The Set Covering and Other Problems: An Empiric Complexity Analysis Using the Minimum Ellipsoidal Width
Round 1
Reviewer 1 Report (Previous Reviewer 2)
1. The authors have carried out an interesting study. However, the study is limited in small number of samples. Could a simulation be performed to increase the sample size? This would also improve the generalizability of the study findings.
2. Can the authors provide a 95% or 90% confidence interval for the reliability observed in the present study? This might also improve the generalizability and help the readers understand the importance according to their local context.
Language needs moderate revision. Recommend seeking editing by professional service.
Author Response
- The authors have carried out an interesting study. However, the study is limited in small number of samples. Could a simulation be performed to increase the sample size? This would also improve the generalizability of the study findings.
It is not possible to increase the size of the sample since we only have 10 days for corrections.
- Can the authors provide a 95% or 90% confidence interval for the reliability observed in the present study? This might also improve the generalizability and help the readers understand the importance according to their local context.
A new subsection was created to present the reliability of the work and generality of the results. In this table 12 and a paragraph explaining the new information delivered were added.
English was reviewed by a professional service provided by the
University of Santiago de Chile
Reviewer 2 Report (Previous Reviewer 5)
The reviewer has expressed a positive view of the manuscript since the first review.
The reviewer is of the same opinion in this second review.
Therefore, the reviewer judges this manuscript as acceptable again.
The reviewer finds the English text in this manuscript to be acceptable.
Author Response
English was reviewed by a professional service provided by the
University of Santiago de Chile
Author Response File: 
Author Response.docx
Reviewer 3 Report (New Reviewer)
the paper has good style, and the authors stated the method in proper style.
Author Response
English was reviewed by a professional service provided by the
University of Santiago de Chile
Author Response File: Author Response.docx
Reviewer 4 Report (New Reviewer)
This is an interesting research-expository paper regarding the empirical computational complexity of Karp's by now classical 1972 list of twenty-one problems. It provides its readers with a valuable, rather detailed, discussion of the set covering and related problems (see, for example, lines 299 and 300). Its main contribution concerns an application of the concept of ellipsoidal width to the study of the problem of estimating the Branch & Bound tree. Since I believe that this paper is indeed appropriate for the Special Issue on Operations Research and Optimization, my recommendation is that (a revised version of) it be accepted for publication. When the authors prepare the revised version of their paper they should take into account the following (rather minor) comments, questions and suggestions.
(1) Although six chapters are mentioned in the Introduction (see lines 13--18), it seems to me there are only four chapters in the paper itself, namely the Introduction, Methods and Materials, Experimental Design, and Results.
(2) Line 123: "Data taken" ---> "Data were taken"
(3) Line 124--130: please see the first item above.
(4) Line 149: what is the exact meaning of the phrase "problem specific instance"?
(5) Line 322: "an nonlinear" ---> "a nonlinear"
(6) Lines 411--421 seem to be written in Spanish.
(7) Line 462: "the-orem" ---> "theorem"
(8) Line 463: "devel-oped" ---> "developed"
Author Response
Reply to reviewer 4
Comments, questions and suggestions.
- Although six chapters are mentioned in the Introduction (see lines 13--18), it seems to me there are only four chapters in the paper itself, namely the Introduction, Methods and Materials, Experimental Design, and Results.
Corrected
- Line 123: "Data taken" ---> "Data were taken"
Corrected
- Line 124--130: please see the first item above.
Corrected
(4) Line 149: what is the exact meaning of the phrase "problem specific instance"?
It refers that d=(A,b) is an instance of the problem. The specific word was eliminated
(5) Line 322: "an nonlinear" ---> "a nonlinear"
Corrected
(6) Lines 411--421 seem to be written in Spanish.
Corrected
(7) Line 462: "the-orem" ---> "theorem"
Corrected
(8) Line 463: "devel-oped" ---> "developed"
Corrected
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report (Previous Reviewer 2)
Nil
Author Response
Thank you.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
First major problem: The english is very unprofessional. There is a typo in the title ("un" instead of "an"). The first sentence of the abstract should be "This paper searches to explain ..."! The authors must use the present tense for the verbs. So, the bad writing is big obstacle to follow the explanaition.
Another major aspect consists of the organization of the paper. The current organization consists of: Sec 1: Introduction; Sec 2: Background; Sec3- Problems Solved (describing the set covering problem and three configurations of the knapsack problem); Sec 4: Experimental design; Sec 5: Discussion; Sec 6: Conclusions. I wonder: where the contribution of the work is described! Also, there is no section that describes the current state-of-the-art, which mandatory if one wants to establish the novelty of the proposed work.
The third major limitation of this work is the lack of comparison of the obtained results to those yielded by existing related work. Only by providing these kind of comparison one can weight the quality and impact of the contribution of the work.
For the aforementioned reasons, I'm sorry to advise against the consideration of publication of this paper, even after a revision. A new submission must be done if the authors feel to be able to provided an improved version of this paper wherein all the above major issues have been throughly addressed.
Author Response
First major problem: The english is very unprofessional. There is a typo in the title ("un" instead of "an"). The first sentence of the abstract should be "This paper searches to explain ..."! The authors must use the present tense for the verbs. So, the bad writing is big obstacle to follow the explanaition.
Answer: The paper was again written by a British English speaker.
Another major aspect consists of the organization of the paper. The current organization consists of: Sec 1: Introduction; Sec 2: Background; Sec3- Problems Solved (describing the set covering problem and three configurations of the knapsack problem); Sec 4: Experimental design; Sec 5: Discussion; Sec 6: Conclusions. I wonder: where the contribution of the work is described! Also, there is no section that describes the current state-of-the-art, which mandatory if one wants to establish the novelty of the proposed work.
Answer: The sections were reorganized in their content and a sub chapter was added with the state of the art (number 1.1). We also added a subchapter explaining in detail the contribution of the article (numner 1.2).
The third major limitation of this work is the lack of comparison of the obtained results to those yielded by existing related work. Only by providing these kind of comparison one can weight the quality and impact of the contribution of the work.
Answer: In the section called Discussion (chapter 5) we made a comparison with the only known study on the subject that belongs to the research group of the Zuse Center in Berlin.
For the aforementioned reasons, I'm sorry to advise against the consideration of publication of this paper, even after a revision. A new submission must be done if the authors feel to be able to provided an improved version of this paper wherein all the above major issues have been throughly addressed.
Answer: The paper that we upload should be considered as a new document. Since it has big changes compared to the previous one.
Author Response File: Author Response.docx
Reviewer 2 Report
1. The present study is a reasonably good study evaluating the utility of complexity analysis.
2. What are the measures of precision & accuracies for each of the estimates?
3. Validation of the models evaluated in the present study would add more value.
Author Response
Comments and Suggestions for Authors
- The present study is a reasonably good study evaluating the utility of complexity analysis.
Answer: Thanks for your kind comment.
- What are the measures of precision & accuracies for each of the estimates?
Answer: New tables were constructed that explain the reliability of the study for each of the regression models tested. (tables 12 and 13)
- Validation of the models evaluated in the present study would add more value.
Answer: We add the coefficient of determination, the F-test, and the p-value to each of the aggregate tables showing the precision & accuracies data. (tables 12 and 13)
Author Response File: Author Response.docx
Reviewer 3 Report
The manuscript has major shortcomings that I believe should be addressed, as outlined below:
General comments:
1- The manuscript suffers from improper English grammar. A full English revision is necessary.
Main Comments:
1- The Abstract is an important part of the paper, because it shows your work briefly. The purpose of the research is not properly stated in the abstract.
2- What is the MSC?
3- The introduction seems to be a significant part of the paper. Hence, the Introduction should be modified, the novelty of this study become not too clear and need to be more emphasized and justified in the end of this section.
4- In the Background section, past studies deserve more attention. This work can be done by explaining more about the work done in recent years. Authors should add and update references.
5- The authors should give more details about the test problems (Table 1).
6- Why is table 2 introduced in section 3, but table 2 is displayed in section 4? More explanations about the details of Table 2 are necessary.
7- The discussion of the results is not really sufficient. The results in the discussion section require thorough rewriting and expansion. Right now, it is very brief and poorly written.
8- The authors should add more explanation about the limitations of their methodology in the discussion section.
Author Response
Comments and Suggestions for Authors
- The present study is a reasonably good study evaluating the utility of complexity analysis.
Answer: Thanks for your kind comment.
- What are the measures of precision & accuracies for each of the estimates?
Answer: New tables were constructed that explain the reliability of the study for each of the regression models tested. (tables 12 and 13)
- Validation of the models evaluated in the present study would add more value.
Answer: We add the coefficient of determination, the F-test, and the p-value to each of the aggregate tables showing the precision & accuracies data. (tables 12 and 13)
Author Response File: Author Response.docx
Reviewer 4 Report
This paper deals with an optimization problem of nonlinear problem (min-max problem) subject to inequality constraints. The ellipsoidal formulation has been used as a solving tool. Some numerical algorithms have been presented where a comparison with other algorithms have also given
Overall, the optimization problem is by and large interresting but clear innovation and contributions are missing. Such problem has been widely used using nowadays several metaheuristic algorithms and that work well. I do not feel an thed see the importance of the presented solutions. They work but why they have been done? what is the problematic of the optimization problem? Why you refered to this solutions and not other ones?
I propose to clearly improve the paper according to the previous comments.
Author Response
Comments and Suggestions for Authors
This paper deals with an optimization problem of nonlinear problem (min-max problem) subject to inequality constraints. The ellipsoidal formulation has been used as a solving tool. Some numerical algorithms have been presented where a comparison with other algorithms have also given. Overall, the optimization problem is by and large interresting but clear innovation and contributions are missing. Such problem has been widely used using nowadays several metaheuristic algorithms and that work well. I do not feel an thed see the importance of the presented solutions. They work but why they have been done? what is the problematic of the optimization problem? Why you refered to this solutions and not other ones?
I propose to clearly improve the paper according to the previous comments.
Answer: The development of metaheuristics has been a tremendous contribution to the solution of many mathematical and engineering problems. However optimization methods will continue to be used. The idea of this work is to be able to predict the complexity of the B&B algorithm. that is to say, estimate the number of nodes that will be used and the processing time. In addition, to clarify the contribution, a subsection was added explaining the contribution. (1.2)
Reviewer 5 Report
The reviewer judges that the content of this manuscript is consistent with the purpose of the Mathematics.
The reviewer then give the following comments to the authors.
The authors are requested to respond to the following comments.
(1) The authors should clarify the difference between Section 1 and Section 2.
(2) The authors should refer to reliability of experimental design in Section 4.
(3) The authors should improve the quality of Figures 1 and 2. For example, there are no titles for the X and Y axes.
(4) The authors need more discussion in Section 4.
(5) The authors should itemize the conclusions drawn in Section 5.
Author Response
Comments and Suggestions for Authors
The reviewer judges that the content of this manuscript is consistent with the purpose of the Mathematics.
The reviewer then give the following comments to the authors.
The authors are requested to respond to the following comments.
- The authors should clarify the difference between Section 1 and Section 2.
Answer: They were rewritten. Section 1 is for introduction and section 2 is for materials and methods
(2) The authors should refer to reliability of experimental design in Section 4.
Answer: We rewrite Section 1 is for introduction and Section 2 is for materials and methods. We add the coefficient of determination, the F-test, and the p-value to each of the aggregate tables showing the precision & accuracies data. (tables 12 and 13)
(3) The authors should improve the quality of Figures 1 and 2. For example, there are no titles for the X and Y axes.
Answer: the figures were redone.
(4) The authors need more discussion in Section 4.
Answer: A discussion was made about other results of other investigations and about the limitations of the study.
(5) The authors should itemize the conclusions drawn in Section 5.
Done. It is a good suggestion.
Round 2
Reviewer 1 Report
The way the corrections are presented make the review of the amendments impossible for me. I cannot review the paper in this form. I advise on submitting the work as a new submission.
Author Response
First major problem: The english is very unprofessional. There is a typo in the title ("un" instead of "an"). The first sentence of the abstract should be "This paper searches to explain ..."! The authors must use the present tense for the verbs. So, the bad writing is big obstacle to follow the explanaition.
Answer: The paper was again written by a British English speaker.
Another major aspect consists of the organization of the paper. The current organization consists of: Sec 1: Introduction; Sec 2: Background; Sec3- Problems Solved (describing the set covering problem and three configurations of the knapsack problem); Sec 4: Experimental design; Sec 5: Discussion; Sec 6: Conclusions. I wonder: where the contribution of the work is described! Also, there is no section that describes the current state-of-the-art, which mandatory if one wants to establish the novelty of the proposed work.
Answer: The sections were reorganized in their content and a sub chapter was added with the state of the art (number 1.1). We also added a subchapter explaining in detail the contribution of the article (numner 1.2).
The third major limitation of this work is the lack of comparison of the obtained results to those yielded by existing related work. Only by providing these kind of comparison one can weight the quality and impact of the contribution of the work.
Answer: In the section called Discussion (chapter 5) we made a comparison with the only known study on the subject that belongs to the research group of the Zuse Center in Berlin.
For the aforementioned reasons, I'm sorry to advise against the consideration of publication of this paper, even after a revision. A new submission must be done if the authors feel to be able to provided an improved version of this paper wherein all the above major issues have been throughly addressed.
Answer: The paper that we upload should be considered as a new document. Since it has big changes compared to the previous one.
Author Response File: Author Response.docx
Reviewer 3 Report
I think the authors uploaded the answer file wrongly. Although I did not find the authors' answers to my questions in a separate file, I noticed the changes by checking the text of the article. But I invite the authors for another minor review.
Author Response
First major problem: The english is very unprofessional. There is a typo in the title ("un" instead of "an"). The first sentence of the abstract should be "This paper searches to explain ..."! The authors must use the present tense for the verbs. So, the bad writing is big obstacle to follow the explanaition.
Answer: The paper was again written by a British English speaker.
Another major aspect consists of the organization of the paper. The current organization consists of: Sec 1: Introduction; Sec 2: Background; Sec3- Problems Solved (describing the set covering problem and three configurations of the knapsack problem); Sec 4: Experimental design; Sec 5: Discussion; Sec 6: Conclusions. I wonder: where the contribution of the work is described! Also, there is no section that describes the current state-of-the-art, which mandatory if one wants to establish the novelty of the proposed work.
Answer: The sections were reorganized in their content and a sub chapter was added with the state of the art (number 1.1). We also added a subchapter explaining in detail the contribution of the article (numner 1.2).
The third major limitation of this work is the lack of comparison of the obtained results to those yielded by existing related work. Only by providing these kind of comparison one can weight the quality and impact of the contribution of the work.
Answer: In the section called Discussion (chapter 5) we made a comparison with the only known study on the subject that belongs to the research group of the Zuse Center in Berlin.
For the aforementioned reasons, I'm sorry to advise against the consideration of publication of this paper, even after a revision. A new submission must be done if the authors feel to be able to provided an improved version of this paper wherein all the above major issues have been throughly addressed.
Answer: The paper that we upload should be considered as a new document. Since it has big changes compared to the previous one.
Reviewer 4 Report
It is difficult to read the paper under its present form. Authors should provide the corrected manuscript without old text and mark the new text in a different color.
However, I followed some parts of the paper, and I see that authors have mad a signification correction and improvements. But as I said it is difficult to follow the entire corrected paper.
Update the paper.
Author Response
Comments and Suggestions for Authors
This paper deals with an optimization problem of nonlinear problem (min-max problem) subject to inequality constraints. The ellipsoidal formulation has been used as a solving tool. Some numerical algorithms have been presented where a comparison with other algorithms have also given. Overall, the optimization problem is by and large interresting but clear innovation and contributions are missing. Such problem has been widely used using nowadays several metaheuristic algorithms and that work well. I do not feel an thed see the importance of the presented solutions. They work but why they have been done? what is the problematic of the optimization problem? Why you refered to this solutions and not other ones?
I propose to clearly improve the paper according to the previous comments.
Answer: The development of metaheuristics has been a tremendous contribution to the solution of many mathematical and engineering problems. However optimization methods will continue to be used. The idea of this work is to be able to predict the complexity of the B&B algorithm. that is to say, estimate the number of nodes that will be used and the processing time. In addition, to clarify the contribution, a subsection was added explaining the contribution. (1.2)
Author Response File: Author Response.docx
Round 3
Reviewer 1 Report
The paper has been re-written. However, I cannot assess the contribution of the work as the previous (being cut in this version) text is too large, and it is hindering the evaluation of the new version of the paper.
This paper must be rejected and the authors should, if they prefer make a new submission with the new version of the paper. Only then, one can review the proposed work.
For the above reason, I'm compelled to reject this version too.
Author Response
Dear Reviewer
The previous paper seemed deleted and you couldn't see it.
This happened because I hid the previous revisions in the word document.
Now I uploaded the document showing the previous and current versions.
I hope you can see them without problems.
The different versions can be seen with the change control option in the top bar.
Author Response File: Author Response.docx
