Dear Dr. An,

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Partly

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

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The PLOS Data policy

Reviewer #1: No

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Reviewer #1: Yes

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Reviewer #1: The underlying principle may be of interest, although it is not entirely novel (see, for example, a keyword search for "Self-adaptive Differential Evolution with Lévy Mutation").

The algorithm introduces too many parameters without providing any justification for their choice.

The experimental results are not sufficiently comprehensive to support the claimed comparisons.

There are also no comparisons with the winners of the CEC 2017 competition.

Overall, the proposed algorithm, in its present form, is not convincing.

----------------------- More detailed remarks

p. 2

"We conduct an extensive empirical study on the IEEE CEC 2017 benchmark suite across multiple dimensions, including comparisons with state-of-the-art DE variants and controlled comparisons with CP and ADCP."

The top three winners, which you do not cite, are

EBOwithCMAR

Kumar, A., Misra, R. K., & Singh, D. (2017). "Improving the local search capability of Effective Butterfly Optimizer using Covariance Matrix Adapted Retreat Phase." In 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 1835–1842.

jSO

Brest, J., Maučec, M. S., & Bošković, B. (2017). "Single objective real-parameter optimization: algorithm jSO." In 2017 IEEE Congress on Evolutionary Computation (CEC).

LSHADE-SPACMA

Mohamed, A. W., Hadi, A. A., Fattouh, A. M., & Jambi, K. M. (2017). "LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems." In 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 145–152.

Please compare your L-SRTDE-ALP to them.

And you could remove many of the eleven DE-based methods you consider, for they are not very competitive. Quantity does not mean quality.

Here's a polished version in natural British English:

You could also remove many of the eleven DE-based methods you consider, as they are not particularly competitive. Quantity should not be confused with quality.

In addition, please provide more comprehensive results. Reporting only the mean and standard deviation, as in Tables S1–S4, is not particularly informative. First, the distribution of the results may not be symmetric. Second, readers are interested in knowing the best result that an algorithm is capable of achieving. At the very least, the tables should report the best, median, and standard deviation.

An even more informative presentation would be to provide the cumulative distribution functions (CDFs), based on, say, 100 independent runs. This would allow readers to estimate the probability of obtaining a result below any given threshold.

p. 6

"This section introduces ALP, a perturbation operator for DE recombination that assigns distinct tail behaviors to individual solutions"

You may have a look at

Das & Suganthan, "Differential Evolution: A Survey of the State-of-the-Art," IEEE Transactions on Evolutionary Computation*, 15(1), 2011.

It reviews self-adaptive parameter schemes and Lévy variants.

Beyer & Schwefel, Evolution Strategies – A Comprehensive Introduction, Natural Computing, 1, 2002.

p. 11

"Ninit = 20D, Nmin = 4, H = 5, k = 1, nc = 1, kp = 3, MCr,r = 1, SR = 0.5, JRmin = 0.1, JRmax = 0.2, αmin = 0.3, αmax = 1.7"

13 parameters, together with six additional hard-coded ones (formulae 15, 16, and 17), are used without any justification, apart αmin and αmax. This is far from sufficient.

Moreover, you do not consider the two other parameters: the pseudo-random number generator (PRNG) and its seed.

You may wish to consult the following paper, which cites several studies on the influence of these parameters:

Antunes, Benjamin A. 2025. ‘The Influence of the Random Numbers Quality on the Results in Stochastic Simulations and Machine Learning’. arXiv:2510.25269. Preprint, arXiv, October 29. https://doi.org/10.48550/arXiv.2510.25269.

Minor point

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The quality of the figures on pages 26–28 is poor, at least in the PDF I downloaded.

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A rank-conditioned α-stable perturbation for differential evolution: Separating perturbation frequency and tail heaviness

PONE-D-26-37177R1

Dear Dr. An,

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PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: (No Response)

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3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: (No Response)

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: (No Response)

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: (No Response)

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Reviewer #1: (No Response)

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what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

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