The paper proposes a method to solve the wind farm layout optimization problem while taking into account alignment constraints. These can be relevant when the navigability of vessels within the wind farm is considered. This method is based on an algorithm that parametrizes the possible turbines’ positions within the domain through the intersections of a grid based on parallelograms. This enables to reduce the size of the problem and to obtain an effective convergence. The problem is rigorously formulated and the algorithm is widely described within the document. Finally, the selection of the hyperparameters are discussed and the algorithm is used to solve a widely known example to prove its effectiveness. Overall, this work introduces an interesting method to tackle the challenging layout optimization problem, but it could be further improved by making some modifications. Here I have included my suggestions.

GENERAL COMMENTS

The contributions of this paper should be highlighted more within the methodology. This comment mainly refers to the identification of the innovative aspect introduced in this research with respect to the several works available in literature where the turbine layouts are parameterized through angles and distances of a regular grid. For instance, many studies do not consider the possibility of “not occupying” a grid intersection (which is considered here). Another innovative aspect is the application of a domain composed by multiple regions. Such aspects (along with the other differences) should be highlighted.

Overall, the paper defines the optimization problem using clear and rigorous mathematical expressions and definitions. However, a more detailed description of such expressions within the text could facilitate the readability of the work.

The aspect of introducing  the alignment constraint to focus for instance on the navigability of vessels within the farm is innovative and interesting. To give additional value to this aspect, I would suggest to add some references where this requirement is mentioned.

The fact that the parameters Delta_1 and Delta_2 do not depend on each turbine ensure the alignment constraint. However, it could be interesting to mention (as future work) that allowing small deviations of these parameters for every turbine could be the starting point for a sensitivity analysis based on the relaxation of such constraint.

Several times the authors refer to the description of the algorithms included in the Appendix. To facilitate the reading, I would suggest to include a description of the algorithm (e.g. using some block visualizations) within the main text.

SPECIFIC COMMENTS

In the lines 33-34, it is mentioned that there is no method in the literature that takes into account the alignment constraints. However, these are implicitly taken into account when the turbines are placed at the intersection points of a regular grid. Despite the number of optimization variables that define such a grid are limited in most of the studies, this should be mentioned in the introduction.

In section 3.1, the parameters used for the parameterization of the grid shape are described only by referring to the Figure 1. However, a brief description within the text could facilitate the reading.

The mathematical formulation of the objective function (Equation 8) is clear but “over-complicated” with respect to the ones usually present in the literature (even though they are equivalent). I would suggest to provide further description within the text to facilitate the reading.

I would suggest to modify the notation used to indicate the turbine diameter to make the expressions more clear.

Figures 4 and 5 are quite difficult to understand and interpret. I would suggest to use a 2d visualization including various lines/points for the different parameters.

In section 5.1 the method used to compute the AEP is described. I would include also the discretization adopted to for the wind speed and the wind direction values, which are relevant for the computational time that is further described.

In table 2, it is not clear if the computational time column refers to the step 4 of the algorithm described in section 4.1. If this is the case, it would be helpful to mention also the computational time required for the step 2 (section 4.1) as a function of the hyperparameters. Moreover, please highlight why only some combinations of angles are present in the table.

In every table that the computational time is mentioned, the processor that has been used should be mentioned to facilitate the reading.

The title of section 6 does not match exactly its content. I would recommend to modify it in order to enhance that a new method is introduced to increase the performance. Moreover, in this section it is not clear why the focus of the modified algorithm is on the AEP increase instead of the computational time reduction, please provide some arguments. My concern arises since at the beginning you highlight the need of increase the speed of convergence instead of the need of converging to a better result. Finally, I would consider using a visualization to show the increased performance of this method (more effective than a table), e.g. increase of AEP as a function of the number of turbines, also to enhance the linear behavior mentioned in the text.

The reviewer strongly believes that the paper presents critical wind farm layout optimization aspects. The results appear original and very well written.

Page1: Title. While it is generally understood why the author is discussing wind farm layout, it might be clear to revise the title to explicitly mention "offshore" wind farm layout to clarify the study's focus, as offshore constraints differ widely from onshore. This would also improve clarity for future citations.

Page1: Line4. “to the authors’ best knowledge” is unnecessary. It is expected that the author performs extensive research and could state that they performed an extensive literature review and did not find any prior studies on the topic.

Page1: Abstract. Generally, improve clarity in the abstract. For instance, when stating, “the contributions of this paper are twofold,” explicitly mention the method – heuristics - rather than vaguely referring to it as a method to handle the optimization problem.

Page1: Line13. Provide reference to the claim in Line 13/14

Page3: Line60. Z* is redundant. Not utilized in the rest of the paper

Page3: Line81. Clarify how the random wind variable was determined. Because the probability distribution of wind speed and direction were introduced on Page 4.

Page4-8: Study domain. Was a regularization term introduced to prevent overfitting specific wind conditions for wake? How will this change the result?

Page5: Line116. θ1 is a constraint as provided in Fig1, which means the wind farm is constrained to θ1 between −90 and 90. Are wind farms never aligned outside these angles? See comments on Fig7.

Page5: Line18. Dmin and Dmax are not specified as a multiplication of rotor diameter. Some wake models utilize 5D, 6D, 7D etc of the rotor diameter (D)

Page8: Line184. The authors compare their case study to Thomas et al. (2023) DEBO algorithm, but they do not provide a direct numerical comparison of the results

Page14: Line246. The conclusion claims that their proposed method outperforms a baseline but does not specify by what percentage.

General comments:

The heuristic model lacks sufficient detail in the explanation. Because it did not compare with the baseline models to see how they outperformed the others.

Results lack error analysis, confidence intervals, or sensitivity to other wake model assumptions.

Basic explanations for the choice of constraints made are generally not provided. For instance, how does reducing Δr (grid spacing) affect AEP and computational cost?

Wind farm layout optimization with alignment constraints

The article tackles a relevant and interesting topic in wind energy: alignment constraints imposed on wind farm developers by maritime authorities to secure the navigation of boats near wind farms. Despite being well-written from the mathematical point of view, in my view, the article needs improvements in all the bullet points described below.

Line 18: Many other reviews have come up since Herbert-Acero.

Line 25: “12” should be written as “twelve”.

Introduction: I didn’t understand the criteria for this literature review. For instance, why are genetic algorithms and particle swarms even mentioned? Did you do anything related? The idea of randomly mentioning a few papers does not seem scientifically sound. I would stick to papers that are at least more or less related to the general topic. What are the papers that were the closest to analyzing alignment constraints? For instance, line 39 would align well with Fischetti's work cited in line 24.

In the Introduction, it is not clear (or not easy to identify) what benchmark the authors refer to. Is this the benchmark by Thomas et al. (2023)? What are you benchmarking? AEP?

Line 71 and 72: I tried the search for “conjonction” in some dictionaries, but I am suspicious there is a typo mistake in there.

Figure 1 legend: there should be an endpoint on that sentence (and all the other subfigures).

Section 5.2: why do you need to use Dmax? Not clear.

Figure 2. This figure seems a bit raw and could be further improved. Probably, at the very least, with the names of each zone. The size can be reduced. It is right now occupying unproportional space in the article.

The whole section 5.2 talks about the influence of hyper-parameters on the AEP. How does that relate to your storylines? Aren’t you showcasing your methodology for alignment constraints? Shouldn’t you only have sections that support that? I didn’t understand the point of this section and how that supports the storyline.

Line 227: what kind of heuristics? I get that it is confidential, I just don’t get why are you showing it in this open-access scientific publication. No one can replicate/confirm/compare the results.

Line 249: not demonstrated (the benefits of heuristics).

Line 250: The wind community cannot use the heuristics; it is proprietary.

In my opinion, the paper should focus on showcasing the methodology for the alignment constraints. I think it is well contextualized in that sense, as lines 35-38 describe. Other than that, I couldn’t understand how all the hyperparameter analysis contributed to advancing the state of the art in the topic.