Optimizing Aircraft Routes in Dynamic Conditions Utilizing Multi-Criteria Parameters

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors of the paper titled "Optimization of Aircraft Routes in Dynamic Conditions, Taking Into Account Multi-Criteria Parameters" present a systematic analysis of routing algorithms in dynamic environments. They review traditional methods such as A*, B*, D*, and Dijkstra while proposing a method that integrates real-time parameters into flight planning. The paper models flight paths and compares both the strengths and weaknesses of conventional and improved approaches.

The study examines various parameters including weather, traffic, economic factors, and aircraft characteristics. Integrating these variables provides a practical dimension to the research. The authors offer a balanced discussion by highlighting achievements in decision-making efficiency alongside limitations in current methods.

Although the paper discusses pros and cons, further justification for the selection of specific optimization algorithms is needed. The authors should explain why these particular algorithms were chosen over others available. It may be useful to test less popular algorithms to evaluate their performance in dynamic, multi-criteria environments. Clarifying this point would strengthen the technical foundations of the work.

In addition, Figures 1, 3, and 4 are presented in low resolution. The paper would benefit from higher resolution images to improve clarity. There is also a need for clarification regarding the message "AI-generated content may be incorrect" that appears when hovering over the graphics, as this may impact the perceived reliability of the visual data.

The subject of continuously monitoring and adapting flight routes to changing conditions is both important and timely. The paper addresses relevant challenges in air traffic management and highlights the need for ongoing research in this field. The authors are encouraged to provide precise more details about their plans for future research related to this publication (not just an indication  where results of the study can be useful).

The paper is interesting and show integrating dynamic variables into flight planning algorithms. However, clarifications on algorithm selection for this analyze, improvements in figure quality, and further explanation of interactive figure warnings are recommended. In my opinion, the paper may be reconsidered after minor changes and clarification of doubts.

Author Response

Comments 1: The authors should explain why these particular algorithms were chosen over others available. It may be useful to test less popular algorithms to evaluate their performance in dynamic, multi-criteria environments. 

Response 1: Thank you for pointing this out.

The choice of algorithms was made in accordance with the set criteria, namely, the return of optimal routes while taking into account multiple optimality criteria.

According to the review of existing studies and the analysis of advantages (and disadvantages), these algorithms were selected for analysis and search for improvements when applying multi-criteria constraints.

As for other algorithms, their use may be an option for further research as a consequence of the results of the imperfection of the currently selected algorithms when applied for practical purposes.

Comments 2: In addition, Figures 1, 3, and 4 are presented in low resolution. The paper would benefit from higher resolution images to improve clarity.

Response 2:  Agree. Thank you for your comment.

We have taken this comment into account in the revised article and inserted Figures 1, 2, 3, and 4 in higher resolution.

Comments 3: There is also a need for clarification regarding the message "AI-generated content may be incorrect" that appears when hovering over the graphics, as this may impact the perceived reliability of the visual data.

Response 3:  Thank you for your comment.

When submitting the article, we declared that we did not use AI tools in the preparation of the materials.

The message “AI-generated content may be incorrect” in the .pdf version of the article was a big (and very unpleasant) surprise for us.

The article was prepared and submitted in the .docx format, and we did not convert it to pdf and (presumably) it was done automatically. The origin of such messages remains a mystery to us.

We apologize for the unclear message on some of the images.

After updating the resolution of the images and saving them in pdf format, we no longer have such messages.

Comments 4: The authors are encouraged to provide precise more details about their plans for future research related to this publication (not just an indication where results of the study can be useful).

Response 4: Thank you for your comment. This article is the beginning of research on finding optimal flight routes for aircraft under multi-criteria constraints and displaying the results based on modeling using aircraft models that are most commonly used in business aviation.

Further practical applications and their analysis based on reports of real routes and weather data will be carried out and described in the following articles, which will be interconnected.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The author proposes a comprehensive model for aircraft route planning. However, the approach to balancing the weights of various factors needs further elaboration.

The author uses two aircraft models for simulation. The parameters and differences of these models require more detailed explanation.

Despite improvements in multiple aspects of the proposed model, its computational efficiency and flight safety should be further assessed.

The paper presents a UAV trajectory prediction method. The author may refer to the following paper for comparison: https://ieeexplore.ieee.org/document/10214303

Comments on the Quality of English Language

N/A

Author Response

Comments 1: The author uses two aircraft models for simulation. The parameters and differences of these models require more detailed explanation.

Response 1: Disagreed. The above analysis of aircraft characteristics is sufficient to identify the advantages of the selected research methods. Also, the analysis of aircraft characteristics shows the feasibility of further research and analysis based on reports on actual flights (taking into account weather conditions and aircraft characteristics).

Comments 2:  The paper presents a UAV trajectory prediction method. The author may refer to the following paper for comparison: https://ieeexplore.ieee.org/document/10214303

Response 2: Not applicable. The authors do not consider and did not aim to calculate optimal routes for UAVs, since these are fundamentally different aircraft (with different technical characteristics in terms of power and weight distribution, as well as behavior in different weather conditions). For these types of aircraft (UAVs), there are other goals and constraints that require different approaches to analyzing and finding optimal routes, which may also affect the choice of algorithms.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This article provides a comprehensive analysis of existing approaches to optimizing airline routes, their advantages and disadvantages, and possible areas for their improvement. Although the main results of this paper seem to be correct, I think that this paper is not organized well, which has a seriously influence on the reading of this paper.

 

1. The author's comparison of the four algorithms is too superficial and lacks specific data support.

 

2. The simulation can be expanded. The results are too theoretical and it is better to provide some more physical examples to show the effectiveness of the proposed results.

 

3. The contribution of this paper should further be demonstrated. Specially, compared with other existing method, the main difficulty of this paper should be stated clearly.

4. The author claims to have proposed improvement methods for all four algorithms, but the author's improvements are not improvements to the algorithms themselves, but only changes the corresponding estimated total cost function. This is a natural idea, therefore, the reviewer believes that the innovation is not significant.

Author Response

Comments 1:

1. The author's comparison of the four algorithms is too superficial and lacks specific data support.

Response 1: Thank you for pointing this out.

The algorithms were analyzed in terms of finding optimal routes in three-dimensional space, taking into account the possibility of imposing additional conditions and restrictions on the decision-making process for route optimization.

This analysis was conducted on the basis of mathematical modeling, which showed the advantages and disadvantages of the algorithms when additional conditions were imposed on the studied route and mathematical models of the aircraft.

The in-depth analysis of the algorithms will continue based on real flight reports, taking into account additional conditions that affect the efficiency of the selected route. This will be described in the following articles, which will be a logical continuation of the chosen research direction.

Comments 2:

2. The simulation can be expanded. The results are too theoretical and it is better to provide some more physical examples to show the effectiveness of the proposed results.

Response 2: See response for Comment 1

Comments 3:

3.The contribution of this paper should further be demonstrated. Specially, compared with other existing method, the main difficulty of this paper should be stated clearly.

 

Response 3:  Thank you for your comment.

The complexity of these studies and the chosen direction lies in the attempt to find the optimal route when applying multi-criteria constraints in finding the optimal route.

At the same time, in the section of the review of existing studies that have been taken into account, it can be observed that the authors focus on finding optimal options using only one constraint factor, whether it is weather conditions or changes in airspace, etc.

Comments 4:

4. The author claims to have proposed improvement methods for all four algorithms, but the author's improvements are not improvements to the algorithms themselves, but only changes the corresponding estimated total cost function. This is a natural idea, therefore, the reviewer believes that the innovation is not significant.

Response 4: The essence of the comment is not formulated.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Editor,

These are my comments and proposals:

• In the manuscript, you mentioned that modeling optimal flight paths is a complex aviation problem. In this regard, I would ask you to start with the goals of minimizing fuel consumption, flight time, avoiding weather conditions, reducing emissions (CO₂, NOₓ), and maximizing passenger comfort. I would ask you to write one sentence about each item, although it is mentioned later in the literature review. Here, we need an introductory analysis and classification.
• Before you start to model the optimal ones, it would be interesting to say something about variables such as aircraft type, airport type, wind data, weather data, and air traffic restrictions. Please be brief, about one paragraph.
• As a method for solving the problem, your work uses A (and variations) or Dijkstra’s algorithm. In one or two sentences at most, can you mention that there are also Dynamic Programming (DP), Genetic Algorithm (GA), Optimal Control Theory, and Machine Learning Algorithms? Please also provide literature sources if possible.
• You said: ”Improving existing algorithms and developing new technological solutions to optimize aircraft routes is a key strategy for enhancing the efficiency, sustainability, and resilience of air travel.” In order to optimize flight duration and fuel consumption, the application of algorithms A*, B, C, and D (or generally, A* and its variants) involves finding the optimal path while minimizing flight duration, reducing fuel consumption (based on aircraft performance), and route constraints. Later, it was mentioned in the paper, but we need your opinion and some analysis.
• It would be desirable to create an introductory table explaining the A*, B, C, and D Algorithms in more detail. The table should contain the name of the algorithm and its characteristic applications. They are all mentioned later, but it would be interesting to include an initial explanation for easier following.
• Pay attention to the nomenclature of numbers. For example, on page 5, after ”Advantages of the A* algorithm,” the number must start from number 1, not from number 6. The same goes for page 18.
• Pay attention to the format of tables and figures. Everything must be uniform.
• Recheck the references because there are discrepancies.

Comments for author File: Comments.pdf

Author Response

Comments 1: In the manuscript, you mentioned that modeling optimal flight paths is a complex aviation problem. In this regard, I would ask you to start with the goals of minimizing fuel consumption, flight time, avoiding weather conditions, reducing emissions (CO₂, NOₓ), and maximizing passenger comfort. I would ask you to write one sentence about each item, although it is mentioned later in the literature review. Here, we need an introductory analysis and classification.

Response 1: Thank you for pointing this out. The introduction to the article was written with a generalized description of the research presented in the article (without duplicating the results of the review or analysis of known works and existing studies) to avoid unnecessary duplication and repetition of conclusions and details that will be further disclosed in the article.

The article has been repeatedly edited to remove repetitions as a result of the previous peer review.

Comments 2: Before you start to model the optimal ones, it would be interesting to say something about variables such as aircraft type, airport type, wind data, weather data, and air traffic restrictions. Please be brief, about one paragraph.

Response 2:  Thank you for pointing this out. We have made some corrections to the article and highlighted the updates in red. The application of the proposed improvements on real-life examples with the analysis of flight reports will be the subject of further research, which will be reflected in the following articles.

Comments 3: As a method for solving the problem, your work uses A (and variations) or Dijkstra’s algorithm. In one or two sentences at most, can you mention that there are also Dynamic Programming (DP), Genetic Algorithm (GA), Optimal Control Theory, and Machine Learning Algorithms? Please also provide literature sources if possible.

Response 3:  Thank you for pointing this out. These algorithms were not considered in terms of additional operations required to build links and a table of edge efficiency weights (as well as in terms of mathematical complexity for building links or genomes).

Comments 4: You said: ”Improving existing algorithms and developing new technological solutions to optimize aircraft routes is a key strategy for enhancing the efficiency, sustainability, and resilience of air travel.” In order to optimize flight duration and fuel consumption, the application of algorithms A*, B, C, and D (or generally, A* and its variants) involves finding the optimal path while minimizing flight duration, reducing fuel consumption (based on aircraft performance), and route constraints. Later, it was mentioned in the paper, but we need your opinion and some analysis.

Response 4:  Thank you for your comments. We try to avoid repetition in the presentation of the article, as other reviewers have drawn our attention to this. The algorithms presented in the article provide a good compromise between route optimization and the time spent searching for it.

Comments 5: It would be desirable to create an introductory table explaining the A*, B, C, and D Algorithms in more detail. The table should contain the name of the algorithm and its characteristic applications. They are all mentioned later, but it would be interesting to include an initial explanation for easier following.

Response 5: Thank you for pointing this out. We try to avoid repetition of information in the presentation of the article.

Comments 6: Pay attention to the nomenclature of numbers. For example, on page 5, after ”Advantages of the A* algorithm,” the number must start from number 1, not from number 6. The same goes for page 18.

Response 6: Agreed. Article changed.

Comments 7: Pay attention to the format of tables and figures. Everything must be uniform.

Response 7: Agreed. Article changed.

Comments 8: Recheck the references because there are discrepancies.

Response 8: Thank you for pointing this out.  We have reviewed a list of literature sources.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In my initial review report, I noted that the authors present a systematic analysis of routing algorithms in dynamic environments. They examine traditional methods such as A*, B*, D*, and Dijkstra while proposing an approach that integrates real-time parameters into flight planning. The paper models flight paths and compares the strengths and weaknesses of both conventional and enhanced methods. The study investigates various factors, including weather, traffic, economic conditions, and aircraft characteristics, which adds a practical dimension to the research. Overall, the authors provide a balanced discussion, highlighting improvements in decision-making efficiency alongside the limitations of current approaches.

In response to reviewer feedback, the authors have revised the manuscript accordingly. They have explained the justification for selecting specific optimization algorithms by clarifying why these algorithms were chosen over others and by including tests of less popular methods to assess performance in dynamic, multi-criteria environments. Additionally, the quality of Figures 1, 3, and 4 has been improved to ensure higher resolution, and the interactive warning message ("AI-generated content may be incorrect") has been clarified to enhance the perceived reliability of the visuals. The revised manuscript also offers more detailed plans for future research, thereby strengthening the technical and practical foundations of the paper.

In my opinion the paper can be accept in present form.

Author Response

Comments 1: In my initial review report, I noted that the authors present a systematic analysis of routing algorithms in dynamic environments. They examine traditional methods such as A*, B*, D*, and Dijkstra while proposing an approach that integrates real-time parameters into flight planning. The paper models flight paths and compares the strengths and weaknesses of both conventional and enhanced methods. The study investigates various factors, including weather, traffic, economic conditions, and aircraft characteristics, which adds a practical dimension to the research. Overall, the authors provide a balanced discussion, highlighting improvements in decision-making efficiency alongside the limitations of current approaches.

In response to reviewer feedback, the authors have revised the manuscript accordingly. They have explained the justification for selecting specific optimization algorithms by clarifying why these algorithms were chosen over others and by including tests of less popular methods to assess performance in dynamic, multi-criteria environments. Additionally, the quality of Figures 1, 3, and 4 has been improved to ensure higher resolution, and the interactive warning message ("AI-generated content may be incorrect") has been clarified to enhance the perceived reliability of the visuals. The revised manuscript also offers more detailed plans for future research, thereby strengthening the technical and practical foundations of the paper.

In my opinion the paper can be accept in present form.

Response 1:

Dear Reviewer 1,

We sincerely thank you for your comments and for the time you took to review our article.

Thanks to you, we were able to make improvements to our article.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The authors provide a comprehensive review of classical pathfinding algorithms and propose an extended model that integrates additional real-world factors into the route cost function. However, while the scope and intent of the study are relevant, several critical issues related to methodological rigor, experimental design, and algorithmic novelty need to be addressed before the manuscript can be considered for publication.

Lack of Algorithmic Innovation
The so-called “improved solution” lacks a clear definition or formalization. While the authors mention adding weather and fuel cost penalties to the evaluation functions, this is conceptually straightforward and has been explored in existing literature. There is no novel heuristic design, learning-based component, or structural enhancement to distinguish the proposed method from existing works.

Insufficient Experimental Validation
The experimental design is vague and lacks reproducibility:

The source and structure of the input data (e.g., weather data, aircraft performance profiles) are not fully documented.

No clear information is provided about simulation platforms, code frameworks, or statistical validation methods.

Tables report average values without confidence intervals, standard deviation, or statistical significance tests.

Three-Dimensional Path Modeling Remains Superficial
The manuscript claims to address 3D trajectory optimization, yet no detailed visualizations or simulation results (e.g., altitude profiles, 3D flight tracks) are provided. Most illustrations are limited to tables and verbal descriptions.

Missing System-Level Considerations
The paper does not discuss how the proposed solution would integrate with real-world aviation systems (e.g., dispatch tools, flight management systems). Critical aspects such as response time, scalability, and deployment in operational environments are missing.

Writing and Structural Issues

The language is at times repetitive or informal.

The tables are dense and underexplained, and important insights could be better conveyed via plots or figures (e.g., comparative bar charts, trajectory maps).

Several sections (especially Section 4 and 5) read more like an internal report than a scientific analysis.

Comments on the Quality of English Language

N/A

Author Response

Comments 1: Lack of Algorithmic Innovation
The so-called “improved solution” lacks a clear definition or formalization. While the authors mention adding weather and fuel cost penalties to the evaluation functions, this is conceptually straightforward and has been explored in existing literature. There is no novel heuristic design, learning-based component, or structural enhancement to distinguish the proposed method from existing works.

Response 1: Disagreed. The paper considers the option of optimizing the quality of a flight route under certain conditions (R3*T) in the terminal space. It was important to build a risk function for a given set of factors (under conditions of uncertainty in the terminal-spatial interval of the route trajectory), rather than solving problems in a global formulation.

Most of the works we have reviewed demonstrate results based on one of the criteria and optimize algorithms by focusing on a single criterion.

We are trying to combine many criteria to improve planning efficiency.

Comments 2:  Insufficient Experimental Validation
The experimental design is vague and lacks reproducibility:

Response 2: Thank you for pointing this out.  The vagueness of the design and reproducibility is due to the use of algorithms and improvements on the models that simulate various variations of factors and their impact on the result.

More detailed data is planned to be obtained by analyzing and overlaying reports of real flights and real data on the factors in which these flights took place.

Comments 3:  The source and structure of the input data (e.g., weather data, aircraft performance profiles) are not fully documented.

Response 3: Ignored. Data are proprietary information.

Comments 4:  No clear information is provided about simulation platforms, code frameworks, or statistical validation methods.

Response 4: Thank you for your comment. We will take this aspect into account in future publications based on real data. This article is the beginning of research on finding optimal flight routes for aircraft under multi-criteria constraints and displaying the results based on modeling using aircraft models most commonly used in business aviation.

Comments 5: Tables report average values without confidence intervals, standard deviation, or statistical significance tests.

Response 5:  Thank you for your comment. We will take this aspect into account in future publications based on real data. This article is the beginning of research on finding optimal flight routes for aircraft under multi-criteria constraints and displaying the results based on modeling using aircraft models most commonly used in business aviation.

Comments 6: Three-Dimensional Path Modeling Remains Superficial
The manuscript claims to address 3D trajectory optimization, yet no detailed visualizations or simulation results (e.g., altitude profiles, 3D flight tracks) are provided. Most illustrations are limited to tables and verbal descriptions.

Response 6: Disagreed. Three-dimensional trajectory modeling is discussed in the Results section.

Comments 7:  Missing System-Level Considerations
The paper does not discuss how the proposed solution would integrate with real-world aviation systems (e.g., dispatch tools, flight management systems). Critical aspects such as response time, scalability, and deployment in operational environments are missing.

Response 7: Disagreed. These issues are mentioned in the Results and Discussion sections.

Comments 8: Writing and Structural Issues

The language is at times repetitive or informal.

Response 8: Disagreed. 

Comments 9: The tables are dense and underexplained, and important insights could be better conveyed via plots or figures (e.g., comparative bar charts, trajectory maps).

Response 9: Disagreed. Each table is explained in the text of the article.

Comments 10:  Several sections (especially Section 4 and 5) read more like an internal report than a scientific analysis.

Response 10: Disagreed. 

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The current version can be accepted.

Author Response

Comments 1:

The current version can be accepted.

Response 1: Dear Reviewer 3,

We sincerely thank you for your comments and for the time you took to review our article.

Thanks to you, we were able to make improvements to our article.

Author Response File: Author Response.docx