A Modified Shuffled Frog Leaping Algorithm for the Topology Optimization of Electromagnet Devices

Round 1

Reviewer 1 Report

The paper describes an enhancement of the existing biologically inspired method for topology optimization known as shuffled frog leaping algorithm. Efficiency of the algorithm was demonstrated on multiphysics problem related to topology optimization of the iron part in the interior permanent-magnet motor. The work could be interesting for the Reader of the Journal, however several concerns listed below should be addressed prior its publication.

1. In the introductory part of the manuscript the Authors mentioned only papers dealing with biologically inspired methods for topology optimization. They completely ignored other heuristic gradient free methods such as ones described by -Fan, Z., et al. Evolutionary topology optimization of continuum structures with stress constraints. Struct Multidisc Optim 59, 647–658 (2019). https://doi.org/10.1007/s00158-018-2090-4, or -Blachowski, B., et al. Yield limited optimal topology design of elastoplastic structures. Struct Multidisc Optim 61, 1953–1976 (2020). https://doi.org/10.1007/s00158-019-02447-9
2. What is also surprising is the fact that in the proposed methodology there is lack of constraint on the amount of material. In my opinion the objective function should be equal either the amount of iron used or maximal torque under volume constraint. Please comment on that!
3. On page 7, in line 231 it is written that results shown in the paper have been averaged from “several” repetitions of the optimization procedure. The Authors should report the exact number of these repetitions? Moreover, additional data such as standard deviation would be very interesting. It provides information about certainty of results generated by the algorithms.
4. The weights w_1 and w_2 in equation (9) are not described in the text. There is no any information about their values. There is also conflict in notation, because the weights in Equation (6) also are written as w_i
5. Another conflict in notation is between function M(x) in Equation (7) and limit M in the sum from Equation (6).
6. The term “optimum ID” in Tables 2 and 3 is not explained. What does this quantity denote? Is the Optimization run time in Table 2 given in seconds or number of iterations?
7. On page 6, in line 180 the sentence “…in both x and y directions…” seems to be too informal. The shape of the mesh of design domain is not rectangular (see Figure 2). Moreover, in Figure 2 there is no any “xyz” coordinate system like in the other figures containing results. Maybe “…both in radial direction and along the arcs…” would be better.
8. All figures in the paper have very low resolution. Additionally, legends, symbols and labels on axes in all figures containing results are too small and unreadable.
9. In Figures 4-6 on page 8 the red lines describing the time histories of the torque have sharpened shape. I believe that significantly smaller time step would result in more smooth shape of the plot. It could reveal exact character of the time history of the torque, especially in Figures 5 and 6.
10. The “PSO” abbreviation on page 2, line 62 is not explained.
11. After Equations (2), (3) and (6) the new line should not start as a new paragraph (capital letter and/or intent). The authors should check correctness of other paragraphs preceded by equations. Additionally, some mistakes are to be corrected:

a) function in Equation (7) should by written as small letter as in remaining part of the paper – line 146, page 5,

b) “Th” should by replaced with “The” – line 212, page 7,

c) the space should be added between the number and newton-metre in row “Optimized results” in table 2 – page 7.

Author Response

The authors are grateful for the valuable comments from the reviewers. the response is given in the pdf attached.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors present a novel design approach based on a meta-heuristic optimization method SFLA. They compared the proposed algorithm with the conventional SFLA and LS-GA applying them to optimize an IPM prototype.

The paper is well presented and could be of interest for the scientific community, I have just one minor integration to suggest:

1. The SFLA algorithm is an extension of the classical PSO. In fact the authors compared the proposed SFLA with the classical one and LS-GA but I suggest the author to add some consideration/comparison with other evolutionary algorithms based on PSO such as QPSO and EWQPSO.

Author Response

The authors are grateful for the valuable comments from the reviewers. Please see the attachment for the response to the reviewers. Thank you.

Author Response File: Author Response.pdf

Reviewer 3 Report

Paper presents a modified shuffled frog‐leaping algorithm that is suitable for complex electromagnetic problem. Paper is quite well written, the results are resonable and covered by the data supported in the paper. The presentation of the algorithms could be improved. Since algorithms are of stochastic nature it will be good to present more runs to show some statistics.

Author Response

The authors are grateful for the valuable comments from the reviewers. Please see the attachment for the response. Thank you.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The Authors have corrected most of the issues indicated in the previous review. However, some shortcoming are still present in the revised. The manuscript can accepted for publication provided that the following issues are properly addressed:

1. In eqn.(9) the “predefined” coefficients c1 and c2 still do not have assigned exact values.
2. The Authors did not provide proper answer on the question about the amount of the material. The question concerned the amount of material AFTER optimization process. The lower amount of the material, the lower price (and weight) of the electric motor. The Authors should compare and comment the obtained amount of the material in the optimal design. Perhaps ratio of the maximized function to remaining amount of the material would be appropriate indicator?
3. There is quite large difference between the current and the previous values of the averaged torque and torque ripple (e.g. 19.8% vs 14.1% for the proposed algorithm in Table 3). How do the Authors know that the currently applied step “period/100” for the motor is sufficiently small? Can the authors compare the results with even smaller step?
4. Looking at Figure 3 from the previous and the current version of the manuscript there are significant differences in the torque plots. The torque plot from the previous version of the manuscript seems to be closer to the sinus function (relatively low contain of higher harmonics), whereas the current plot is strongly perturbated. The results shown in remaining figures also are different from their counterparts in previous version of the manuscript. These differences are very large, even for modification of the time step. It makes the accuracy of the results unclear. The Authors should show which equations are integrated and describe integration process in detail. Moreover, accurate and unique results are required.
5. Scales on Y-axes in Figures 3-6 should be the same to compare differences among analysed cases.

Comments for author File: Comments.pdf

Author Response

The authors are grateful for the valuable comments. Please refer to the attachment for the response.

Author Response File: Author Response.pdf