Path Planning of an Underwater Vehicle by CFD Numerical Simulation Combined with a Migration-Based Genetic Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Статья рассматривает актуальную научно-техническую проблему повышения эффективности планирования и управления траекторным движением подводного аппарата в условиях течений и препятствий. В статье авторы предлагают две ключевые идеи. Первая заключается в использовании комбинации вычислительной гидродинамики с генетическим алгоритмом для подводных аппаратов (CFD + GA), большинство существующих работ в этой области либо используют эмпирические модели потока, либо игнорируют его полностью. Вторая ключевая идея состоит в использовании концепции миграции из алгоритма биогеографической оптимизации для обмена информацией между решениями, что является новым для задач планирования маршрутов подводных аппаратов. Такой подход позволяет популяции "учиться" более эффективно. Предлагаемые методы делают хороший академический вклад в развитие теории, но для промышленного применения потребуются значительные доработки в областях онлайн-адаптации, обработки в реальном времени и более полного учёта гидродинамики.

 

Замечания к статье:

1. Основным недостатком предлагаемого метода CFD + GA является отсутствие инструментов адаптации к изменяемым течениям. Если течения в реальности отличаются от CFD-модели (что почти всегда гарантировано), оффлайн рассчитанная модель течений становится непригодной. Это существенно ограничивает применимость метода, т.к. перед каждым запуском аппарата нужно иметь актуальную карту течений на текущий период времени для рабочей акватории.
2. Рассматриваемые примеры с сеткой 25х25 ячеек с одной стороны охватывают не сильно большой участок акватории (реальные миссии как правило имеют больший масштаб), но при этом уже требуют достаточной вычислительной мощности для расчёта онлайн на борту аппарата. Поэтому как следует из статьи CFD расчет выполняется предварительно. Это не позволяет учитывать изменения по ходу движения аппарата.
3. В статье подводный аппарат рассматривается в виде точечной массы, что является существенной идеализацией реального движения подводного аппарата. Такой подход игнорирует гидродинамические эффекты (присоединённые массы, сопротивление, зависящее от ускорения, моменты инерции и динамика ориентации аппарата и др.).
4. В статье авторы не сравнивают свой метод с другими известными подходами на основе глубокого обучения или современными методами оптимизации (например, муравьиные колонии, оптимизация роем частиц). Авторы ограничиваются сравнением с базовым GA и одним улучшенным GA.
5. Технические вопросы.

5.1. В алгоритме 1 не ясно как вычисляются Evaluate((P_i)), Migrate((P_i)), Selection((P_i)),  Crossover((P_i)), Mutation((P_i)). В чем отличие P(i)  от P?

5.2. В алгоритме 2 не ясно как вычисляются CurrentAngle(Path), AngleSubtraction(A, FluidData), MaxIntensity(Pos, FluidData)?

 

Статья носит существенный теоретический характер и требует доработки указанных замечаний.

 

 

 

The article considers an urgent scientific and technical problem of increasing the efficiency of path planning of an underwater vehicle motion in conditions of currents and obstacles. In the article, the authors propose two key ideas. The first is to use a combination of computational fluid dynamics with a genetic algorithm for underwater vehicles (CFD+GA). Most existing work in this field either uses empirical flow models or ignores it completely. The second key idea is to use the migration concept from the biogeographic optimization algorithm to exchange information between solutions, which is new for underwater vehicle path planning tasks. This approach allows the population to "learn" more efficiently. The proposed methods make a good academic contribution to the development of theory, but industrial applications will require significant improvements in the areas of online adaptation, real-time processing, and more comprehensive accounting of hydrodynamics.

Comments on the article:

1. The main disadvantage of the proposed CFD + GA method is the lack of adaptation tools to changing currents. If the flows in reality differ from the CFD model (which is almost always guaranteed), the offline calculated flow model becomes unusable. This significantly limits the applicability of the method, because before each launch of the device, you need to have an up-to-date current map for the current time period for the working water area.
2. The examples under consideration with a grid of 25x25 cells on the one hand cover a small area of the water area (real missions usually have a larger scale), but it already require sufficient computing power to calculate online on board the vehicle. Therefore, as follows from the article, the CFD calculation is performed in advance. This does not allow us to account for changes during the movement of the vehicle.
3. In the article, the underwater vehicle is considered as a point mass, which is a significant idealization of the real movement of the vehicle. This approach ignores hydrodynamic effects (added masses, acceleration-dependent drag, moments of inertia, and vehicle orientation dynamics, etc.).
4. In the article, the authors do not compare their method with other well-known deep learning approaches or modern optimization methods (for example, ant colonies, particle swarm optimization). The authors limit themselves to a comparison with the basic GA and one improved GA.
5. Technical issues.

5.1. In algorithm 1, it is not clear how Evaluate((P_i)), Migrate((P_i)), Selection((P_i)), Crossover((P_i)), Mutation((P_i)) are calculated. What is the difference between P(i) and P?

5.2. In algorithm 2, it is not clear how currentAngle(Path), AngleSubtraction(A, FluidData), MaxIntensity(Pos, FluidData) are calculated?

 

The article is of a theoretical nature and requires further elaboration of above comments.

Author Response

The article considers an urgent scientific and technical problem of increasing the efficiency of path planning of an underwater vehicle motion in conditions of currents and obstacles. In the article, the authors propose two key ideas. The first is to use a combination of computational fluid dynamics with a genetic algorithm for underwater vehicles (CFD+GA). Most existing work in this field either uses empirical flow models or ignores it completely. The second key idea is to use the migration concept from the biogeographic optimization algorithm to exchange information between solutions, which is new for underwater vehicle path planning tasks. This approach allows the population to "learn" more efficiently. The proposed methods make a good academic contribution to the development of theory, but industrial applications will require significant improvements in the areas of online adaptation, real-time processing, and more comprehensive accounting of hydrodynamics.

Comment 1: The main disadvantage of the proposed CFD + GA method is the lack of adaptation tools to changing currents. If the flows in reality differ from the CFD model (which is almost always guaranteed), the offline calculated flow model becomes unusable. This significantly limits the applicability of the method, because before each launch of the device, you need to have an up-to-date current map for the current time period for the working water area.

Response 1: Thank you for your valuable comments. We agree that the lack of tools for handling dynamically changing flow fields could limit the applicability of the CFD+GA approach. The main objective of this paper is to establish a high-fidelity prediction and evaluation framework, aiming to verify whether the paths generated by our algorithm in complex flow environments remain optimal, compared to traditional and some improved GA methods. Our method can help underwater vehicle avoid unfavorable flow fields and ensure navigation safety. In many practical scenarios, flow velocity and direction remain relatively stable over short periods. The proposed framework serves as the foundational part of a "perception–prediction–optimization–control" closed-loop system. In future work, we plan to incorporate varying flow fields to enhance the applicability of the algorithm, as mentioned in the revised manuscript.

Comment 2: The examples under consideration with a grid of 25x25 cells on the one hand cover a small area of the water area (real missions usually have a larger scale), but it already require sufficient computing power to calculate online on board the vehicle. Therefore, as follows from the article, the CFD calculation is performed in advance. This does not allow us to account for changes during the movement of the vehicle.

Response 2: Thanks for the comments. In the revised manuscript, we have added the results of 20×20 grid map and 30×30 grid map to verify the proposed GAM. Regarding the changes during the movement of the vehicle, we will incorporate varying flow fields to enhance the applicability of the algorithm in our future work, as replied above.

Comment 3: In the article, the underwater vehicle is considered as a point mass, which is a significant idealization of the real movement of the vehicle. This approach ignores hydrodynamic effects (added masses, acceleration-dependent drag, moments of inertia, and vehicle orientation dynamics, etc.).

Response 3: Thanks for the comment. Indeed, this is a limitation of the study. In this paper, the primary objective is to tackle the coupling between complex flow environments and global path planning. The reason for adopting a point-mass representation is that we focus on “how flow-field information can drive global path optimization.” In our future work, we will take into account the dynamic model of underwater vehicle to improve the feasibility of the path planning strategy. In the conclusion of revision, we have explained the future work on the dynamic model of underwater vehicle.

Comment 4: In the article, the authors do not compare their method with other well-known deep learning approaches or modern optimization methods (for example, ant colonies, particle swarm optimization). The authors limit themselves to a comparison with the basic GA and one improved GA.

Response 4: Thank you for your comments. Indeed, we did not compare our method with other algorithms such as ACA and PSO. The main goal of this paper is to investigate how the introduction of flow fields affects path planning for underwater vehicles. Each algorithm has it merits and demerits. In this paper, we chose GA and made some improvement to evaluate whether our proposed approach maintains desirable performances after incorporating flow effects. Conventional GA and an improved GA are selected to be compared. In the next work, a comparative analysis with other advanced algorithms will be conducted for a comprehensive evaluation of GAM, as mentioned in the revision.

Comment 5: In algorithm 1, it is not clear how Evaluate((P_i)), Migrate((P_i)), Selection((P_i)), Crossover((P_i)), Mutation((P_i)) are calculated. What is the difference between P(i) and P?

Response 5: Thanks for the comments. In the revised manuscript, more details have been added before Algorithm 1 to explain these operations, as follows. Evaluate(P(i)) refers to the calculation of the fitness value for each path in the i-th population generation using the path fitness function E (Equation 5)；Migrate(P(i)) denotes the migration operation applied to the paths generated after the i-th iteration；Selection(P(i)) represents the selection process for the paths produced in the i-th generation. In this step, the probability of each individual being selected is computed based on its fitness value (higher fitness corresponds to a greater probability). These probabilities are summed to form a cumulative probability distribution over the interval [0,1]. A random number is then generated, and the individual corresponding to the cumulative probability interval in which this number falls is selected. This process is repeated until the new population reaches the size of the original population；Crossover(P(i)) performs the crossover operation as follows: First, the population is sorted in descending order based on fitness and then divided into three groups. Within each group, two paths are randomly selected. It is then determined whether these two paths share any common points (excluding the start point and end point). Next, a random number x between 0 and 1 is generated. If x < PC, a common point is randomly selected and crossover is performed at that point. If x≥PC，no crossover is applied. If the two paths do not share any common points (other than the start and end points), a segment from each path is randomly selected and joined together. If this process fails to produce a valid path after 100 attempts, the original paths are retained to avoid generating invalid solutions. Mutation(P(i)) refers to the mutation operation applied to the paths generated in the i‑th iteration. First, all paths are sorted according to their fitness values. The top 1/5 of the paths are preserved without any mutation. For each of the remaining paths, a random number y between 0 and 1 is generated. If y < Pm , a mutation operation—specifically, path segment replacement—is performed on that path; otherwise, no mutation is applied. P(i) denotes the path generated after the i-th iteration, while P denotes the path with the highest fitness value after 50 iterations.​

Comment 6: In algorithm 2, it is not clear how currentAngle(Path), AngleSubtraction(A, FluidData), MaxIntensity(Pos, FluidData) are calculated?

Response 6: Thanks for the comments. In the revised manuscript, more details have been added before Algorithm 2, as follows. CurrentAngle（Path）is obtained by extracting the flow field angle at each node along the path from Fluent; MaxIntensity(Pos,FluidData) retrieves the flow velocity value at a given position from the Fluent-derived fluid data; AngleSubtraction(A, FluidData) calculates the angular difference between the current path angle θ (computed via the cosine theorem) and the local flow field angle.

Reviewer 2 Report

Comments and Suggestions for Authors

1. The combination of a Genetic Algorithm (GA) with a Migration Operator is not a novel contribution, as the concept is directly borrowed from the Biogeography-Based Optimization Algorithm (BBOA), which is already cited in the literature review [17] [18]. The authors must clearly define the novelty beyond a simple hybridization.
2. The abstract seems to be lacking crucial information, including an outline of the results that will be presented in the study, the methodology used to achieve those results, a clear description of the objectives, and a comprehensive discussion of the approach taken in each stage of the research.
3. In the abstract: The sentence "A computational fluid dynamics (CFD) numerical simulation is performed to obtain the information about the flow field through which an underwater vehicle will pass" is verbose and awkward. A more concise phrasing is required
4. The claim of proposing a "hierarchical underwater path planning strategy" is an overstatement. The work appears to be a standard two-step process: (1) environment modeling (CFD) and (2) path search (GAM), which is not a hierarchical strategy in a formal sense.
5. The literature review (Section 1) merely lists various algorithms without providing a deep, critical analysis of their specific weaknesses in the context of underwater vehicle path planning with flow fields.
6. The research gap is not properly identified and explained in the introduction section.
7. The abstract mentions simulation results but fails to specify which algorithms the proposed GAM is compared against. For high-impact publication, a comparison against state-of-the-art algorithms (e.g., DRL-based methods) is essential, not just the traditional GA.
8. The entire study relies on numerical simulation. The lack of any experimental validation, even in a simplified test tank environment, severely limits the practical significance and suitability for a journal focused on Marine Science and Engineering.
9. There is no mention of how underwater vehicle dynamics constraints (e.g., maximum turning rate or acceleration) affect the planned path, making the resulting paths potentially physically infeasible.
10. The environment modeling section (2.1) uses a simple 2D grid method. This is a significant oversimplification for a 3D underwater environment. The authors must justify why a 2D model is sufficient or expand the formulation to 3D.
11. Section 2.3 mentions using the RANS (Reynolds-average Navier Stokes) method for CFD simulation due to calculation efficiency, but fails to specify the turbulence model used, which is critical for reproducibility.

 

12. The initial population generation strategy (Section 3.1) is overly complex and poorly described. The use of "mean value interpolation" (Equation 3) to ensure continuity is a heuristic that may introduce bias or non-optimal paths, and its effect on initial population diversity is not analyzed.
13. Lines 95-97: states that CFD is "more accurate than empirical formula or database method" without providing any evidence or reference to support this claim in the context of underwater environment modeling.
14. There is no analysis of the algorithm's sensitivity to variations in the grid size (n×n) or the resolution of the flow field data derived from CFD.
15. Ensure that appropriate references should be included to all mathematical expressions.
16. The English quality is unacceptable and requires comprehensive language editing.
17. The conclusions section requires significant improvements and should be effectively rewritten after addressing the aforementioned comments.

 

 

Author Response

Comment 1: The combination of a Genetic Algorithm (GA) with a Migration Operator is not a novel contribution, as the concept is directly borrowed from the Biogeography-Based Optimization Algorithm (BBOA), which is already cited in the literature review [17] [18]. The authors must clearly define the novelty beyond a simple hybridization

Response 1:  Thank you for the comments. Compared with the Biogeography-Based Optimization Algorithm (BBOA) proposed in [17] and [18]. We have introduced a different “change_path” operator that integrates intersection-based path crossover and a heuristic bridging mechanism, offering greater efficiency and robustness than traditional BBO migration. When an inferior path shares nodes with an elite path, our proposed operator does not perform random component migration. Instead, it executes topology-aware path crossover. This is equivalent to directly grafting the "wisdom of the latter segment" from the elite path onto the inferior one. This design offers three advantages: (1) Maintaining path continuity; (2) Inheriting validated feasible segments; (3) Facilitating efficient learning. To address the potential failure of traditional BBO when no common nodes exist, we designed a heuristic bridging mechanism. It randomly extracts a front segment from the inferior path and makes multiple attempts to connect it to a node on the elite path. We also incorporated a “remove-loops” operator to eliminate redundant cycles. Our method ensures the stability and robustness of the migration operation, preventing population degradation that may arise from traditional migration.

In the revised manuscript, we have added the these comments in the third paragraph of introduction.

Comment 2: The abstract seems to be lacking crucial information, including an outline of the results that will be presented in the study, the methodology used to achieve those results, a clear description of the objectives, and a comprehensive discussion of the approach taken in each stage of the research.

Response 2: Thanks for your comments. In the revised manuscript, some quantitative results have been added to confirm the advantages of the proposed method. The objectives and methodology are also explained.

Comment 3: In the abstract: The sentence "A computational fluid dynamics (CFD) numerical simulation is performed to obtain the information about the flow field through which an underwater vehicle will pass" is verbose and awkward. A more concise phrasing is required.

Response 3: Thanks for your suggestion. In the revised manuscript, the statement has been simplified as “The CFD simulation models the flow field along the planned path of the underwater vehicle.”

Comment 4: The claim of proposing a "hierarchical underwater path planning strategy" is an overstatement. The work appears to be a standard two-step process: (1) environment modeling (CFD) and (2) path search (GAM), which is not a hierarchical strategy in a formal sense.

Response 4: Thank you for the comments. the statement has been revised as “This paper proposes a physics-informed global path planning framework for under-water vehicles integrating CFD simulation and genetic algorithm.”

Comment 5: The literature review (Section 1) merely lists various algorithms without providing a deep, critical analysis of their specific weaknesses in the context of underwater vehicle path planning with flow fields.

Response 5: Thanks for your comments. In the revised manuscript, more description has been added to explain the weakness of existing path planning algorithms, in the first paragraph of introduction.

Comment 6: The research gap is not properly identified and explained in the introduction section.

Response 6: Thanks for the comment. Complied with the suggestion, some sentences have been added to the introduction to explain the weakness of existing studies, in the first paragraph of introduction; and the difference between literature and our proposed method, in the third paragraph.

Comment 7: The abstract mentions simulation results but fails to specify which algorithms the proposed GAM is compared against. For high-impact publication, a comparison against state-of-the-art algorithms (e.g., DRL-based methods) is essential, not just the traditional GA.

Response 7: Thanks for your comments. In the revised manuscript, the algorithms to be compared have been mentioned in the abstract.

Indeed, we did not compare our method with state-of-the-art algorithms. The main goal of this paper is to investigate how the introduction of flow fields affects path planning for underwater vehicles. Each algorithm has it merits and demerits. In this paper, we chose GA and made some improvement to evaluate whether our proposed approach maintains desirable performances after incorporating flow effects. Conventional GA and an improved GA are selected to be compared. In the next work, a comparative analysis with other advanced algorithms will be conducted for a comprehensive evaluation of GAM, as mentioned in the revision.

Comment 8: The entire study relies on numerical simulation. The lack of any experimental validation, even in a simplified test tank environment, severely limits the practical significance and suitability for a journal focused on Marine Science and Engineering.

Response 8: Thanks for the comment. We acknowledge that the lack of experimental validation is a limitation of the current study. The primary objective of this paper is to propose and validate that the path planning framework maintains its efficacy after incorporating CFD based flow field data. The simulation study is not an end but a crucial step toward practical implementation. We have commenced constructing a tank and an experiment platform for underwater vehicles. Experimental validation will be carried out in the future.

Comment 9: There is no mention of how underwater vehicle dynamics constraints (e.g., maximum turning rate or acceleration) affect the planned path, making the resulting paths potentially physically infeasible.

Response 9: Thanks for the comment. Indeed, this is a limitation of the study. In this paper, the primary objective is to tackle the coupling between complex flow environments and global path planning. In our future work, we will take into account the dynamic model of underwater vehicle to improve the feasibility of the path planning strategy. In the conclusion of revision, we have explained the future work on the dynamic model of underwater vehicle.

Comment 10: The environment modeling section (2.1) uses a simple 2D grid method. This is a significant oversimplification for a 3D underwater environment. The authors must justify why a 2D model is sufficient or expand the formulation to 3D.

Response 10: Thanks for your suggestion. In revised manuscript, we have added results regarding 3D path planning.

Comment 11: Section 2.3 mentions using the RANS (Reynolds-average Navier Stokes) method for CFD simulation due to calculation efficiency, but fails to specify the turbulence model used, which is critical for reproducibility.

Response 11: Thanks for your comment. In the paragraph after Figrue 7, it is stated that the turbulence model used is k-ω model.

Comment 12: The initial population generation strategy (Section 3.1) is overly complex and poorly described. The use of "mean value interpolation" (Equation 3) to ensure continuity is a heuristic that may introduce bias or non-optimal paths, and its effect on initial population diversity is not analyzed.

Response 12: Thank you for your comment. Traditional GA initializes paths through pure randomness, resulting in a low probability of feasible paths near large obstacles and computationally wasteful repair attempts. Our method overcomes this by directly generating a higher-quality initial population, requiring no repair. The design is two-fold: Row-by-row progression provides macro-directional bias from start to goal, avoiding local traps; In-row randomization preserves micro-level exploration as a form of constrained randomness. Path diversity will be further supplemented by subsequent migration, mutation, and crossover operations. In the revised manuscript, the above explanation has been added, before Algorithm 1.

Comment 13: Lines 95-97: states that CFD is "more accurate than empirical formula or database method" without providing any evidence or reference to support this claim in the context of underwater environment modeling.

Response 13: Thank you for the comment. In the revised manuscript, the statement has been removed.

Comment 14: There is no analysis of the algorithm's sensitivity to variations in the grid size (n×n) or the resolution of the flow field data derived from CFD.

Response 14: Thanks for your comment. In the revised manuscript, we have added the results of 20×20 grid map and 30×30 grid map to verify the proposed GAM.

Comment 15: Ensure that appropriate references should be included to all mathematical expressions.

Response 15: Thanks for your comment. In the revised manuscript, the main formulas have been added by reference citation. Two references have been added in the reference list.

Comment 16: The English quality is unacceptable and requires comprehensive language editing.

Response 16: Thank you for your suggestion. In revising the manuscript, we try our best to improve the English writing. Some statements are rewritten. Grammar errors and typos have been corrected.

Comment 17: The conclusions section requires significant improvements and should be effectively rewritten after addressing the aforementioned comments.

Response 17: Thanks for the suggestion. The conclusion has been rewritten. Improvement and some comments on future work have been mentioned.

 

Reviewer 3 Report

Comments and Suggestions for Authors

In the presented manuscript “Path planning of underwater vehicle by CFD numerical simulation combined with migration based genetic algorithm” the authors focus on a highly topical and important problem in the field of autonomous underwater vehicles (AUVs) – path planning in environments with strong and complex currents. The presented hierarchical strategy, which combines computational fluid dynamics (CFD) simulations for flow modeling and an advanced genetic algorithm (GAM), is an intelligent and significant contribution to the literature. The authors successfully integrate CFD-derived current velocity and direction data into the environmental model, allowing the GAM algorithm to avoid unviable paths (where the current velocity may exceed the maximum speed of the AUV). The improved genetic algorithm (GAM) with migration, elite selection, segmented crossover, and adaptive mutation operators demonstrates promising results in terms of convergence and path smoothness in the simulated scenarios (e.g., fewer breakpoints).

 

The manuscript contains significant elements of novelty, mainly in the area of ​​integrating CFD simulation with path planning and improving the genetic algorithm (GA).

 

The author has chosen to upload his research as scientific article and they have formally followed the related structure – Introduction and Literature Review, Materials and Methods, Results, Discussion and Conclusion. All these parts are well distinguished through by other names but with the same meanings.

 

The manuscript is well structured in terms of the literature review. Out of a total of 35 listed literature sources, 20 (approximately 57%) were published in the last five years (2021-2025), indicating that the review is up-to-date. The literature review (Section 1. Introduction) is logically and hierarchically well-structured, smoothly guiding the reader from the general problem to the specific solution proposed by the authors.

 

All figures and tables are well visible and readable.

 

Overall, the manuscript is easy to read and follows the standard scientific structure, but there are some specific shortcomings that could make it difficult for the reader, especially one who is not closely specialized in Genetic Algorithms and CFD. If a reader is a person with general technical experience, he will struggle in the "Methods" section, as the lack of mathematical rigor and insufficient explanation of specific GAM operators make key components of the study unclear.

 

I have the following remarks to particular points in the manuscript:

 

1. Missing Definition of Path Smoothness (S): The full mathematical formula for the "path smoothness cost" (S), which is a key part of the fitness function (Equation 5), needs to be added. Without this definition, the optimization criterion is unclear.
2. Missing algorithm parameters (GAM): It is mandatory to provide a table or paragraph with all key parameters used in the simulations: population size, maximum number of iterations, crossover and mutation probabilities, as well as the weight coefficients from the fitness function.
3. Unclear GAM Operators: Provide more details about the segmented crossover mechanism – how exactly the population is divided and how this prevents low-quality crossover.
4. In Section 4.1, where inflection points are compared, clearly define what an "inflection point" means in the context of your path and how it is calculated.
5. Add a comparison of execution time (Computational Time) in Table 1. This is an essential metric when comparing path planning algorithms.

Author Response

In the presented manuscript “Path planning of underwater vehicle by CFD numerical simulation combined with migration based genetic algorithm” the authors focus on a highly topical and important problem in the field of autonomous underwater vehicles (AUVs) – path planning in environments with strong and complex currents. The presented hierarchical strategy, which combines computational fluid dynamics (CFD) simulations for flow modeling and an advanced genetic algorithm (GAM), is an intelligent and significant contribution to the literature. The authors successfully integrate CFD-derived current velocity and direction data into the environmental model, allowing the GAM algorithm to avoid unviable paths (where the current velocity may exceed the maximum speed of the AUV). The improved genetic algorithm (GAM) with migration, elite selection, segmented crossover, and adaptive mutation operators demonstrates promising results in terms of convergence and path smoothness in the simulated scenarios (e.g., fewer breakpoints).

 

The manuscript contains significant elements of novelty, mainly in the area of ​​integrating CFD simulation with path planning and improving the genetic algorithm (GA).

The author has chosen to upload his research as scientific article and they have formally followed the related structure – Introduction and Literature Review, Materials and Methods, Results, Discussion and Conclusion. All these parts are well distinguished through by other names but with the same meanings.

The manuscript is well structured in terms of the literature review. Out of a total of 35 listed literature sources, 20 (approximately 57%) were published in the last five years (2021-2025), indicating that the review is up-to-date. The literature review (Section 1. Introduction) is logically and hierarchically well-structured, smoothly guiding the reader from the general problem to the specific solution proposed by the authors.

All figures and tables are well visible and readable.

Overall, the manuscript is easy to read and follows the standard scientific structure, but there are some specific shortcomings that could make it difficult for the reader, especially one who is not closely specialized in Genetic Algorithms and CFD. If a reader is a person with general technical experience, he will struggle in the "Methods" section, as the lack of mathematical rigor and insufficient explanation of specific GAM operators make key components of the study unclear.

 I have the following remarks to particular points in the manuscript:

Comment 1: Missing Definition of Path Smoothness (S): The full mathematical formula for the "path smoothness cost" (S), which is a key part of the fitness function (Equation 5), needs to be added. Without this definition, the optimization criterion is unclear.

Response 1: Thanks for your comment. In the revision, we have added the formula for the "path smoothness cost". (Equation (7)).

Comment 2: Missing algorithm parameters (GAM): It is mandatory to provide a table or paragraph with all key parameters used in the simulations: population size, maximum number of iterations, crossover and mutation probabilities, as well as the weight coefficients from the fitness function.

Response 2: Thank you for your comment. The GAM algorithm parameters are configured as follows: a population size of 50, a crossover probability of 0.8, a mutation probability of 0.2, and a maximum of 50 iterations. The weight coefficient of path length is 1 and the weight coefficient of path smoothness is 9. The parameters for the aforementioned algorithms have been added to the revised manuscript. In the revision, the description of parameters are added after Figure 1.

Comment 3: Unclear GAM Operators: Provide more details about the segmented crossover mechanism – how exactly the population is divided and how this prevents low-quality crossover.

Response 3: Thank you for your comment. In the revision, more details on the segmented crossover mechanism have been added as follows. First, all feasible solutions are ranked by their fitness values. Based on this ranking, they are categorized into three groups (good, medium, poor). Subsequently, within the same group, two feasible solutions are selected. A common node (excluding the start and end points) is randomly chosen as the crossover node to exchange their path segments. These solutions of intra-group crossover inherently impose a degree of constraint on the search direction. Compared to the traditional genetic algorithm, where two solutions are randomly selected from the entire population for crossover, our method substantially reduces the generation of low-quality offspring, thereby accelerating the convergence rate. The added details are located in the paragraph after Eq.(4).

Comment 4: In Section 4.1, where inflection points are compared, clearly define what an "inflection point" means in the context of your path and how it is calculated.

Response 4: Thank you for your comment. In the presence of currents, the presence of inflection points implies extra energy cost for steering; therefore, fewer turns lead to lower energy consumption over paths of the same length. In the study, the inflection point is determined by comparing the of the two movement directions of the adjacent three nodes. In the revision, the description of inflection point has been added, in the paragraph after Figure 3.

Comment 5: Add a comparison of execution time (Computational Time) in Table 1. This is an essential metric when comparing path planning algorithms.

Response 5: Thank you for your comment. We acknowledge that the comparison of execution time is an essential metric when comparing path planning algorithms. In the study, it is found both the traditional genetic algorithm (0.06 s) and the improved genetic algorithm (0.09 s) outperform the proposed algorithm (0.71 s) in terms of execution time. Nevertheless, the underwater vehicle is unable to reach the target point along the paths generated by the conventional GA and improved GA. To illustrate the path feasibility, we did not show the computational time.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors responded to all comments, but most of them essentially indicate that the authors have not yet resolved the issues raised and plan to explore them in the future.
This is acceptable for a number of issues, in the reviewer's opinion. However, for comments 5 and 6, the authors did not provide answers to specific questions regarding how certain calculation procedures specified in Algorithms 1 and 2 are performed. It is recommended that these procedures be clearly described in terms of mathematical operations and auxiliary algorithms, or that precise references be provided where this information is provided. Otherwise, it is impossible to reproduce these algorithms.

Author Response

Comment 1: The authors responded to all comments, but most of them essentially indicate that the authors have not yet resolved the issues raised and plan to explore them in the future.
This is acceptable for a number of issues, in the reviewer's opinion. However, for comments 5 and 6, the authors did not provide answers to specific questions regarding how certain calculation procedures specified in Algorithms 1 and 2 are performed. It is recommended that these procedures be clearly described in terms of mathematical operations and auxiliary algorithms, or that precise references be provided where this information is provided. Otherwise, it is impossible to reproduce these algorithms.

Response 1: Thanks for the comment. In the revised manuscript, important formulas have been added to explain Algorithm 1 and Algorithm 2.

Reviewer 2 Report

Comments and Suggestions for Authors

I am satisfied with the current revisions, as the authors have effectively resolved most of my initial concerns.

Author Response

Comment 1: I am satisfied with the current revisions, as the authors have effectively resolved most of my initial concerns.

Response 1: Thanks.