Historical Elite Differential Evolution Based on Particle Swarm Optimization Algorithm for Texture Optimization with Application in Particle Physics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors of the manuscript propose a new meta-heuristic variant of the differential evolution algorithm that incorporates aspects of the particle swarm optimization algorithm called ``Historical Elite Differential Evolution Based on Particle Swarm Optimization (HE-DEPSO)", to obtain chi-squared values are less than a bound value, which exhaustive and traditional algorithms cannot obtain. The results show that the proposed algorithm can optimize the chi-square function according to the required criteria.\\

 

In the manuscript, the authors have shown that the proposed algorithm can optimize different functions efficiently, particularly those from the CEC 2017 single-objective benchmark functions set. The HE-DEPSO appears to have good convergence properties in the balance between solution precision and convergence speed in most cases.\\

 

The authors have improved the differential evolution algorithm greatly in overcoming the premature convergence and stagnation in local minima.\\

 

I would like to suggest accepting the manuscript in current form.\\

Comments for author File: Comments.pdf

Author Response

Comments 1: [I would like to suggest accepting the manuscript in current form.]

Response 1: [Thank you for your review and kind suggestion.]

Reviewer 2 Report

Comments and Suggestions for Authors

The authors propose the HE-DEPSO algorithm for texture optimization, which presents an interesting approach to the problem at hand.

Before recommending publication, I suggest a few comments to further enhance the manuscript:

1. It would be beneficial to give a brief comment on  the potential application of this method to more complicated problems beyond 4-zero texture.

2. To what extent can this approach enhance the predictions compared to the approximate analytic studies referenced on the 4-zero texture?

3. The authors focus on the 4-zero texture of the quark mass matrices. It would be advisable to reference earlier studies, such as:

   K. Kang and S. K. Kang, "New class of quark mass matrix and calculability of flavor mixing matrix," Phys. Rev. D 56, 1511-1514 (1997) doi:10.1103/PhysRevD.56.1511 [arXiv/9704253[hep-ph]].

    

   To my knowledge, this was the first study to examine the 4-zero texture.

Author Response

Comments 1: [It would be beneficial to give a brief comment on the potential application of this method to more complicated problems beyond 4-zero texture.]

Response 1: [Thank you for your observation. We added the text of lines 781-786 in the conclusions section to comment on the potential applications.]

Comments 2: [To what extent can this approach enhance the predictions compared to the approximate analytic studies referenced on the 4-zero texture?]

Response 2: [Thank you for this comment. We respond by adding the text of lines 41-46.]

Comments 3: [The authors focus on the 4-zero texture of the quark mass matrices. It would be advisable to reference earlier studies, such as: 
K. Kang and S. K. Kang, ”New class of quark mass matrix and calculability of fla- vor mixing matrix,” Phys. Rev. D 56, 1511-1514 (1997) doi:10.1103/PhysRevD.56.1511 [arXiv/9704253[hep-ph]]. 
To my knowledge, this was the first study to examine the 4-zero texture.]

Response 3: [Thank you for your advice. We added the suggested reference as [19] and used it in line 45.]

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript studies a novel algorithm called HE-DEPSO, which includes differential evolution (DE) and particle swarm optimization (PSO) to verify the 4-zero texture model in particle physics. This model is used to understand fermion mass generation and the CKM matrix in the Standard Model of particle physics. This algorithm introduces a new mutation strategy to improve the balance between exploration and exploitation in optimization. The algorithm works better than other optimization methods like DE, PSO, and SHADE, for the chosen benchmark tests. I have the following questions from authors:

 

• How much is the efficiency of HE-DEPSO algorithm in comparison to previously proposed ones in terms of time and computational power?
  
  

• Can it be generalized to models other than the 4-zero texture model in particle physics?
  
  

• Why is this algorithm proposed for this kind of problem? What was the disadvantage/problem of previous methods?

 

If the authors clarify these points inside the main text, the manuscript can be published in the Applied Sciences Journal.

 

Author Response

Comments 1: [ How much is the efficiency of HE-DEPSO algorithm in comparison to previously proposed ones in terms of time and computational power?]

Response 1: [A complexity analysis of the HE-DEPSO algorithm is presented in Section 4.3, showing that the algorithm has a complexity comparable to recent DE variants (lines 505-515).]

Comments 2: [ Can it be generalized to models other than the 4-zero texture model in particle physics?]

Response 2: [We answer “like the 2 and 5 zeroes texture models” in lines 781-782, and also we added the text of lines 783-786 in the conclusions section to comment on the potential applications.]

Comments 3: [ Why is this algorithm proposed for this kind of problem? What was the disadvan- tage/problem of previous methods?]

Response 3: [Thank you for this observation. We explain the reasons for the use of our algorithm from lines 108 to 117.  Regarding the disadvantages/advantages, the previously used methods are mainly analytical. This explanation was added in lines 41-43. On the other hand, authors using numerical approaches do not  report the used optimization method; this is explained in lines 47-48.]

Reviewer 4 Report

Comments and Suggestions for Authors

Comment to the authors

I proceeded to re-analyze the manuscript entitled:

HE-DEPSO algorithm for textures optimization with application in particle physics

writtem by

Emmanuel Martínez-Guerrero, Pedro Lagos-Eulogio, Pedro Miranda-Romagnoli, Roberto, Noriega-Papaqui and Juan Carlos Seck-Tuoh-Mora

This manuscript examines the feasibility of the 4-zeros texture model in particle physics by comparing its theoretical predictions with recent experimental data. The authors use a Chi-square fit to align the model's theoretical expressions with experimental values of physical observables. They develop an optimization model using chi^2(X) function to identify parameter regions consistent with the data.

To optimize the Chi-square (X) function, the paper introduces a new variant of the Differential Evolution Particle Swarm Optimization (DEPSO) algorithm, called Historical Elite Differential Evolution Based on Particle Swarm Optimization HE-DEPSO. This algorithm efficiently optimizes various functions, including those from the CEC 2017 benchmark set, showing a good balance between solution precision and convergence speed. HE-DEPSO outperforms other algorithms like SHADE and CoDE in optimizing the Chi-square (X) function.

The study concludes that the 4-zeros texture model is compatible with current experimental data, affirming its physical feasibility. The research may also expand to analyze additional texture models and their validity based on experimental data.

The topic is, in my opinion, interesting and with practical application. The manuscript reveals a systematic, well conducted investigation with a lot of work to test the model. The figures are suggestive and support the statements. References are in good amount amount and they indicate that the authors are well aware of what has been published on the subject they are writing about. The article is well written, using good English, in my opinion. The content of the article sustains the conclusion.

   Moving to details, I have some minor observations:

-line 22: define the VCKM matrix, as the journal is not a typical High Energy Physics journal. The same for any quantity use used.

-lines 27 – 29: “Radiative mechanisms [1,2]; Textures [3–5]; Symmetries between families [6,7]; and Seesaw mechanisms [8–10]. These approaches are interrelated.” Write in manuscript a few words on each of them, for the same reason.

-check eq. (33)

Author Response

Comments 1: [line 22: define the VCKM matrix, as the journal is not a typical High Energy Physics journal. The same for any quantity use used.]

Response 1: [Thank you for your observation. We added a footnote 1 to explain the VCKM matrix and also added some references (page 1).]

Comments 2: [lines 27 – 29: “Radiative mechanisms [1,2]; Textures [3–5]; Symmetries between families [6,7]; and Seesaw mechanisms [8–10]. These approaches are interrelated.” Write in manuscript a few words on each of them, for the same reason.]

Response 2: [Thank you for this comment. We added a brief description of each mechanism and also give examples of its interrelations in lines 27-35.]

Comments 3: [check eq. (33)]

Response 3: [Thank you for this observation. We corrected equation 33 by checking the use of parentheses in the exponential.]

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Having been revised in line with my suggestions, I now confidently recommend the manuscript for publication in Applied Sciences.