planning solutions), is improved approximating the complex PL model by a ML-based PL model, that is much more agile in evaluations. It is shown that the accuracy of the ML PL model is satisfactory and that a GA manages to find a better network planning solution, thanks to the ability to evaluate many more candidate solutions, thanks to the agility of the ML-based PL model.

Validation of the proposed optimized solution, again using the original (computationally expensive) PL model, proves that the proposed solution is accurate (i.e., able to provide the required coverage), contains fewer APs (lower cost), is obtained in a faster way, and allows accounting for additional constraints (more planning flexibility). We have tried to better clarify this contribution in the manuscript as well:

"We show that an advanced, but computationally expensive path loss model, that builds on the physical properties of propagation, can be well approximated by a ML-based PL model that allows much faster PL estimations for a given link. Such quick, but still accurate PL model unlocks the possibility of a more thorough exploration of the optimization space to find the optimal network deployment (number and location of APs). It is shown that the proposed approach is accurate (i.e., is able to provide the required coverage according to the complex PL model), is 15 times faster than a heuristic optimization algorithm (and thus more flexible towards recalculations with adjusted optimization settings), finds a better solution (with fewer APs), and allows accounting for additional constraints such as striving for a maximal received power."

2. The authors do not well present the ML model and learning method they used. They need to provide the network model in more detail. More formal mathematical descriptions are also needed.

*Thanks for your comment. We agree that the ML was not well explained in the manuscript. We have now introduced a new section where we explain in detail the ML model.

“3.1.2.1 Ensembles Trees: Bagging algorithm

Bootstrap Aggregation or Bagging ensemble is a technique to combine multiple ML algorithms to make a single model with more accurate predictions than an individual model. The Bagging Ensemble technique can be used for base models that have low bias and high variance, typically the Decision Trees algorithm. Otherwise, Decision trees are sensitive to the specific data on which they are trained. If noise is added to the training dataset the resulting decision tree can be quite different and in turn, the predictions can be quite different. Typically, the Random Forest is an algorithm with high variance [37], then applying the bootstrap aggregation technique the variance can be reduced.

The training algorithm for random forests applies the general technique of bootstrap aggregating, or bagging, to tree learners. Given a training dataset , with responses , bagging repeatedly (B times) selects a random sample with replacement of the training set and fits trees to these samples. For each iteration  ( ), a dataset is created with input and output , and an function is obtained from the training process with ,  . After training, a test for unseen samples x' can be made by averaging ( in equation 3) the predictions from all the individual regression trees on x'.

As this bootstrapping procedure decreases the variance of the model, this means that while the predictions of a single tree can be highly sensitive to noise in its training dataset, the average of many trees will not, while the trees are not correlated. The problem is solved simply by training many trees on a single training dataset, at the end it gives strongly correlated trees. Additionally, an estimation of the prediction’s uncertainty can be made based on the standard deviation (see equation (4) of the predictions from all the individual regression trees on x'. The number of samples/trees, B, is a free parameter and an optimal number of trees B can be found using k cross-validation [38]. The accuracy achieved in this research was obtained bagging the random forest algorithm with B = k = 5, minimum leaf size equal to 8, and the number of learners equal to 30.”

3. Using genetic algorithms generally suffers from long training time. I cannot understand the claim that the proposed scheme is 15 times faster than the legacy scheme.

*We try to better clarify when and how our ML+GA approach has better performance than the heuristic tool. The main reason why the proposed scheme is much faster, is because (1) the original scheme uses a time-consuming advanced path loss model that is being replaced by a much faster ML approximation, and (2) the heuristic network optimization algorithm from [12] which uses the advanced PL model, is being replaced by a GA using the quicker ML-based PL model.

The ML+GA approach works in two stages. First, we account for the building geography, find all possible AP locations with a 4 m spanning size, and using the ML model, we calculate all possible AP-Rx links. This is what we called in Table 4 (Section 4.2) ‘Pre-processing Time [min]’. In terms of time, this value is not comparable to the heuristic tool, but this calculation is required just in the initial stage and can be reused to account for another deployment (e.g., higher or lower throughput or different additional design constraints). In the second stage, we use the previously calculated AP-Rx link values to find the optimal deployment with the GA. 

 We also modified Section 3.4.2 to make it clear to the reader.

“The core of the architecture is a GA [13] taking as inputs the floor plan and the PL estimation made with the ML algorithm for every possible AP-Rx link (we refer the reader to Section 4.2.1 for more details).”

4. Introduction is poorly written and at least not much informative. The motivation, contributions, basic approach and idea of this paper must be well presented in there.

* We improved the introduction section adding a brief discussion to better introduce the reader to our work. As a result, 9 new references were added. 

“Fifth Generation (5G) cellular networks are promising to be a real improvement compared to all the previous mobile generation networks [1]. It brings three main services for end-users i.e., Extreme Mobile Broadband (eMBB), Massive Machine Type Communications (eMTC), and Ultra-Reliable Low Latency Communication (URLLC) [1][2]. The 5G New Radio (5G-NR) operates over two frequencies ranges, Frequency Range 1 (FR1 includes sub-6 GHz), and Frequency Range 2 (FR2, which includes the millimeter-wave band, from 24.25 to 52.6 GHz). A significant number of commercial 5G networks are currently under deployment in the sub-6 GHz band, particularly in the 3.3-3.8 GHz (3.5 GHz band) portion, which offers a good trade-off between coverage and capacity [3]. Therefore, understanding signal propagation characteristics in the 3.5 GHz band is particularly important, especially in the 5G indoor scenarios where many applications are being developed.  

Some 5G use cases target indoor scenarios, such as smart building monitoring with different types of sensors, factory automation, object tracking inside a building, and automated vehicles (logistic applications) [4][5]. These indoor scenarios are likely to be addressed via an outdoor (outdoor-to-indoor, O2I) deployment of the 5G Base Station (BS) [6][7][8]. However, it was demonstrated in [9] that the PL for O2I increases by approximately 100 dB when the distance between the BS and the building is increased by 50 m, and the use of indoor-to-indoor (I2I) deployments can reduce the PL up to 60 dB compared to O2I deployments. This emphasizes the need for understanding propagation characteristics in indoor scenarios with I2I deployments.”

“In this research work, we propose a generic method based on the Decision Tree Ensembles (Bagging) algorithm for the estimation of the PL experienced by 5G signals at 3.5 GHz in indoor scenarios. Subsequently, the obtained model is used in a Genetic Algorithm (GA) [12] to perform 5G network planning. The novelty of this work is (i) to build a generic (applicable to other buildings) ML model able to accurately approximate an advanced PL model, (ii) use the ML estimation in a combination with a GA for wireless network planning, and (iii) obtain deployment solutions with a similar or better performance than existing heuristic tools (e.g., the one developed in [11]) but, in less time.

We show that an advanced, but computationally expensive path loss model, that builds on the physical properties of propagation, can be well approximated by a ML-based PL model that allows much faster PL estimations for a given link. Such quick, but still accurate PL model unlocks the possibility of a more thorough exploration of the optimization space to find the optimal network deployment (number and location of APs). It is shown that the proposed approach is accurate (i.e., is able to provide the required coverage according to the complex PL model), is 15 times faster than a heuristic optimization algorithm (and thus more flexible towards recalculations with adjusted optimization settings), finds a better solution (with fewer APs), and allows accounting for additional constraints such as striving for a maximal received power.”

[1]          R. Dangi, P. Lalwani, G. Choudhary, I. You, and G. Pau, “Study and Investigation on 5G Technology: A Systematic Review,” Sensors, vol. 22, no. 1. 2022. doi: 10.3390/s22010026.

[2]          U. Ali et al., “Large-Scale Dataset for the Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks,” Data, vol. 7, no. 3. 2022. doi: 10.3390/data7030034.

[3]          E. I. Adegoke, R. M. Edwards, W. G. Whittow, and A. Bindel, “Characterizing the Indoor Industrial Channel at 3.5GHz for 5G,” in 2019 Wireless Days (WD), 2019, pp. 1–4. doi: 10.1109/WD.2019.8734160.

[4]          M. Attaran, “The impact of 5G on the evolution of intelligent automation and industry digitization,” J. Ambient Intell. Humaniz. Comput., vol. 1, p. 3, 2021, doi: 10.1007/s12652-020-02521-x.

[5]          B. El Boudani et al., “Implementing Deep Learning Techniques in 5G IoT Networks for 3D Indoor Positioning: DELTA (DeEp Learning-Based Co-operaTive Architecture),” Sensors, vol. 20, no. 19. 2020. doi: 10.3390/s20195495.

[6]          M. U. Sheikh, L. Mela, N. Saba, K. Ruttik, and R. Jäntti, “Outdoor to Indoor Path Loss Measurement at 1.8GHz, 3.5GHz, 6.5GHz, and 26GHz Commercial Frequency Bands,” in 2021 24th International Symposium on Wireless Personal Multimedia Communications (WPMC), 2021, pp. 1–5. doi: 10.1109/WPMC52694.2021.9700427.

[7]          M. E. Diago-Mosquera, A. Aragón-Zavala, and M. Rodriguez, “Testing a 5G Communication System: Kriging-Aided O2I Path Loss Modeling Based on 3.5 GHz Measurement Analysis,” Sensors, vol. 21, no. 20. 2021. doi: 10.3390/s21206716.

[8]          M. A. Samad, F. D. Diba, Y.-J. Kim, and D.-Y. Choi, “Results of Large-Scale Propagation Models in Campus Corridor at 3.7 and 28 GHz,” Sensors, vol. 21, no. 22. 2021. doi: 10.3390/s21227747.

[9]          U. Ullah, U. R. Kamboh, F. Hossain, and M. Danish, “Outdoor-to-Indoor and Indoor-to-Indoor Propagation Path Loss Modeling Using Smart 3D Ray Tracing Algorithm at 28 GHz mmWave,” Arab. J. Sci. Eng., vol. 45, no. 12, pp. 10223–10232, 2020, doi: 10.1007/s13369-020-04661-w.

Author Response File: Author Response.pdf

Reviewer 3 Report

My remarks are in a separate letter.

Comments for author File: Comments.pdf

Author Response

*We have put an asterisk (*) before every response.

1. It would have been better to give more information about the choice of the different steps of the used algorithms

*We have extended the manuscript with more information on the ML algorithm. We give more information (1) about the motivation of the choice for the bagging algorithm and (2) about the bagging algorithm itself.

• Motivation for the choice of Ensemble Trees: Bagging algorithm.

We improved our overview about the state-of-the-art of ML models to approximate complex path loss models (e.g., ray-tracing). Three research were found demonstrating that Random Forest (adding the bagging technique) algorithm can be used for estimating this kind of computationally expensive path loss models.

“In [20], the authors proposed a path loss model for a Unmanned Aerial Vehicle (UAV) air-to-air (AA) scenario based on ML. Two ML algorithms (K nearest neighbors (kNN) and Random Forest) were used to build the models and the results were compared to the data generated by the ray-tracing software developed in [20]. Both ML models have better performance than the empirical models (COST231 and SUI model), the Random Forest algorithm even outperforms the kNN by 2 dB. The calculation times for Random Forest and kNN to make predictions are 8.71 s and 5.95 s, respectively. However, running the ray-tracing software took more than 10 minutes. In [21], the authors compared three ML algorithms: kNN, SVR, and Random Forest. In this case, to avoid time-consuming and expensive measurement campaigns, the PL values to train/validate the ML algorithms were generated with a 3D ray-tracing model in the city center of Tripoli, Greece. As results, they obtained estimations with a Mean Absolute Error (MAE) less than 3 dB for the three ML algorithms, which prove that ML can be both a fast and accurate approach to approximate complex PL models (e.g., ray-tracing). Looking for further improvements, we use in our research the Ensembles trees: Bagging algorithm, which is a combination of Random Forest algorithm and the Bagging technique to reduce the standard deviation of the error (we refer the reader to Section 3.1.2). Further, we introduce the opportunities that such quick ML-based PL model brings: wireless network planning using (ML-approximated) advanced PL models is made possible, allowing for better results and more flexibility in the planning process.”

* The current approach is now only considered for the Indoor Dominant Path model (more accurate model in [12]). Future work consists of testing the approach for accurate wireless network planning using ray-tracing path loss models. We have referred to this future work in the conclusions section.

“Future work will consist of a time optimization for the features (inputs) calculation process, where the PL for all possible AP-grid point links is calculated to be used in the GA. A modification to the cost function in the GA will be added to target a minimal human exposure, and a higher SIR. Finally, this approach will be tested for accurate wireless network planning using ray-tracing path loss models

• the bagging algorithm itself

“3.1.2.1 Ensembles Trees: Bagging algorithm

Bootstrap Aggregation or Bagging ensemble is a technique to combine multiple ML algorithms to make a single model with more accurate predictions than an individual model. The Bagging Ensemble technique can be used for base models that have low bias and high variance, typically the Decision Trees algorithm. Otherwise, Decision trees are sensitive to the specific data on which they are trained. If noise is added to the training dataset the resulting decision tree can be quite different and in turn, the predictions can be quite different. Typically, the Random Forest is an algorithm with high variance [37], then applying the bootstrap aggregation technique the variance can be reduced.

The training algorithm for random forests applies the general technique of bootstrap aggregating, or bagging, to tree learners. Given a training dataset, with responses, bagging repeatedly (B times) selects a random sample with replacement of the training set and fits trees to these samples. For each iteration  ( ), a dataset is created with input and output, and an function is obtained from the training process with ,  . After training, a test for unseen samples x' can be made by averaging ( in equation 3) the predictions from all the individual regression trees on x'.

As this bootstrapping procedure decreases the variance of the model, this means that while the predictions of a single tree can be highly sensitive to noise in its training dataset, the average of many trees will not, while the trees are not correlated. The problem is solved simply by training many trees on a single training dataset, at the end it gives strongly correlated trees. Additionally, an estimation of the prediction’s uncertainty can be made based on the standard deviation (see equation (4) of the predictions from all the individual regression trees on x'. The number of samples/trees, B, is a free parameter and an optimal number of trees B can be found using k cross-validation [38]. The accuracy achieved in this research was obtained bagging the random forest algorithm with B = k = 5, minimum leaf size equal to 8, and the number of learners equal to 30.”

*Finally, we also motivate the use of a Genetic Algorithm for the network optimization step. In [25], a NN was used to estimate the signal strength and avoid the architectural complexity of an indoor environment. In this research, the author compared the NN performance with four different optimization algorithms: the PSO algorithm, GA, Powell’s conjugate method, and the Simplex search method. The simulation results show that all four methods have similar performance in terms of the required number of base stations. However, in terms of computational time, the GA has a slightly better performance compared to the other three models. Also, we add this explanation in the manuscript to highlight the motivation to use a GA.

   “In [25], a NN was used to estimate the signal strength and avoid the architectural complexity of an indoor environment. In this research, the authors compared the NN performance with four different optimization algorithms: the PSO algorithm, GA, Powell’s conjugate method, and the Simplex search method. The simulation results show that all four methods have similar performance in terms of the required number of base stations. However, in terms of computational time, the GA has a slightly better performance compared to the other three models.”

2. In the row 331 there is a sentence “a new population is created where the best individuals (5) from the previous population are transferred unchanged to the new population”, but I have not found the equation (5) in the paper.

*Thanks for noticing this. It does not refer to equation 5. It refers to the maximum number of best individuals from the previous population that is transferred to the new population. We have clarified this in the manuscript.

“•           Crossover – from the sorted population, a new population is created where the best_individuals (five individuals) from the previous population are transferred unchanged to the new population. The other new child solutions (population_size – best_individuals) are obtained from a crossover operation between two individuals, each chosen as the fittest individual out of a set of 5 random individuals from the population of the previous generation. Each child gene is inherited from either one of the corresponding parent genes, with equal probability. The newly created child solution is added to the new population.”

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Compared to the previous version, much improvement have been made in this manuscript.