Hybrid Strategy Improved Beetle Antennae Search Algorithm and Application

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

authors have introduced a Hybrid Strategy Based Beetle Antennae search algorithm. Comparative analysis with alternative algorithms has been presented and the proposed algorithm confirms its superiority, which is subsequently applied to the altitude compensation module of a solar wing-based gravity offloading device to validate its efficacy in practical settings. The study demonstrates the effectiveness and practical applicability of HSBAS in addressing real-world engineering challenges. However, some concerns must be addressed.

1. The computational complexity of the proposed algorithm must be discussed

2. According to authors why the proposed algorithm performs better than other, in other terms what is the deferent between the presented algorithm that allow the proposed one to be the best one.

3. Figure 4 show that the proposed algorithm has similar performance with benchmarked algorithms, there is threshold effect between the performance of these algorithms

4. Many mathematical equations are given without background and references

5. What is exactly the novelty of this works: is it its applicability to the mechanical design or something else, please state clear the novelty of the paper

6. Based on figure 4, if authors can combine the proposed algorithme with PSO algorithme it will give better result, please discuss the feasibility of this proposition.

 

 

 

 

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Dear Reviewers,

Thank you for your letter dated March 07. We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. (red).

1. The computational complexity of the proposed algorithm must be discussed.

We are grateful for the instructive suggestion. In response to this suggestion, the paper has added Section 4.3. on algorithmic computational complexity analysis and further subdivided the Chapter 4 sections.

2. According to authors why the proposed algorithm performs better than other, in other terms what is the deferent between the presented algorithm that allow the proposed one to be the best one.

We think this is an excellent suggestion. The algorithm proposed in this paper is mainly improved by adding several strategies to the Beetle Antennae search algorithm. Compared with GA and PSO, in fact, the two algorithms have their own advantages, only that the algorithm proposed in this paper is more adaptable to the multidimensional optimization of institutions. We have re-written Section 4.2. according to the Reviewer’s suggestion. This paper has modified the description of the algorithm calibration comparison to highlight the advantages of the algorithm over the rest of the algorithms.

3. Figure 4 show that the proposed algorithm has similar performance with benchmarked algorithms, there is threshold effect between the performance of these algorithms.

We are grateful for the instructive suggestion. The threshold effect of the HSBAS algorithm is further complemented in the algorithm convergence analysis in Section 4.2 according to the Reviewer’s suggestion. The stage at which it starts to converge is described and briefly compared with the other three algorithms.

4. Many mathematical equations are given without background and references.

We are grateful for the instructive suggestion. In response to your valuable suggestion, We have checked the literature carefully and labeled the formulas cited in the manuscript, in the hope of clearly conveying the provenance of the formulas cited in the text.

5. What is exactly the novelty of this works: is it its applicability to the mechanical design or something else, please state clear the novelty of the paper.

We are grateful for the instructive suggestion. This work is applied to multi-dimensional optimization of mechanical design. For this suggestion, we have revised the application scenarios of the algorithm in the abstract introduction and conclusion of this paper to clarify the application novelty of the work further.

6. Based on figure 4, if authors can combine the proposed algorithme with PSO algorithme it will give better result, please discuss the feasibility of this proposition.

We are grateful for the instructive suggestion. The algorithm combining PSO and BAS algorithm is indeed also a very worthwhile research direction, and there are also previous researchers who have studied and applied PSO and BAS algorithms. However, considering that the HSBAS algorithm proposed in this paper has a lower complexity than the algorithm combining PSO and BAS, and the algorithm proposed in this paper is also able to converge to a certain accuracy value in solving the multi-dimensional optimization of the mechanism, which meets the design requirements. On this basis, the algorithm in this paper is proposed. Of course, if we can further combine PSO and HSBAS, we believe that the accuracy of the algorithm can be further improved and can be applied in more delicate design fields. Based on the combination of your and another reviewer's suggestions, this part is briefly discussed in the conclusion section of Chapter VI.

Thanks again!

Sincerely,

Shasha Lu

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I recommend this paper for publication after minor revision.

Comments for author File: Comments.pdf

Author Response

Dear Reviewers,

Thank you for your letter dated March 11. We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. (red).

1. In Section 3.1, the authors introduce an adaptive update step length strategy to balance the global search capability and convergence speed. How did the authors determine the values of the exploration step threshold (δthreshold) and the maximum exploration step lengthening number (jmax)? It would be helpful if the authors could provide more information on the selection criteria for these parameters and discuss their impact on the algorithm's performance.

We are grateful for the instructive suggestion. In 3.1 of the manuscript, according to Reviewer’s suggestion, we have added discussion on the value of step threshold (δthreshold)  and maximum exploration step lengthening number (jmax), as well as their impact on the performance of the algorithm, to make the algorithm more complete.

 

2. In Section 5.2, the authors mention the use of a penalty function method to handle constraints in the optimization problem. How was the penalty factor λ determined, and what is its sensitivity to the algorithm's performance?

We think this is an excellent suggestion. According to Reviewer’s suggestion, we have added the information about penalty factor λ in Section 5.2, including the determining factor and its effect on the algorithm.

 

3. The authors mention that further improvement of the HSBAS algorithm can focus on joining the group strategy or combining it with other algorithms. Can the authors elaborate on the potential benefits and challenges of incorporating these strategies into the current HSBAS framework? Discussing the future research directions in more detail would strengthen the paper's contribution.

We are grateful for the instructive suggestion. According to Reviewer’s suggestion, we have added this part of the supplement in the Chapter 6, which mainly analyzes the feasibility of combining PSO and BAS algorithms and HSBAS with other strategies and algorithms.

 

Thanks again!

Sincerely,

Shasha Lu

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

applsci-2918862

The manuscript with the title “Hybrid strategy improved Beetle Antennae search algorithm and application” proposes a sophisticated approach to enhancing the Beetle Antennae Search (BAS) algorithm by integrating adaptive variable step-size strategy, multi-directional exploration, and Lens Opposition-Based Learning (LOBL). These modifications are aimed at overcoming the limitations of the traditional BAS, particularly its propensity for getting trapped in local optima and its limited efficacy in high-dimensional optimization problems. The manuscript contributes to the field of computational optimization and algorithm development.

However, the manuscript also has some limitations and weaknesses that need to be addressed and improved. Here are some specific suggestions and recommendations for the article:

1. Abstract Enhancement: The abstract should include specific quantitative data to substantiate the claims of the algorithm’s effectiveness and its comparative advantage over existing methods.
2. Figure Presentation: Ensure that all figures are discussed in the text before they are presented along with their captions. This helps in maintaining a logical flow and aids reader comprehension.
3. Consistency in Terminology: Decide on a consistent format for referring to figures throughout the manuscript (either “Figure” or “Fig.”) and apply it uniformly to avoid confusion.
4. Conclusions with Data: Strengthen the conclusions section by incorporating quantitative data from the results, which will provide a solid backing for the conclusions drawn.

Addressing these points will require a major revision of the manuscript. By implementing these suggestions, the manuscript’s clarity, consistency, and overall quality will be significantly enhanced, making it a stronger candidate for publication.

Author Response

Dear Reviewers,

Thank you for your letter dated March 12. We feel great thanks for your professional review work on our article. As you are concerned, there are several problems that need to be addressed. According to your and other reviewers’ nice suggestions, we have made extensive corrections to our previous draft, the detailed corrections are listed below. (red).

1.abstract Enhancement: The abstract should include specific quantitative data to substantiate the claims of the algorithm’s effectiveness and its comparative advantage over existing methods.

We are grateful for the instructive suggestion. As suggested by the reviewer, some specific data have been added to the abstract of the manuscript to support the conclusion of this work.

 

2.Figure Presentation: Ensure that all figures are discussed in the text before they are presented along with their captions. This helps in maintaining a logical flow and aids reader comprehension.

We sincerely thank the reviewer for careful reading. As suggested by the reviewer, all the pictures in the manuscript have been added to the place discussed in the first time, hoping to make it clear.

 

3.Consistency in Terminology: Decide on a consistent format for referring to figures throughout the manuscript (either “Figure” or “Fig.”) and apply it uniformly to avoid confusion.

We sincerely thank the reviewer for careful reading. As suggested by the reviewer, the figure numbers in this manuscript have been changed to Fig. to avoid confusion.

 

4.Conclusions with Data: Strengthen the conclusions section by incorporating quantitative data from the results, which will provide a solid backing for the conclusions drawn.

We are grateful for the instructive suggestion. As suggested by the reviewer, some specific data have been added to the Chapter VI Conclusion of the manuscript to provide a solid backing for the conclusions drawn.

 

Thanks again!

Sincerely,

Shasha Lu

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

all my concerns were addressed. 

Reviewer 3 Report

Comments and Suggestions for Authors

I have thoroughly evaluated the submission and have decided to accept it in its present form.