Study on Multi-UAV Cooperative Path Planning for Complex Patrol Tasks in Large Cities
Round 1
Reviewer 1 Report (Previous Reviewer 1)
The paper's subject is interesting and relevant/ The presentation and proposed method are described clear. The introduction provides information about the problem state. I have not recommendations for the modifications of this paper.
Author Response
Comment1. The paper's subject is interesting and relevant/ The presentation and proposed method are described clear. The introduction provides information about the problem state. I have not recommendations for the modifications of this paper.
Responses. Thank you for your positive feedback on our paper. We appreciate your time and effort in reviewing it. We are grateful for your assessment and the fact that you do not have any recommendations for modifications. Your feedback encourages us and validates our efforts in addressing the research problem. Once again, thank you for your valuable feedback and for considering our paper.
Author Response File: 
Author Response.pdf
Reviewer 2 Report (New Reviewer)
Comments for author File: Comments.pdf
Author Response
Comment1. The manuscript's contributions currently appear somewhat limited and unclear. To provide greater clarity and emphasize the study's significance, please elaborate on the unique contributions in relation to the state-of-the-art within the relevant field. This will help readers better understand the presented research's importance and novelty.
Responses. Thank you very much for your valuable feedback on our manuscript. We sincerely appreciate your insightful comments and suggestions. Your input has been extremely helpful in improving the clarity and significance of our study. We acknowledge that in the previous version of the manuscript, the summary of our contributions was not sufficiently detailed and thorough. We have taken your advice into consideration and made significant revisions to the conclusion section of the manuscript. These revisions provide a comprehensive and detailed explanation of our unique contributions to the relevant field.
“1.The manuscript introduces the concept of UAV urban patrol, which addresses the need for efficient surveillance and monitoring in urban environments. Furthermore, a reality-based model of the urban environment is developed, providing a realistic representation for evaluating the proposed solutions.
- In order to address the challenges of UAV urban patrol effectively, the mathematical model has been expanded to consider various factors. These include the impact cost of UAV operations, flight energy consumption cost, and mission execution rate. Moreover, the model takes into account the constraints imposed by the UAV's flight range and range limitation, resulting in a comprehensive approach to optimizing UAV patrol strategies.
- To enhance the performance of the Lightning Search Algorithm (LSA) and achieve better resource allocation optimization, a novel approach called the Multi-Level Nesting and Random Walk Strategy (MNRW-LSA) has been developed. The MNRW-LSA algorithm incorporates multiple levels of nesting and employs a random walk strategy to improve the search efficiency and accuracy, enabling more effective allocation of resources for UAV urban patrol.
- The reliability and integrity of the MNRW-LSA model are validated through simulation experiments. These experiments demonstrate the effectiveness of the proposed algorithm in comparison to other existing algorithms commonly used in UAV urban patrol scenarios. The comparison provides valuable insights into the superior performance and benefits of the MNRW-LSA approach.”
Comment2. What is the reference of this sentence“The RRT algorithm is currently considered the most advanced method for UAV path planning.”?
Responses. Thank you for your valuable feedback. We have reworked the meaning of this sentence to make it more complex and logical.
“The RRT algorithm is currently considered one of the most advanced methods for UAV path planning.”
RRT algorithm is the most popular algorithm in path planning research. Many scholars have improved its principle and performance, and proposed many improved algorithms. Almost every year, many researches on the improvement of the RRT algorithm are released, and it is also recognized as the most mature and advanced algorithm. For this reason, we have added two references as a basis.
“Qureshi, A. H., Ayaz, Y. Intelligent bidirectional rapidly-exploring random trees for optimal motion planning in complex cluttered environments. Robotics And Autonomous Systems, 2015.”
“Jeong, I. B., Lee, S. J., Kim, J. H. Quick-RRT*: Triangular inequality-based implementation of RRT* with improved initial solution and convergence rate. Expert Systems With Applications, 2019.”
Comment3. the quality of the figures should be improved especially figures 4 and 5.
Responses. Thank you for your feedback. We appreciate your comments and have improved all images in the manuscript. We have checked and corrected all images for pixel, size and clarity according to the journal format requirements to ensure the quality of the figures. At the same time, we adjusted the content in some of the figures. We hope these revisions will improve the readability and comprehensibility of the figures.
Comment4. There are errors like “chapter” in this sentence “In this chapter, the mission description of UAV city patrol is first introduced, and then the environmental model is established.” The full text should be revised.
Responses. Thank you very much for reviewing our paper and providing valuable feedback. We carefully proofread the relevant statements in the full text and corrected them. At the same time, in order to make the manuscript more logical and readable, we have unified the sentences and language styles with similar structure in the manuscript.
“In this section, the mission description of UAV city patrol is first introduced, and then the environmental model is established, and a multi-UAV mission planning model that considers UAV mission execution rate, flight energy consumption cost and impact cost is developed.”
“This section proposes two improvements to the RRT algorithm for UAV trajectory planning. Firstly, the greedy strategy is integrated into the RRT algorithm. Secondly, the lightning search algorithm is enhanced by introducing multi-layer nesting and random walk strategy, which is combined with the improved RRT algorithm for UAV mission planning.”
Comment5. Please add the time complexity analysis of the proposed Lightning Search Algorithm (LSA) based on multi-layer nesting and random walk strategies (MNRW-LSA) and how the average running time of it is less than the original LSA algorithm. Please check this carefully and prove that it is correct.
Responses. Thank you very much for your comments. We have carefully studied many references on algorithm time complexity analysis and summarized the calculation and analysis methods. The time complexity analysis of algorithms plays an important role in many algorithm applications, so we have seriously added relevant content. In Section 5 of the revised manuscript, we add a description of time complexity according to the analysis steps and requirements, and analyze the time complexity comparison between the algorithm proposed in this paper and the LSA algorithm. We also explain the reasons for this result of the two algorithms at the principle level. More changes are made in 5.4. UAV path planning optimization results of the revised manuscript.
Comment6. Does the proposed method have some shortcomings? In fact, shortcomings don't reduce the availability of the proposed method. By contrast, it is a very suitable way to help readers to understand the proposed method comprehensively in my opinion.
Responses. Thank you for your feedback. We appreciate your comments and have made significant revisions to the conclusion to make it more self-contained and easier to understand. The model and algorithm proposed in this study can effectively solve the related static path planning problems, and can provide some research help for UAV flight path control problems. In fact, the three-dimensional environment in practice is not static, and there are usually more obstacles and no-fly zones. Therefore, this study has certain limitations in dynamic path planning, which is also the direction that this research can continue to deepen in the future. We have added more clarification to the conclusion section of the revised draft, indicating the areas in which this manuscript can be improved. We hope these revisions will improve the readability and comprehensibility of the algorithm description:
“This paper provides a new improvement idea for UAV path planning, which can effectively solve the related planning problems in static path planning. However, there are still limitations in the current research process. For example, the interference of weather factors during UAV flight and the changes in vehicle and population density in the real-time environment are not considered.”
Comment7. How tuned the Authors the parameters of the proposed algorithm? Please give more information.
Responses. Thank you for your valuable feedback. In general, the parameters in an algorithm are related to their principles. For general parameters, population size is set with reference to the environmental extent of the path planning. The dimension in 3D path planning is usually set to 3. The number of cycles is set with reference to the number of path nodes and time efficiency. The parameters in the algorithm principle, such as the exponential coefficient in the normal distribution, are adjusted based on repeated experiments and practical problems. The parameters obtained based on experiments are more practical and reliable, and can solve the path optimization problem in a targeted manner. We have added more explanations to the manuscript, hoping to give readers a better understanding of the proposed method.
Comment8. Concerning Conclusion section, it would be better "Conclusions and Future Research", and it is strongly suggested to include future research of this manuscript. What will be happen next? What we supposed to expect from the future papers?
Responses. Thank you for your question and feedback. We highly appreciate your suggestion and have carefully considered and summarized, and briefly described the direction in which existing research can continue to develop. We hope that our changes will make this clearer:
“In future research, more improvement strategies should be tried to be introduced, which will better improve the algorithm performance. At the same time, we will consider applying machine learning methods to learn and optimize the search strategies of heuristic algorithms to improve the efficiency of solving and the quality of solutions, thereby addressing more complex task environments.”
We believe that your feedback has been very constructive and valuable. We are grateful for your guidance and suggestions, which have helped us to improve the quality and persuasiveness of our paper. Once again, thank you for your review and suggestions. We will continue to work hard to improve the quality and value of our research.
Author Response File: Author Response.pdf
Reviewer 3 Report (New Reviewer)
Well written, just a few suggested wording changes and nomenclature miss steps like Table 4 instead of Table 1. See attached PDF file with changes. Remove the yellow highlights every where.
Comments for author File: Comments.pdf
Better than most I have reviewed lately.
Author Response
Thank you very much for your comments and we have corrected the errors you pointed out in the manuscript. Under the premise of ensuring that the manuscript chart format is correct, the content of the manuscript is supplemented, and the order of some content is adjusted to ensure that the manuscript is easy to interpret. In response to your feedback, we have mainly made the following corrections:
- We modified the presentation of the sentences in the manuscript to make it more in line with the journal's language style.
- We adjusted the position and order of some of the images in the text to make them more beautiful and readable in the layout format.
- We have added more explanations of formulas to make them easier to understand.
- We have changed the names of some chapters to supplement the description of the algorithm in the text.
Thank you again for your valuable comments, and thank you for making detailed and specific marks for the authors in the manuscript, so that the authors can better revise. Once again, thank you for your review and suggestions. We will continue to work hard to improve the quality and value of our research.
Author Response File: Author Response.pdf
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
The content of the paper is interesting. The study subject is relevant. The presentation of the result is acceptable. Analysis of the state of the problem requires improving. The abstract should be modified taking into account the goal of the study and proposed principal result.
The recommendations:
- the goal of the study should be indicated more clearly.
- there are many study in path planning in different areas of UAVs use. The application areas (agriculture, confined spaces, city area, etc.) and drone mission (monitoring, control, transportation, etc) impact the specific in UAVs path planning. It should be reflected in the introduction and justified why one of known decision can not be used in another are. I’d like to recommend to consider several reviews of drone applications areas, for example:
- Mukhamediev, R.I., Symagulov, A., et al. Review of some applications of unmanned aerial vehicles technology in the resource-rich country, Applied Sciences (Switzerland), 2021, 11(21), 10171
- Li, Y., Liu, M., Jiang, D., Application of Unmanned Aerial Vehicles in Logistics: A Literature Review, Sustainability, 2022, 14(21), 14473
- What is difference between multi-UAVs and swarm/fleet of UAVs? Why are you using the concept of the multi-UAVs?
- What do you can say about the computational complexity? Is it important in this study?
- Pls, explain of the presented result advantages in more detail. Way is it important to analyze the system lifetime if all components are work? Could you approach be used if some of components are failed?
- Could the proposed methods be used in other areas?
Author Response
Comment1. The goal of the study should be indicated more clearly.
Responses. Thank you for your valuable feedback. The authors greatly appreciate your insights and have given careful consideration to your suggestions. We have revised our manuscript to more clearly define our research objectives, ensuring that they accurately reflect our intentions and align with reader expectations. Specifically, we have modified Section 1 of the Introduction to highlight our focus on the application of unmanned aerial vehicles (UAVs) in urban patrol and defense, and to emphasize the aim of our proposed algorithm in optimizing trajectory planning for multiple UAVs, with the goal of improving their execution coverage and reducing energy consumption, among other important metrics.
Comment2. There are many study in path planning in different areas of UAVs use. The application areas (agriculture, confined spaces, city area, etc.) and drone mission (monitoring, control, transportation, etc) impact the specific in UAVs path planning. It should be reflected in the introduction and justified why one of known decision can not be used in another are. I’d like to recommend to consider several reviews of drone applications areas, for example:
Mukhamediev, R.I., Symagulov, A., et al. Review of some applications of unmanned aerial vehicles technology in the resource-rich country, Applied Sciences (Switzerland), 2021, 11(21), 10171
Li, Y., Liu, M., Jiang, D., Application of Unmanned Aerial Vehicles in Logistics: A Literature Review, Sustainability, 2022, 14(21), 14473
Responses. Thank you for your valuable feedback. We have made revisions to the introduction section, incorporating more details on the various applications of UAV path planning and emphasizing the importance of selecting suitable approaches for specific areas of use. Additionally, we have considered and included the two literature reviews you suggested, along with two other relevant references on the topic of UAV path planning applications in our manuscript.
Comment3. What is difference between multi-UAVs and swarm/fleet of UAVs? Why are you using the concept of the multi-UAVs?
Responses. Thank you for your insightful comment. We appreciate your inquiry on the difference between multi-UAVs and swarm/fleet of UAVs. In terms of UAV technology, multi-UAVs refer to independent UAV that can perform different tasks separately or cooperate to complete the same task. Each UAV has its own independent control system and flight plan, with no direct communication or coordination between them. On the other hand, swarm/fleet of UAVs involve a group of UAVs that work together in a coordinated manner, communicating with each other to achieve a common goal. In our study, we adopt the term multi-UAVs to refer to a group of UAVs that operate cooperatively but with a certain degree of autonomy, while a swarm/fleet of UAVs typically implies a tightly coordinated group that functions as a collective entity. The use of multi-UAVs in our study is more appropriate for the urban patrol and defense application scenario, where UAVs need to cover a large area efficiently and be deployed flexibly. This allows for a more dynamic and adaptable operation compared to a tightly coordinated swarm/fleet of UAVs. We have included a clarification on this point in Section 1 of our manuscript to provide further context and insight into our research approach. Once again, thank you for your valuable feedback.
Comment4. What do you can say about the computational complexity? Is it important in this study?
Responses. Thank you for your question. The computational complexity is indeed an important aspect in this study. As specified in our manuscript, the objective function has a certain level of complexity, with each polynomial term holding its own significance. The number of terms present can indicate the level of computational complexity, as well as the degree of model reduction and matching. Furthermore, the algorithm's results are impacted by the computational complexity, thus emphasizing the importance of its investigation in this paper. We have added further clarification in our revised manuscript to elaborate on the computational complexity of our proposed algorithm.
Comment5. Pls, explain of the presented result advantages in more detail. Way is it important to analyze the system lifetime if all components are work? Could you approach be used if some of components are failed?
Responses. Thank you for your valuable feedback. The authors have taken your suggestion into consideration and revised the manuscript accordingly. In Section 5.4, we have provided a more detailed explanation of the advantages presented in the UAV path planning optimization results. Additionally, in the Conclusion section, we have further elaborated on the significance and implications of our research findings. Regarding the system life cycle analysis, we agree that it is an important aspect to consider in practical applications of UAVs. However, in our study, we focused on optimizing the trajectory planning for multiple UAVs and improving their performance parameters. As such, we did not specifically consider the system life cycle in this paper. Furthermore, we would like to clarify that our proposed approach can still be effective even if some components of the drone fail, as long as the drone is able to continue its mission. This is because our path planning algorithm can be adapted to modify the UAV's performance parameters. We have added a more detailed explanation of this point in the revised manuscript.
Comment6. Could the proposed methods be used in other areas?
Responses. Thank you very much for your question. The authors add more relevant explanations in the conclusion. In the same or non-special environment, the different part is the performance of the UAV, so by modifying the parameters, the method proposed in this paper can still play a role. Thank you for your question. We appreciate your interest in the potential application of our proposed methods in other areas. In the revised conclusion section of the manuscript, we have added more relevant explanations on this topic. The performance of the UAV may vary in different environments, but we believe that our proposed method can still be applied by modifying the UAV's performance parameters. Therefore, we anticipate that our approach can be adapted to different scenarios and environments beyond the specific application scenario studied in this paper. Thank you again for your valuable feedback. We hope that our revised manuscript has provided a more comprehensive explanation of the potential applicability of our proposed methods.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper presents a method for coverage path planning with a team of UAVs in urban scenarios.
Although the authors addressed a relevant research topic, the scientific soundness of the proposed method can hardly be assessed as the paper presentation is confused and English is incomprehensible.
This is particularly relevant in the presentation and description of the proposed method (Sections 2 to 4) and makes questionable the evaluation of the reported results.
I would suggest the authors to have their paper read by someone not directly involved in their project in order to have a feedback on the clarity of the presentation of the paper. This is crucial to guarantee the replicability of the method which is in fact the final goal of a research paper.
Furthermore there are several repeated words and sentences, English should undergo a serious revision and proof reading.
Detailed comments:
The authors tend to introduce several terms or give for known several concepts. The paper should be much more self-contained and quantities introduced should be clearly explained. For instance what does UAV track cost mean which is given by eq. 3? What is e?
The authors keep referring throughout the paper to an application of the coverage mission with an onboard "Infrared thermal dual-lens camera". Is it actually needed to bind the method to such an application?
What is alpha in eq. 4? It should be a field of view, but do the author refer to the horizontal or the vertical one?
In Eq. 6 what is u? What do the authors mean by flight distance? Shouldn't it be just a Euclidean 3D distance? How can they compare in eq. 5 and 6 a Euclidean distance with a differente in altitude?
Concerning Eq. 12, what does it mean to consider a minimum Patrol Area S_c?
Concerning Eq.s 13-16 I don't understand what the superscript A represents. It should represent at a certain position (xiA, yiA, ziA ). But what does such a position represent? And if it is a fixed position how can xi+1 and xi-1 have both the superscript A? Aren't they different positions?
I was completely lost in the descriptions of the algorithms. Some sentences are completely incomprehensible (e.g., Due to its full search characteristics, it cannot complete the directional search of specific points by UAVs - And the
random touring strategy can well provide a larger search space and expand the path space and diversity on the basis of optimization.). I wasn't able to understand how the greedy policy works. Usually in path planning a greedy approach tends to drive the exploration of the path immediately towards the target. Hence I would expect the greedy policy to intervene at the very beginning of the exploration for the path searching. The authours refer to a policy rule instead. I tried to have a look at the algorithm at the beginning of page 11 but there a lot of parameters that have not been defined (state? n of the for cycle? state CD? state G?) and in the end it is essentially unreadable. Unfortunately the missing definition of parameters is nearly ubiquitous in the paper, from equations to algorithms and flowcharts.
Concerning LSA the authors should make the whole description much more self-contained. The authors should not give for known how the algorithm works (even though it has not been developed by themselves). The point is that several concepts appear again without any explanation (ladder? transition discharger? guide discharger?). Some other concepts may be clear but are just mentioned without explicitly introducing them in the body text (e.g. population size, fitness value etc.).
Concerning Results (probably due to the confused description of the method) I wasn't able to understand what all those functions represent. Furthermore it is currently impossible to fairly compare the method proposed by the authors with other methods.
Since the proposed optimized path planning should be the major contribution of this paper, it should be thoroughly and deeply reworked and revised, as the entire paper.
Author Response
Responses to Comments of Reviewer #2:
Comment1. The authors tend to introduce several terms or give for known several concepts. The paper should be much more self-contained and quantities introduced should be clearly explained. For instance what does UAV track cost mean which is given by eq. 3? What is e?
Responses. Thank you very much for your valuable feedback. We sincerely appreciate the criticisms and suggestions you have provided for our research. We have made corresponding modifications in the paper, especially in the model section, where we have provided more detailed explanations for each formula to ensure that readers can better understand the terms and concepts introduced in the paper. Regarding the ambiguity of the UAV track cost, we have changed it to UAV flight energy consumption cost and clarified the meaning of the symbol e, which represents the energy consumed per unit distance of flight.
Comment2. The authors keep referring throughout the paper to an application of the coverage mission with an onboard "Infrared thermal dual-lens camera". Is it actually needed to bind the method to such an application?
Responses. Thank you for your question and feedback. We are honored to receive your valuable comments. Regarding the repeated mention of the onboard "infrared thermal dual-lens camera" in the paper, we understand your concerns and have made corresponding modifications. In fact, the reason why we introduced the concept of coverage rate in the model is closely related to the practical application of UAVs equipped with cameras to obtain data. Therefore, we provided some useful camera parameters, such as a 90° infrared light, to consider the actual application of UAV inspection tasks and make the established model more complete. We hope that this explanation will make our paper clearer and more understandable. Thank you for your patient reading and guidance.
Comment3. What is alpha in eq. 4? It should be a field of view, but do the author refer to the horizontal or the vertical one?
Responses. Thank you for bringing up this question. We appreciate your attention to detail. In equation 4, the variable alpha refers to the maximum angle that the camera mounted on the UAV can capture in the vertical plane. We have provided a clarification for this variable in the corresponding section of the paper to avoid any confusion. We hope this explanation addresses your concern, and thank you for your valuable feedback.
Comment4. In Eq. 6 what is u? What do the authors mean by flight distance? Shouldn't it be just a Euclidean 3D distance? How can they compare in eq. 5 and 6 a Euclidean distance with a different in altitude?
Responses. Thank you for bringing up this question. We appreciate your careful review of our paper. Upon thorough examination, we have found an error in the notation used in Equation 6. We have since corrected this error and can confirm that u represents the flight distance between the two UAVs, while uo denotes the minimum distance required to avoid repeated patrols. We agree that the distance between UAVs is relevant for patrol coverage, and there is no altitude difference involved in Equation 6. Thank you for pointing out the ambiguity in our previous formula. We apologize for any confusion caused by the inappropriate notation, which may have led to a misunderstanding between the Euclidean distance and the difference in height. We have revised the notation and clarified the meaning of the variables to avoid any future confusion. Your feedback has been valuable in improving the quality of our paper.
Comment5. Concerning Eq. 12, what does it mean to consider a minimum Patrol Area S_c?
Responses. Thank you for raising this question. We appreciate your attention to detail. According to the patrol mission requirements, the minimum patrol area is defined as Sc. We have provided this clarification in the corresponding section of the paper to avoid any confusion. We hope this explanation addresses your concern, and thank you for your valuable feedback.
Comment6. Concerning Eq.s 13-16 I don't understand what the superscript A represents. It should represent at a certain position (xiA, yiA, ziA ). But what does such a position represent? And if it is a fixed position how can xi+1 and xi-1 have both the superscript A? Aren't they different positions?
Responses. Thank you very much for bringing up this question. We appreciate your careful review of our paper. In regards to Eq.s 13-16, we apologize for the confusion caused by the superscript A. This was an error in our notation, and we have carefully checked and corrected all the equations in the paper to avoid any further confusion. Thank you again for pointing out this issue, and we hope that our revised notation will be clear and unambiguous.
Comment7. I was completely lost in the descriptions of the algorithms. Some sentences are completely incomprehensible (e.g., Due to its full search characteristics, it cannot complete the directional search of specific points by UAVs - And the random touring strategy can well provide a larger search space and expand the path space and diversity on the basis of optimization.). I wasn't able to understand how the greedy policy works. Usually in path planning a greedy approach tends to drive the exploration of the path immediately towards the target. Hence I would expect the greedy policy to intervene at the very beginning of the exploration for the path searching. The authours refer to a policy rule instead. I tried to have a look at the algorithm at the beginning of page 11 but there a lot of parameters that have not been defined (state? n of the for cycle? state CD? state G?) and in the end it is essentially unreadable. Unfortunately the missing definition of parameters is nearly ubiquitous in the paper, from equations to algorithms and flowcharts.
Responses. Thank you for your valuable feedback. We apologize for the confusion caused by the unclear descriptions of our algorithms. We have carefully reviewed and revised the algorithm section, ensuring that all formulas are explained and parameters are defined. We would like to specifically address your concern regarding the number of iterations in the pseudo code, which is denoted as "Unknown". We have now included an explanation for this in the revised manuscript：
“ represents a new location node, and represents a set of location points where the building is located.”
“The output includes the detection results for collision detection , the result of collision detection , and the result of greedy detection , as well as the number of iterations.”
“ represents the position of the space discharge body, and represents the solution in the calculation formula.”
“However, the new position does not guarantee channel formation unless is a better solution. If provides a better solution in the next step, then will be updated to , otherwise it will remain unchanged. If is better than the current iteration, then the Spatial Discharger becomes Guide Discharger.”
Regarding the RRT algorithm, we agree that it is a random search algorithm that can generate redundant paths and consume a significant amount of time. However, in our proposed approach, we have incorporated a greedy strategy that performs detection at the start of each step on every node. This strategy helps to avoid unnecessary path points, leading to significant time savings and path optimization.
Once again, thank you for your valuable input. We carefully checked and modified the algorithm description. We hope that our revised manuscript will address all of your concerns and improve the overall clarity of our work.
Comment8. Concerning LSA the authors should make the whole description much more self-contained. The authors should not give for known how the algorithm works (even though it has not been developed by themselves). The point is that several concepts appear again without any explanation (ladder? transition discharger? guide discharger?). Some other concepts may be clear but are just mentioned without explicitly introducing them in the body text (e.g. population size, fitness value etc.).
Responses. Thank you for your feedback. We appreciate your comments and have made significant revisions to the LSA algorithm description to make it more self-contained and easier to understand. We have added detailed explanations of the unique concepts used in the algorithm, such as the ladder, transition discharger, and guide discharger. Additionally, we have provided explicit definitions of other concepts such as population size and fitness value. We have also referred to related algorithm improvement papers and incorporated their excellent expressions to enhance the clarity and flow of the article. We hope these revisions will improve the readability and comprehensibility of the algorithm description.
“In this study, we propose a multi-layer nested synchronization optimization mechanism to address the challenge of optimizing the paths of multiple UAVs during collaborative patrols. While it is relatively easy for UAVs to exchange information with each other, optimizing the coverage, cost, and repetition rate of each UAV patrol is a complex task. Our approach considers these factors and aims to find an optimal solution. The algorithm has been optimized by storing the optimized and unoptimized parts in separate spaces. This approach is superior to traditional optimization methods and makes the algorithm more effective in solving the model.
In the above step 5, if the renewal of the transient discharge body is not completed within the maximum conduction time, the time channel is eliminated. However, at the maximum conduction time, the transient discharge body of this time channel is superior to that of any other time channel. To prevent the loss of a more efficient discharge channel, this article utilizes a multi-level nesting operation in step 5 to enhance the performance of the algorithm.”
When using the algorithm to solve the model, the calculation formula of the fitness function is the objective function proposed in the model, and the parameters such as the population size will be determined according to the needs of the simulation.
Comment9. Concerning Results (probably due to the confused description of the method) I wasn't able to understand what all those functions represent. Furthermore it is currently impossible to fairly compare the method proposed by the authors with other methods.
Responses. Thank you very much for your comments. We performed performance validation on the proposed algorithm at the beginning of our experiment, including its convergence and accuracy. To evaluate the algorithm's performance, we optimized multiple optimization algorithms on the same test function and judged them based on the optimization results. Our model's objective function consists of a complex polynomial with each term having a unique meaning. Therefore, we selected eight representative complex polynomial test functions, including unimodal and multimodal functions, as our test functions. The experimental results obtained using the test functions directly show the function's computational values, enabling us to compare algorithm differences. Furthermore, to further clarify the algorithm's performance, we conducted Friedman and Nemenyi tests. These two testing methods utilize statistical thinking to show the algorithm's performance changes in different dimensions and performance differences between algorithms. After completing the algorithm testing, we conducted a final simulation experiment, and the results showed that our proposed improved algorithm performed better for the target function in our study or similar objective functions. Once again, thank you for your valuable comments. We hope that the revised manuscript will clarify this section.
Comment10. Since the proposed optimized path planning should be the major contribution of this paper, it should be thoroughly and deeply reworked and revised, as the entire paper.
Responses. Thank you very much for reviewing our paper and providing valuable feedback. We highly appreciate your suggestion and have made significant revisions to the paper based on your recommendations. In particular, we have thoroughly examined our proposed path planning algorithm and made significant improvements to it. Additionally, we have also refined and polished the language throughout the paper to ensure accuracy and professionalism. We believe that your feedback has been very constructive and valuable. We are grateful for your guidance and suggestions, which have helped us to improve the quality and persuasiveness of our paper. Once again, thank you for your review and suggestions. We will continue to work hard to improve the quality and value of our research.
Author Response File: Author Response.docx
Reviewer 3 Report
please consider my critics
Comments for author File: Comments.pdf
Author Response
Responses to Comments of Reviewer #3:
We would like to express our sincere gratitude for the insightful feedback you provided on our paper. We highly value the time and effort you have invested in reviewing our work. Based on your comments, we have diligently revised the language of our manuscript and made significant modifications to its content and structure. We have also thoroughly addressed the errors reviewers pointed out during the review process. We are confident that our revised manuscript now boasts better clarity and quality and meets your expectations. Thank you once again for your invaluable feedback, and we eagerly anticipate your positive response.
Author Response File: Author Response.docx
