Swarm Division-Based Aircraft Velocity Obstacle Optimization Considering Low-Carbon Emissions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors present a swarm division strategy to refine the Velocity Obstacle method and reduce CO2 emissions. I recommend minor revisions focused on the following:

 

1.      Use first name abbreviations in references per journal style.

2.      Acknowledge the CO2 simulation's limitations and suggest expanding to full flight dynamics in future work. There are some air traffic simulation tools that the authors can consider. These two recent open-source platforms are as examples:

 

Hoekstra, Jacco M., and Joost Ellerbroek. "Bluesky ATC simulator project: an open data and open source approach." Proceedings of the 7th international conference on research in air transportation. Vol. 131. USA/Europe: FAA/Eurocontrol, 2016.

 

Hui, Ka Yiu, et al. "AirTrafficSim: An open-source web-based air traffic simulation platform." Journal of Open Source Software 8.86 (2023): 4916.

 

3.      The computational efficiency is a critical point for this method, there are only 10 aircraft as the model input. I suggest the author elaborate more on the computational efficiency quantitatively and discuss how to improve it in future work.

4.      Table 3 description, what does it mean by “Four Different Types of Aircraft”? If I get it right, there are 10 aircraft and 5 aircraft types as shown in Table 1.

5.      Revise overlapped fraction in Equation 4.

6.      Line 252. The optimization problem for the ellipse protection zone is an important part of this paper, please elaborate.

7.      Line 274, the sentence is compounded, confusing, and incomplete, please revise.

8.      Line 296, as I understand, V_j*t is already the distance, what does P V_j*t P mean? Is it a typo?

9.      Line 303, it’s better to add the reference of the Minkowski vector

10.  For the velocity vector, what does the different superscript mean? For instance, what is the difference between velocity in Line 311 and Line 275 with the same subscript “i”?

11.  Line 371, “next”

12.  Eq 14, please elaborate, these are very informative formulation which requires more explanations

 

Addressing these areas related to presentation, explanations, and clarity will further strengthen the quality of the paper. Please let me know if any comments need expansion or examples. I appreciate the authors' work and believe these revisions will nicely polish the manuscript.

Comments on the Quality of English Language

Minor editing of English language required.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

this paper talk about A dynamic elliptical protection zone model forms the core of this innovative approach. Specifically, this dynamic elliptical protection zone is created based on the difference in aircraft velocity, and a swarm division strategy is introduced in this process.

we need to update introduction with the receach goals 

please add a related work section to talk about the previous work you mention in the refernces 

please list the prevoius results in the topics as it's important for the reader

your simulations models used pythons you should talk about other methods can be used to simulate the model

pleae review the journal format for the size of the mathematical equations like 14 and discuss it more 

figure 11 must be as journal format 

all tables data size and font not like the journla format please update

figure 14 and figure 17 need update also 

please add more finiding from your research in the concolosion section 

also add a future work 

thanks

Comments on the Quality of English Language

english need revision

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

To improve the quality of the paper, the reviewer gives the following comments.

(1) In Section 1, many research results have not been provided with their citations, for example, “HyunJae J and Du Zhe, in their comparative analysis of the VO and Artificial Potential Field (APF) algorithms, highlighted the VO's superior capability in maintaining safe distances and aiding in formation transformations”.

(2) Section 2 says “Swarm S={S₁, S₂}, with S₁={P₁, P₂, P₃} and S₂={P₄, P₅}, i=1, 2, 3”. However, the index i is never used here.

(3) The equation (1) does not address the ellipse's minor semi-axis b_i. Please explain it in more detail.

(4) According to the equation (2), the S is a condition not a conflict area. Please ensure the accuracy of all formulas in the paper.

(5) Section 3.3.1.1 says “The Minkowski vector is denoted by the ⊕ operation”. This makes the reviewer confused. A vector is not an operation.

(6) Please show how to use the equation (14) to compute the variables.

(7) In Figure 10, the placement of Yes/No in the first decision box is incorrect.

(8)  It claims that “In Table 2, the results showed that employing the speed-based dynamic protection zone in the experimental group results in a 24.07% reduction in adjustment requirements compared to the traditional protection zone, characterized by minimal relief heading and velocity”. However, a 24.07% reduction is uneasily found in Table 2.

Comments on the Quality of English Language

The paper writing should be improved. The writing errors include “the aircraft on the same route, of the same type, with similar vector velocities and distances, are divided into swarms using clustering” in lines 13-15, “This ensures that aircraft within a swarm avoid conflicts during the relief phase” in lines 139-140, and “the aircraft are simplified as mass points” in lines 159-160, etc.

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

I congratulate the authors for their work.

Remarks:

-lines 153-155: the index "i" refers to "swarms Si", it has nothing to do with the explanation of "S1 and S2"

- the color of the S1 cluster would be useful if it were different from the red spectrum, like the cone

- the writing of the velocity vector in the text is not clearly distinguishable, the letter "r" is not distinguishable

- some citations are written as an exponent (starting with line 270)

- improper spacing regarding punctuation marks, all text must be revised especially after notations (no space is left before them)

-lines 402-405 and Figure 9 it is not clear where E and F is defined. Reference to Figure 8(b) would be Figure 9(b)

-line 469, the reference "i=1,2,3" is not found in the context of the phrase.

-lines 536-544, it is not clear how to reach the consumption reduction of 72.47% and 1.34%, respectively.

- the DOI must be presented in the bibliography (where it exists), and some articles are not correctly identified, e.g. 9 (2021,11(5):2114-2114.), 10 (2017,2017.15(0): A14-A14), 12 (2021,11(10):4706-4706.), 16 (2021,21 (13):4389-4389.), 25 (2022,22(5):1947- 1947), 27 (2017,9(7):1174-1174.). Don't confuse page number with article number.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

(1) The paper still did not provide the full citations for previous research results, for example, “Building on this advancement, Pan W integrated the particle swarm optimization algorithm with the VO method, streamlining the resolution of flight conflicts in two-dimensional spaces and enhancing computational efficiency”.

(2)  The description of Algorithm 1 is not good. The reviewer fails to find the input and the output of Algorithm 1.

Comments on the Quality of English Language

English language still needs to be polished. The errors sentences include “denotes the indexer of the swarm” (index?) in line 160, “Figure 15(a)-(d) demonstrate” in line 581 and “Figure 15(e)-(h) illustrates” in line 582, etc.

Author Response

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Author Response File: Author Response.pdf