Model of an Artificial Neural Network for Solving the Problem of Controlling a Genetic Algorithm Using the Mathematical Apparatus of the Theory of Petri Nets

Round 1

Reviewer 1 Report

To my best understanding, the authors propose to improve the performance of a genetic algorithm by equipping it with a neural network which controls the parameters of the evolutionary process. The method seems to rely on teaching the neural network setting the parameters of the evolution dynamically in such a way that the process avoids typical pitfalls of the genetic algorithms. Then, they test the approach on the problem of structural-parametric synthesis.

While the submitted manuscript has its merits, it also has significant drawbacks.

1. The text is very unclear and requires significant editing before it is acceptable. The general idea is almost lost in the details of the Petri nets formalism. The test case is presented in a very vague way.
2. Similar (or, as far as I understand, virtually identical) approach was already presented in Ref. [1], but the authors fail to mention it, claiming, from what I have understood, that their approach is completely novel.
3. There are many ways of dynamic control of the evolutionary process, the authors fail to compare their method with any of the well-established ones.

Apart from the serious shortcomings, there are also some minor ones. The style, while generally not bad, could use some improvements. Rendering of the formulas is terrible and surely could be refined. A few words in the text were left in Russian, like нейрон коррекции or шт, please translate them.

[1] A. Styrcz, J. Mrozek, G. Mazur, A neural-network controlled dynamic evolutionary scheme for global molecular geometry optimization, International Journal of Applied Mathematics and Computer Science 21 (2011) 559

Author Response

Dear Reviewer,

The team of authors is grateful for your review of the article. All the recommendations were very helpful.

In accordance with the remarks given in the review, the following corrections were made:

1. The article text was edited. The idea of using the mathematical apparatus of the theory of Petri nets to create a single model of an artificial neural network as a control superstructure over a genetic algorithm is highlighted. To this end, the previously developed model of the genetic algorithm is modernized, an approach to modeling an artificial neural network using Petri nets is described, and the use of labels for storing synapse weights is proposed, which simplifies the procedure for storing this information (previously, it was proposed to use transitions to solve this problem). The article provides examples of the proposed model based on the element base of triggers and explains the goals of the computational experiment, which consisted in evaluating the number of solutions found when processing a given number of populations and the time to search for the first solution that meets the specified criteria.
2. The novelty of this article lies in the proposed model of an artificial neural network as a control superstructure over a genetic algorithm described using the mathematical apparatus of the theory of Petri nets. The authors got acquainted with the works proposed by the reviewers, these works did not use the theory of Petri nets to model the work of genetic algorithms and artificial neural networks, which is a novelty of the study and allows to use the properties of parallelism inherent in these evolutionary procedures. One of the proposed works has been added to the list of references.
3. In this paper, a comparison is made with a previously developed genetic algorithm based on Petri nets, adapted to the problem of structural-parametric synthesis by a Petri net. To evaluate the effectiveness of the proposed models and methods in comparison with other dynamic methods of controlling the evolutionary process, it is required: to perform a thorough classification and study the destructive ability of the operators of the genetic algorithm in the subject area under study; to study the control strategies and perform a more fine-tuning of the artificial neural network; to adapt modern approaches to managing the evolutionary search for solutions to the problem of structural-parametric synthesis; to perform their software implementation using GPGPU technology; to draw up a plan for a computational experiment, etc. All of the above is planned by the authors as a continuation of the study.

The team of authors is grateful to you for your review and recommendations that allowed us to improve the article. We look forward to further cooperation.

With all the best wishes,

Petrosov D. A., Lomazov V. A., Petrosova N. V.

Reviewer 2 Report

Dear authors,
I will send you the review of the manuscript, in view of the major improvements, in accordance with the requirements of the journal.

Best regards,

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

The team of authors is grateful for your review of the article. All the recommendations were very helpful.

In accordance with the remarks given in the review, the following corrections were made:

1. Changed introduction: special attention was paid to the novelty and prospects of research in the field of artificial neural networks as a control superstructure over a genetic algorithm, described by the mathematical apparatus of the theory of Petri nets in solving the problem of structural-parametric synthesis of large discrete systems.
2. Added the chapter " Literature review for the research area»;
3. An audit of the list of references and its analysis, taking into account the recommendations, was carried out;
4. The chapter "Materials and methods" has been finalized, special attention is paid to the research methodology;
5. The figures are explained: "An example of an artificial neural network model based on Petri nets" and "An adapted genetic algorithm based on Petri nets". The results of the computational experiment shown in the tables were also explained.
6. Qualitatively improved the display of formulas;
7. Qualitatively improved figures 1 and 5;
8. The text of the article was corrected, the extra paragraphs were removed;
9. Expanded and completed the chapter " Discussion»;
10. Attention is paid to the novelty and innovation in the text of the article;
11. The chapter Conclusions was finalized, the novelty of the approach, as well as its applied nature, was emphasized.
12. Corrected the text of the article, which was not translated;
13. Fixed the design of the article in accordance with the journal template (since the team sends the article to this journal for the first time, errors are possible)
14. Filled in the information about the authors at the end of the article;
15. The text of the article was edited for an international audience.

The team of authors is grateful to you for your review and recommendations that allowed us to improve the article. We look forward to further cooperation.

With all the best wishes,

Petrosov D. A., Lomazov V. A., Petrosova N. V.

Round 2

Reviewer 1 Report

All my previous concerns have been addressed. I tentatively support publication of the revised manuscript pending stylistic improvements. Admittedly, the language is comprehensible, but could still use some improvement.

Author Response

Dear Reviewer,

The authors are very grateful to you for reviewing the materials and recommendations.

Your recommendations helped us to improve the publication. Unfortunately, the authors don’t speak English fluently, so we use the services of a translator. After your comment, we contacted the translator again, and he corrected the text of the article. Then we sent the corrected article to our colleagues, native speakers from California (USA). They also made their own edits. We hope that the quality of the translation will be better.

 

Sincerely,

Petrosov D. A.

Reviewer 2 Report

Dear authors,

The paper has been improved and I consider that it can be accepted in its present form.
Success!

Best regads,

Author Response

Dear Reviewer

The authors are very grateful to you for reviewing the publication.

Your recommendations were very useful and helped us to improve our material. Moreover, in accordance with the comments of the second reviewer, stylistic changes to the text of the article (related to the improvement of the translation) were made.

Best wishes,

Petrosov D. A.,