A New Lagrangian Problem Crossover—A Systematic Review and Meta-Analysis of Crossover Standards
Round 1
Reviewer 1 Report
The paper entitled 'A New Lagrangian Problem Crossover: A Systematic Review and Meta-Analysis of Crossover Standards' presents an overview of crossover standards classification that has been used by researchers for solving engineering operations and problem representation. Moreover, the authors proposed the formulation of the Lagrangian Problem Crossover. I think the article has some potential, however:
1. The paper should undergo linguistic correction (e.g. abbreviations should be introduced only if they are used later in the work, the text lacks the introduction of abbreviations that were introduced in the abstract, on line 122 'for' should be replaced by 'For', on line 164 instead 'Harris hawks optimization' should be 'Harris Hawks Optimization'. Moreover, there is no description of the Y axis for Figures 20-28).
2. Figures should be added in better quality. I also think that pseudocodes should be changed by adding line numbers (and indentation for if operations in Figure 6) and you should unify them (e.g. the then keyword is missing in Figure 6).
3. In my opinion, the weakest part of the work are the deficiencies in the methodology that make it impossible to honestly assess the effectiveness of the Lagrangian Problem Crossover. I think that you should generate a minimum of 30 different pairs of chromosomes for each task and perform optimization using three operators for each of them. Then compare the final results obtained by the three methods by presenting the average result and the standard deviation. In addition, the results should be confirmed by statistical tests (e.g. Wilcoxon). It is also worth presenting an overview of the execution time (giving the configuration of the computer used). Moreover, I think that you should write directly that you maximized the given functions.
Author Response
Response Letter (For Reviewer)
Thank you for taking the time to leave your judgments. We appreciate the effort you put into your comments on our Manuscript on behalf of my co-author. Your feedback is so beneficial. We carefully considered the feedback and made significant changes to the Manuscript. Your valuable and incisive remarks have inspired potential changes to the present version. The authors have given great thought to the comments and have done our best to respond to each one.
Our replies are listed below in a point-by-point format. We've provided a corrected version of our Manuscript, with all of the revisions highlighted in Yellow colour.
- The paper should undergo linguistic correction (e.g. abbreviations should be introduced only if they are used later in the work, the text lacks the introduction of abbreviations that were introduced in the abstract, on line 122 'for' should be replaced by 'For', on line 164 instead 'Harris hawks optimization' should be 'Harris Hawks Optimization'. Moreover, there is no description of the Y axis for Figures 20-28).
Author’s response
Many thanks for giving us this vital comment; we very much appreciate your comments and feedback. As a result of this feedback, this study will be able to control linguistic errors and check all punctuation marks in a significant way. All errors have been corrected during this major revision, as well as the deletion of all abbreviations that have not been used. As an example, lines (191 to 193) and throughout the manuscript as a whole. These uncontrollable errors occurred when the manuscript template was changed. But it wasn't supposed to happen. In addition, we have included the Y axis in the figures (20-28) and in the lines (620-621). Thank you for your accurate advice.
- Figures should be added in better quality. I also think that pseudocodes should be changed by adding line numbers (and indentation for if operations in Figure 6) and you should unify them (e.g. the then keyword is missing in Figure 6).
Author’s response
Thank you so very much for your suggestions. We tried to improve the quality of the Figures. We also added the line numbers for all pseudocodes in Figures (6,8, and 17) and unified them with (if operations) indentation.
- In my opinion, the weakest part of the work are the deficiencies in the methodology that make it impossible to honestly assess the effectiveness of the Lagrangian Problem Crossover.
Author’s response
Many thanks for giving us this vital comment; we very much appreciate your comments and feedback. This feedback has a significant impact on the study. As a result of this comment, we are encouraged to rewrite proposed section and test analyses. We added the experimental evaluation, which is divided into heuristic evaluation and exploitation with convergence evaluation. We hope to find all responses in subsections 5.1 and 5.2 and (Lines 572-649).
I think that you should generate a minimum of 30 different pairs of chromosomes for each task and perform optimization using three operators for each of them.
Author’s response
Thank you very much. We completely agree with your point. In general, we evaluated three standard operators and three random values [Lines 573 to 578, 610-625]. In spite of that, we evaluate by the comparison of convergence rate by LPB algorithm with adding new standard operator (Qubit-crossover) for other three standards at section (5.2) [Lines 627-649].
Then compare the final results obtained by the three methods by presenting the average result and the standard deviation. In addition, the results should be confirmed by statistical tests (e.g. Wilcoxon).
Author’s response
Thank you so very much for mentioning this point. Moreover, we examined how to select a statistical test according to data variable types and variance distributions. We tried to explain each point thoroughly. A second subsection (5.3) confirms all LPX results obtained in the previous subsections (5.1 and 5.2). A Wilcoxon signed-rank sum statistical test was performed. (Lines 650 to 668).
It is also worth presenting an overview of the execution time (giving the configuration of the computer used). Moreover, I think that you should write directly that you maximized the given functions.
Author’s response
Thank you for suggesting such a valuable point. For all four standards, we compared the results by elapsed time during the LPB algorithm test (Table 5) and your comment provided the opportunity for our study to be rich (Lines 645 to 649). In addition, we emphasized maximization of the given functions during the heuristic evaluation test (Lines 621-625).
*Note: While rewriting all sections, we did the highest quality language proofreading as per your suggestion.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1. It is recommended to determine the method for searching the eligible papers in this systematic review. How many articles are considered for this survey?
2. This study suffers from a lack of statistical analysis and visualization.
3. It is recommended to summarize the contribution of this study at the end of the introduction section.
4. Revising the abstract and highlighting this study's novelty is recommended.
5. Crossovers' weak points and strengths should be stated and summarized in a table.
6. The importance of this study is not evident in why the new lagrangian problem crossover is introduced.
7. The proposed method section should be rewritten.
8. It is recommended to boost the description of figure 18.
9. The crossover operator introduced in QANA: Quantum-based avian navigation optimizer algorithm can be compared with the new lagrangian problem crossover.
10. This study suffers from a lack of comprehensive experimental evaluation. It is recommended to boost this section.
11. The complexity of the new lagrangian problem crossover should be calculated and explained.
12. Comparing the new lagrangian problem crossover with the existing crossover is recommended.
Author Response
Response Letter
It could motivate the second party to advance if the first party occasionally criticizes how it performed at the beginning. Your advice was very helpful, and we continued to work on it until we changed the manuscript scientifically. As a result, we have worked intensively these days to improve the paper based on these useful comments.
For your valuable comments and evaluations, we hope you will find our revision a more acceptable alternative to our first draft. We carefully considered your feedback and made significant changes to the manuscript. Our replies are listed below in a step-by-step presentation. Also, we have provided a corrected version of our manuscript, with all the revisions highlighted in Yellow colour.
- It is recommended to determine the method for searching the eligible papers in this systematic review. How many articles are considered for this survey?
Author’s response
Thank you so very much for helping us to explain thoroughly. As part of our study, we focused on these papers that mention the standard of crossover most commonly used as an operator in population-based algorithms, especially for genetic algorithms. As a result, we specialized the query for this method of searching. (Line 131 to 147)
- This study suffers from a lack of statistical analysis and visualization.
Author’s response
Thank you for highlighting this crucial point. The use of statistical methods could help draw meaningful conclusions about these studies if they are related to non-parametric matching data. For this purpose, we added the subsection for our study about statistical analysis in section 5. A Wilcoxon signed-rank sum was used to determine the obtained results. All results are explained in Tables (6&7). Lines 650 to 669 provide more details.
- It is recommended to summarize the contribution of this study at the end of the introduction section.
Author’s response
We appreciate you bringing up this relevant subject and for asking as to summarize this point quite clearly. We have presented the main contributions of the study point by point at Line (106 to 121) at the end of the introduction section. Revising the abstract and highlighting this study's novelty is recommended.
- Revising the abstract and highlighting this study's novelty is recommended.
Author’s response
Thank you very much for pointing out the template for editing manuscripts. According to your comments the manuscript was changed during this process. We checked, full updated and highlighted the novelty in the abstract of the manuscript. (Line 14 to 30)
- Crossovers' weak points and strengths should be stated and summarized in a table.
Author’s response
Thank you so much for allowing us the opportunity to include this excellent addition to our study. We honestly did not remember making these comparisons. A focus was placed on line number 207 in Table 7.
- The importance of this study is not evident in why the new lagrangian problem crossover is introduced.
Author’s response
Thank you very much. We completely agree with your point. we tried to prove the purpose behind to introduce LPX at different points in the manuscript. Line [87 to 92, 197 to 206, and 459 t0 474]
- The proposed method section should be rewritten.
Author’s response
Thank you for this helpful feedback. The right comment, which enables us to better understand why we use the LPX operator to perform analysis. We provided a clear response to the query regarding the updated methodology. Therefore, we have rewritten sections 4 and 5, however, we recommend that you read all LPX-related sections.
- It is recommended to boost the description of figure 18.
Author’s response
Thank you for bringing up this relevant topic and asking for a boost in this description. Moreover, we discussed this point (to better understand Figure 18) during rewriting Section 4 to determine how LPX came to be. Line (480 to 528)
- The crossover operator introduced in QANA: Quantum-based avian navigation optimizer algorithm can be compared with the new lagrangian problem crossover.
Author’s response
We don’t know how to thank you for bringing up this relevant subject and suggesting this scientific article. Honestly, to enhance their knowledge of optimization problem, I sent this paper to all professionals who work on this subject. In addition, we also addressed this article and linked to LPX in the section on section 2 line (200-206). Additionally, we have compared the LPX to Qubit crossover operator with the other operators in Section 5.2.
- This study suffers from a lack of comprehensive experimental evaluation. It is recommended to boost this section.
Author’s response
Actually, it appeared before this revision that our manuscript lacked objective, comparable evaluation results on the effectiveness and limitations of these schemes. Providentially, the revised manuscript includes comprehensive experimental evaluation after revision. We updated Section 5 using a heuristic approach. Also, LPX has been compared with other famous crossover operators to find exploitation and the rate of convergence for three randomized values. Finally, we used statistical methods to help draw meaningful conclusions about the results. Line (572 to 668)
- The complexity of the new lagrangian problem crossover should be calculated and explained.
Author’s response
Thank you for reminding us to show crucial points as complexity of LPX for our findings. Thus, we explained the calculation in the section 4. Line 332 to 356
- Comparing the new lagrangian problem crossover with the existing crossover is recommended.
Author’s response
Thank you so very much. You asked us to compare our findings with other studies and to connect with previous literature. This will enable us to compare our updated findings in the discussion section. Thus, we selected the LPB algorithm as a population-based algorithm to compare with the four standard operators as mentioned. However, we evaluated the elapsed time that we needed to run each standard in classical selection tests. Lines (626 to 649) and Table 5.
*Note: As per your request, we rewrote all sections with the highest quality language proofreading.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
My comments have been taken into account, therefore I recommend accepting the paper after making minor editing corrections (the acronyms LDF and LPX are not introduced in the text).
Author Response
Response Letter
We appreciate your time and insightful feedback and comments throughout all steps of our study. Your accurate comments are greatly appreciated for reaching out to us in the current format.
We hope that you will find our modification to be more acceptable of the manuscript. Our replies are below in a presentation. Also, we have provided a corrected version of our Manuscript, with all the revisions highlighted in Yellow color.
Reviewer Comment:
The acronyms LDF and LPX are not introduced in the text.
Author’s response
It is a very valid point that you make. Thank you very much for your accuracy. There is no reason for the missing these acronyms, and it is uncontrollable. We introduced acronyms LDF in the text at 87 and in abstract at line 22. Also, we introduced acronyms LPX at line 89 to 90 and in abstract at line 22-23.
Author Response File: Author Response.pdf
Reviewer 2 Report
Accept in present form.
Author Response
Response Letter
Your time and thoughtful comments from the previous phase are greatly appreciated, and we appreciate your acceptance of the present study. Your insightful and informative comments have motivated us…
