White-Tailed Eagle Algorithm for Global Optimization and Low-Cost and Low-CO₂ Emission Design of Retaining Structures

Round 1

Reviewer 1 Report

The study proposed a framework for white-tailed eagle algorithm for global optimization and low-cost and low-CO2 emission design of retaining structures. The results show that the proposed algorithm of optimization of retaining structures can be considered a useful tool for engineers. The paper includes new contributions with good merits for publication. However, a number of issues/errors in the manuscript are expected to be solved.

1- The authors may reorganize the abstract to make it reasonable and shed the light on the aim of the proposed work.

2- lines 226 to 252 should have more related citations ( not just one reference for the whole part).

3- Line 298, P_r is not mentioned in the equation.

4- Please recheck the numbering of the figures ( Figure 5 is missing ).

5- The review of optimization methods can be expanded, some works are recommended to be added, such as:‎

 Optimal Plastic Analysis and Design of Pile Foundations Under Reliable Conditions, Periodica Polytechnica Civil Engineering, 65(3), pp. 761–767, 2021. https://doi.org/10.3311/PPci.17402

Reliability based geometrically nonlinear bi-directional evolutionary structural optimization of elasto-plastic material. Scientific Reports, 12(1), 1-22.  Doi: 10.1038/s41598-022-09612-z”

Elasto-Plastic limit analysis of reliability based geometrically nonlinear bi-directional evolutionary topology optimization. Structures 34(December 2021):1720-1733. 10.1016/j.istruc.2021.08.105”

6- The novelty of the paper should be properly addressed in the abstract, the introduction, and the conclusion.

 

7- Please follow the instructions of the journal to prepare the paper (e.g., the font style and size, citation style … etc.).

Author Response

The study proposed a framework for white-tailed eagle algorithm for global optimization and low-cost and low-CO2 emission design of retaining structures. The results show that the proposed algorithm of optimization of retaining structures can be considered a useful tool for engineers. The paper includes new contributions with good merits for publication. However, a number of issues/errors in the manuscript are expected to be solved.

Comment 1- The authors may reorganize the abstract to make it reasonable and shed the light on the aim of the proposed work.

Reply: Thank you for your comment. According to the reviewer’s recommendation, the abstract is reorganized and modified to show the aim of the study. 

Comment 2- lines 226 to 252 should have more related citations ( not just one reference for the whole part).

Reply: Thank you for your notice. The authors considered the reviewer’s comments in the revised manuscript.

Comment 3- Line 298, P_r is not mentioned in the equation.

Reply: Thank you for your attention. Actually, it was a typo. P_r changed to E_r in the revised paper.

 

Comment 4- Please recheck the numbering of the figures ( Figure 5 is missing ).

Reply: Thank you for your attention. The figures’ numbers are modified in the revised paper.

Comment 5- The review of optimization methods can be expanded, some works are recommended to be added, such as:‎

 Optimal Plastic Analysis and Design of Pile Foundations Under Reliable Conditions, Periodica Polytechnica Civil Engineering, 65(3), pp. 761–767, 2021. https://doi.org/10.3311/PPci.17402

Reliability based geometrically nonlinear bi-directional evolutionary structural optimization of elasto-plastic material. Scientific Reports, 12(1), 1-22.  Doi: 10.1038/s41598-022-09612-z”

Elasto-Plastic limit analysis of reliability based geometrically nonlinear bi-directional evolutionary topology optimization. Structures 34(December 2021):1720-1733. 10.1016/j.istruc.2021.08.105”

Reply: Thank you for your comment. According to the reviewer’s recommendation, the mentioned references are added in lines 202 -206 of the revised manuscript.

Comment 6- The novelty of the paper should be properly addressed in the abstract, the introduction, and the conclusion.

Reply: Thank you for your notice! The authors considered the reviewer’s comments in the revised manuscript. The abstract and conclusion sections are modified. In addition, the main contributions of the study are added at the end of the introduction section.

Comment 7- Please follow the instructions of the journal to prepare the paper (e.g., the font style and size, citation style … etc.).

Reply: Thank you for your comment. The authors considered the reviewer’s comments in the revised manuscript.

 

We would like to, once again, appreciate your time and impressive review of our work. Hope the revised items can enhance the manuscript and provide acceptable research.

Author Response File: Author Response.docx

Reviewer 2 Report

In this study a novel and a simple nature-inspired algorithm namely the White-tailed Eagle Algorithm (WEA) inspired by the social life and hunting activity of white-tailed eagles is proposed for mainly low-cost and low-CO2 emission design of retaining structures. Initially the WTA is tested on 13 unimodal and multimodal benchmark test functions, and the obtained results are compared with those previously reported by some well-established optimization methods. Then the newly proposed WTA is used for design optimization of retaining structures under effect of seismic loading. There are two objectives as low-economic cost and low-CO2 emission. In a general perspective, it can be said that the paper fits the scope of the journal. But its content should majorly be improved in several aspects before to be recommended it for publication. Please see the major revision comments below and address all of them in revised version of the study for re-evaluation.

1) The principal gist of this study is not reached easily. The originality and the novelty of the study reflecting the main gist of the paper should more clearly be mentioned in the Introduction section.

2) The Introduction section contains a lot of separate short paragraphs. It should be reduced and collected into three and/or four paragraphs. It is more appropriate that the first sentences should introduce the principal definition of the paragraph.

3) A lot of recent well-known multi-objective metaheuristic algorithm have been developed recently as defined in Related works section. But there is no any justification on newly proposed WTA.

4) The quality of the figures should be enhanced.

5) The third section containing the newly proposed WTA. And, it is obvious that this section is the crucial part of the study. But in its current format it must majorly be revised and expanded by elaborately highlighting the promising aspects and the drawbacks of the existing algorithms and the supremacy of the proposed novel WTA.

6) The challenges of this study are unclear. What are difficult challenges of the proposed novel WTA?

7) The constraint handling strategies of the proposed method are not presented; e.g., How does it handle with constraint violations? Is there any penalty method? How does it tackle with premature solutions?

8) What is the specific termination criterion of the optimization process; e.g., the fitness of the elite design changes little between consecutive iterations? Please elaborate it.

9) The benchmark test problems and retaining structures are selected as to be designed by using continuous design variable. But, since the WTA is a newly proposed metaheuristic algorithm, the algorithmic performance of it should be verified on both various engineering design problems and retaining wall problems including discrete/integer design variables. Please have a look at doi.org/10.3390/math10030327 (Mathematics 2022, 10, 327) as a reference.

10) The Conclusion section should be expanded in terms of content. Hence, this section should be revised to present concise conclusions as bullet points and/or numbered entries. Namely, the conclusions and fundamental motivations of the study should be added in a clearer way in this section.

11) The English of the manuscript necessities major revisions. There are a lot of grammatical errors and instances of badly worded/constructed sentences in the manuscript. Please carefully proofread the whole manuscript once again.

Author Response

Reviewer #2: In this study a novel and a simple nature-inspired algorithm namely the White-tailed Eagle Algorithm (WEA) inspired by the social life and hunting activity of white-tailed eagles is proposed for mainly low-cost and low-CO2 emission design of retaining structures. Initially the WTA is tested on 13 unimodal and multimodal benchmark test functions, and the obtained results are compared with those previously reported by some well-established optimization methods. Then the newly proposed WTA is used for design optimization of retaining structures under effect of seismic loading. There are two objectives as low-economic cost and low-CO2 emission. In a general perspective, it can be said that the paper fits the scope of the journal. But its content should majorly be improved in several aspects before to be recommended it for publication. Please see the major revision comments below and address all of them in revised version of the study for re-evaluation. Comment 1) The principal gist of this study is not reached easily. The originality and the novelty of the study reflecting the main gist of the paper should more clearly be mentioned in the Introduction section. Reply: Thank you for your valuable comment. According to the reviewer’s recommendation, the main contributions of the paper reflecting the main gist of the paper have been presented at the end of the introduction section.     Comment 2) The Introduction section contains a lot of separate short paragraphs. It should be reduced and collected into three and/or four paragraphs. It is more appropriate that the first sentences should introduce the principal definition of the paragraph. Reply: Thank you for your comment. The authors considered the reviewer’s comments in the revised manuscript. Comment 3) A lot of recent well-known multi-objective metaheuristic algorithm have been developed recently as defined in Related works section. But there is no any justification on newly proposed WTA. Reply: Thank you for pointing out this aspect. Actually, as mentioned in the third paragraph of the introduction (line 77), according to the No Free Lunch (NFL) theorem, there is no metaheuristic that can solve all optimization issues effectively. In other words, a metaheuristic may perform excellently on some problems while doing poorly on others. Obviously, the NFL keeps this field of research quite active, resulting in the introduction of new metaheuristics and improvements to current techniques every year. This also motivates our efforts to introduce a more efficient and successful metaheuristic based on white-tailed eagle inspiration. Comment 4) The quality of the figures should be enhanced. Reply: Thank you for your notice! The authors considered the reviewer’s comments in the revised manuscript. The low-quality figures, like Figures 1, 2 and 3, are modified. Comment 5) The third section containing the newly proposed WTA. And, it is obvious that this section is the crucial part of the study. But in its current format it must majorly be revised and expanded by elaborately highlighting the promising aspects and the drawbacks of the existing algorithms and the supremacy of the proposed novel WTA. Reply: Thank you for the comment. According to the reviewer’s recommendation, section 3 is extended and the advantages of the proposed WEA have been presented in the revised paper (lines 249-253). Comment 6) The challenges of this study are unclear. What are difficult challenges of the proposed novel WTA? Reply: Thank you for your comment. Actually, as the title of the paper reveals, the main challenge of this study is proposing a new effective optimization algorithm for global optimization and seismic optimization of retaining structures by considering total cost and CO2 emission as objective functions. By the way, according to the reviewer’s comment, the abstract and conclusions of the revised paper are reorganized and modified to show the aim of the study. In addition, as mentioned in comment 1, the main contributions of the paper have been added at the end of the introduction section. Comment 7) The constraint handling strategies of the proposed method are not presented; e.g., How does it handle with constraint violations? Is there any penalty method? How does it tackle with premature solutions? Reply: Thank you for this valuable comment. As mentioned in lines 541-548 of the revised paper, the constraint optimization problem of retaining walls transforms into an unconstraint problem using the penalty function method as presented in Eq. (23). Comment 8) What is the specific termination criterion of the optimization process; e.g., the fitness of the elite design changes little between consecutive iterations? Please elaborate it. Reply: Thank you for your comment. As mentioned in lines 382-384, WEA has a simple structure and requires just two key parameters: the number of eagles (N) and the maximum iteration number (tMax). Actually, the termination criterion of the algorithm is the maximum number of iterations (tMax). As presented in Table 3, the maximum number of iterations is equal to 1000. Comment 9) The benchmark test problems and retaining structures are selected as to be designed by using continuous design variable. But, since the WTA is a newly proposed metaheuristic algorithm, the algorithmic performance of it should be verified on both various engineering design problems and retaining wall problems including discrete/integer design variables. Please have a look at doi.org/10.3390/math10030327 (Mathematics 2022, 10, 327) as a reference. Reply: Thank you for your comment. Actually, the proposed algorithm is verified using the commonly used benchmark functions for global optimization problems, and the obtained results are compared with other algorithms in Tables 4 and 5 and Figure 4. In addition, according to the title and the main contributions of the paper, to verify the effectiveness of the proposed method for the solution of real-world problems, the new method is applied to retaining wall optimization under static and seismic loads. However, in the mentioned reference by the respected reviewer, the suggested optimization algorithm is applied to different engineering problems based on the paper title and aim of the study (Parameters Optimization of Taguchi Method Integrated Hybrid Harmony Search Algorithm for Engineering Design Problems). Therefore, in the present study, the application of the new method to other engineering problems may be beyond the scope of the paper. In addition, in the current study, the initial version of the WEA is proposed and the binary version of the algorithm for discrete optimization problems will be presented in a future study. It is a normal routine in the field of optimization algorithms. For example, PSO [1] and its binary version [2], GSA [3] and its binary version [4], bat algorithm [5] and its binary version [6], and so on. However, proposing the binary version of the algorithm and application of the new method to other optimization problems are mentioned at the end of the conclusion section as “suggestions for future work”. Comment 10) The Conclusion section should be expanded in terms of content. Hence, this section should be revised to present concise conclusions as bullet points and/or numbered entries. Namely, the conclusions and fundamental motivations of the study should be added in a clearer way in this section. Reply: Thank you for your notice! According to the reviewer’s recommendation, the conclusion section is modified. Comment 11) The English of the manuscript necessities major revisions. There are a lot of grammatical errors and instances of badly worded/constructed sentences in the manuscript. Please carefully proofread the whole manuscript once again. Reply: Thank you for your notice! The authors considered the reviewer’s comment and proofread the whole manuscript for grammar and style of writing.   We would like to, once again, appreciate your time and impressive review of our work. Hope the revised items can enhance the manuscript and provide acceptable research.

 

 

 

1. Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the Proceedings of ICNN'95-international conference on neural networks, Perth, WA, Australia, 1995; pp. 1942-1948.
2. Kennedy, J.; Eberhart, R.C. A discrete binary version of the particle swarm algorithm. In Proceedings of the 1997 IEEE International conference on systems, man, and cybernetics. Computational cybernetics and simulation, 1997; pp. 4104-4108.
3. Rashedi, E.; Nezamabadi-pour, H.; Saryazdi, S. GSA: a gravitational search algorithm. Information Sciences 2009, 179, 2232-2248.
4. Rashedi, E.; Nezamabadi-Pour, H.; Saryazdi, S. BGSA: binary gravitational search algorithm. Natural computing 2010, 9, 727-745.
5. Yang, X.S.; Gandomi, A.H. Bat algorithm: a novel approach for global engineering optimization. Engineering computations 2012.
6. Mirjalili, S.; Mirjalili, S.M.; Yang, X.-S. Binary bat algorithm. Neural Computing and Applications 2014, 25, 663-681.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I suggest accepting the manuscript.

Reviewer 2 Report

In its present revised form, the paper can now be accepted for publication.