A Novel Hybrid Approach for Modeling and Optimisation of Phosphoric Acid Production through the Integration of AspenTech, SciLab Unit Operation, Artificial Neural Networks and Genetic Algorithm
, Lato Pezo 2, Milada Pezo 3, Oskar Bera 1 and Predrag Kojić 1,*Round 1
Reviewer 1 Report
The authors claim at the development of a novel hybrid approach for modeling and optimisation of phosphoric acid production through the integration of AspenTech, SciLab Unit Operation, Artificial Neural Networks and Genetic Algorithm. Although the impressive amount of information as Tables and figures, the paper needs serious efforts in order to meet the standard of such an esteemed journal as Processes. Before the paper to be proceeded to further consideration, I would mention just a few of starting points to be considered and clarified:
1. In general, it is not clear how the designed model looks like?
2. It is at least too bold authors to claim at “to change all process parameters that influence phosphoric acid production on an industrial scale” or “a universal algorithm was developed”…
3. Before Fig. 1, it seems that there is a model, obviously one – “the model was designed to simulate this process”, while in the Section 2.1.4 the authors consider “The first model …”, then “The second model” – need to be clarified.
4. In Section 2.1., “all operating conditions and balances were taken into account to match the industrial conditions”, while in the next paragraph “For this work, only the reaction and filtration sections were singled out.” – need to be clarified.
5. What is the meaning of “This mathematical connection is obtained and can be exported as a function.”?
6. The descriptions of parameters are missing in most of Equations and Tables…
7. I find absolutely redundant including of Tables 1 and 3, since they do not contribute to the subject of paper…
8. In Equations 1 and 2 there are discrepancy between the text and the equations themselves
9. Equation 3 is not a real equation – this is kind of relation, moreover with a probable mistake with using of symbol “-”?
10. There is no Table 4….
11. I would recommend avoiding citation of e.g. [3], [4], [5], 50 [6], [7], [8], [9], [10], [11], [12], [13], with no explanation…
I would suggest moderate editing of English language for better understanding.
Author Response
(Point 1) In general, it is not clear how the designed model looks like?
Response 1: Thank you for your valuable feedback. We apologize for the lack of clarity regarding the design of our model in the manuscript. To address this issue, we have prepared an algorithmic scheme that provides a comprehensive visualization of the model's architecture. This scheme is included as supplementary material to enhance readers' understanding of our design. The supplement will illustrate the different components and their connections, providing a clearer representation of the model's structure. We believe that this addition will greatly enhance the readers' comprehension of our work. As a result, we also have incorporated the changes into the text in revised manuscript (lines 278-281): “An algorithmic scheme that provides a comprehensive visualization of the model's architecture is included as supplementary material to enhance readers understanding of design. The supplement will illustrate the different components and their connections, providing a clearer representation of the model's structure.”
(Point 2) It is at least too bold authors to claim at “to change all process parameters that influence phosphoric acid production on an industrial scale” or “a universal algorithm was developed”…
Response 2: Authors appreciate the reviewer's comment and acknowledge that the language used in those particular statements was overly bold. The objective of our study was to explore and identify key process parameters that have a significant impact on phosphoric acid production on an industrial scale. Our focus was to establish connections between these parameters, as well as investigate their relationship with different qualities of phosphate ore. We acknowledge that claiming to change 'all' process parameters or developing a 'universal' algorithm was an exaggeration, and we apologize for any confusion caused. We revised those statements, as recommended by Reviewer #1. As a result, we have incorporated the changes into the revised manuscript (lines 73-76): “Therefore, the main aim of this study was to investigate the large number of different qualities of phosphate ore and to change and to identify key process parameters that have a significant impact on phosphoric acid production on an industrial scale (both reactors and UCEGO filter sections). In addition, to establish connections between these parameters, as well as investigate their relationship with different qualities of phosphate ore algorithm was developed that can help the broader scientific and engineering community predict the final outcome and quality of the produced acid for any kind and quality of phosphate ore, as well as minimize losses in gypsum.”
(Point 3) Before Fig. 1, it seems that there is a model, obviously one – “the model was designed to simulate this process”, while in the Section 2.1.4 the authors consider “The first model …”, then “The second model” – need to be clarified.
Response 3: Thank you for your valuable feedback on our manuscript. We appreciate your comment and agree that the description in the manuscript may have been confusing. We apologize for any confusion caused and would like to clarify the models mentioned in the text. Before Figure 1, we referred to a model of the separator (This model pertains to the B23 unit mentioned in Table 6), lines 182-183 that was developed as part of the overall simulation process, which serves as an integral component of the UCEGO filter. This model specifically focuses on simulating the separator's behavior within the system. In Section 2.1.4, we presented two distinct artificial neural network (ANN) models. The first ANN model is designed to capture the behavior of the filtration section, while the second ANN model focuses on the reaction section. These models were developed separately to address the specific requirements and characteristics of each section (lines 210-211). We appreciate your feedback for bringing this to our attention. We have revised the manuscript to provide clearer explanations and to avoid any further confusion regarding the different models and their purposes. Once again, we thank you for your valuable input, and we hope that the revisions we have made address your concerns appropriately.
(Point 4) In Section 2.1., “all operating conditions and balances were taken into account to match the industrial conditions”, while in the next paragraph “For this work, only the reaction and filtration sections were singled out.” – need to be clarified.
Response 4: Authors appreciate the valuable feedback provided by the reviewer. The clarification regarding Section 2.1. is indeed essential for the readers' understanding. In the production of phosphoric acid, it is crucial to recognize that the process can be divided into two distinct parts. The first part involves the production of diluted phosphoric acid, which plays a pivotal role in determining the quality of the resulting acid and the losses encountered in the gypsum. The second part comprises the vacuum evaporation process, which aims to concentrate the acid by removing water according to market requirements and desired quality for mineral waste production. Significant consequences arise when the quality of the diluted acid falls below satisfactory limits during the initial stage of acid production. Such a scenario necessitates greater energy consumption during vacuum evaporation and may result in higher gypsum traces within the acid. These gypsum traces can subsequently contribute to the formation of deposits in heat exchangers, ultimately causing a reduction in the capacity of the concentration line. To address these critical factors, we have deliberately focused on tracking the first part of production, encompassing the reaction and filtration sections. This choice allows us to monitor the quality of the acid and its losses in gypsum, as these aspects significantly impact the overall process efficiency. As a result, the second part of the production process, namely vacuum evaporation, was addressed comprehensively in a forthcoming manuscript. As a result, we have incorporated the changes into the revised manuscript (lines 91-103): “In the production of phosphoric acid, it is crucial to recognize that the process can be divided into two distinct parts. The first part involves the production of diluted phosphoric acid, which plays a pivotal role in determining the quality of the resulting acid and the losses encountered in the gypsum. The second part comprises the vacuum evaporation process, which aims to concentrate the acid by removing water according to market requirements and desired quality for mineral waste production. Significant consequences arise when the quality of the diluted acid falls below satisfactory limits during the initial stage of acid production. Such a scenario necessitates greater energy consumption during vacuum evaporation and may result in higher gypsum traces within the acid. These gypsum traces can subsequently contribute to the formation of deposits in heat exchangers, ultimately causing a reduction in the capacity of the concentration line. To address these critical factors, this research deliberately focused on tracking the first part of production, encompassing the reaction and filtration sections. This choice allowed to monitor the quality of the acid and its losses in gypsum, as these aspects significantly impact the overall process efficiency.”
(Point 5) What is the meaning of “This mathematical connection is obtained and can be exported as a function.”?
Response 5: Authors are thankful for this comment and agreed that it is little confusing. After creating ANN model, it is possible to do Code generation in form of MATLAB Matrix-Only function, which is later used in Genetic algorithm. Authors added the following sentence in the revisited manuscript (lines 231-232): “After creating ANN model, it is possible to do Code generation in form of MATLAB Matrix-Only function, which is later used in Genetic algorithm.”
(Point 6) The descriptions of parameters are missing in most of Equations and Tables…
Response 6: Thank you for providing your feedback. We appreciate your attention to detail and acknowledge the need for improved descriptions of parameters in our manuscript. In response to your comment, we have made the necessary revisions to address this concern. Specifically, we have enhanced the descriptions of Equations 1 and 2, providing a more comprehensive explanation of how the parameters are utilized in the respective equations (lines 120-125): “Through a series of carefully conducted experiments and referring to literature [15], it was established a correlation between the quantity of filtrated acid and the time required for its filtration over the woven material. Determining the gradient and intercept of this correlation, enabled to derive the coefficients used in Equations 1 and 2, which facilitated to calculate the permeability and specific resistance, as demonstrated in the literature [15].”
Tables 8-13 are shortened to include only essential parameters. In addition, it was added an extra row to each of these tables that represents the minimum and maximum values achieved for the respective parameters. This will provide a more comprehensive overview of the obtained results. We sincerely value your input and believe that these revisions will greatly enhance the comprehensibility of our manuscript. Thank you once again for your valuable feedback, which has undoubtedly contributed to the overall improvement of our work.
(Point 7) I find absolutely redundant including of Tables 1 and 3, since they do not contribute to the subject of paper…
Response 7: Thank you for your valuable feedback on our manuscript. We appreciate your time and effort in reviewing our work. We have carefully considered your comment regarding the inclusion of Tables 1 and 3. Table 3 represents the parameters and composition of each ore used in the simulation as the inlet material flow. We believe that this information is essential for a comprehensive understanding of the methodology and results presented in the paper. As such, we strongly feel that Table 3 should remain a part of the manuscript. Regarding Table 1, we understand your point that it may be considered redundant. In response to your suggestion, we have decided to remove Table 1. Once again, we sincerely appreciate your feedback and your time spent on reviewing our manuscript.
(Point 8) In Equations 1 and 2 there are discrepancy between the text and the equations themselves
Response 8: Thank you for your valuable feedback regarding Equations 1 and 2 in our manuscript. We appreciate your keen observation and agree that there is a discrepancy between the text and the equations themselves, which may cause confusion for readers. We would like to take this opportunity to provide further clarification on the derivation and application of these equations. The mentioned equations serve as the foundation for calculating permeability and specific resistance in our study, and the following text is added (lines 120-125): “Through a series of carefully conducted experiments and referring to literature [15], it was established a correlation between the quantity of filtrated acid and the time required for its filtration over the woven material. Determining the gradient and intercept of this correlation, enabled to derive the coefficients used in Equations 1 and 2, which facilitated to calculate the permeability and specific resistance, as demonstrated in the literature [15].” We acknowledge that this process could be better explained in the manuscript to ensure clarity for our readers. As a result, we have incorporated the previous sentences into the revised manuscript (lines 120-125) to provide a more detailed and comprehensive explanation of the derivation and application of Equations 1 and 2. We hope that these additions address the concern raised and enhance the overall quality of our manuscript.
(Point 9) Equation 3 is not a real equation – this is kind of relation, moreover with a probable mistake with using of symbol “-”?
Response 9: Thank you for your valuable feedback on our manuscript. We appreciate your insightful comment regarding Equation 3. We agree that it can be misleading to refer to it as a "real equation" since it represents a relationship rather than a traditional mathematical equation. Additionally, we acknowledge that there may have been a mistake in the use of the symbol "-". We would like to clarify that the symbol "-" was employed to denote the value in between the relations of Al2O3, Fe2O3, and P2O5. We apologize for any confusion caused by this choice of notation. Based on your feedback, we understand the need to improve the clarity and accuracy of Equation 3. In our revised manuscript, we made the necessary modifications (instead of "-" it will state from - to) to accurately represent the relationship between Al2O3, Fe2O3, and P2O5, while ensuring that the notation is more explicit and comprehensible.
(Point 10) There is no Table 4….
Response 10: Thank you for your valuable feedback on our manuscript. We sincerely appreciate your keen attention to detail. We acknowledge that there was an error in our manuscript, as Table 4 was inadvertently omitted. We apologize for any confusion caused by this oversight. We have taken immediate action to rectify this issue. All tables in the manuscript have been properly sorted, including the addition of Table 4 in its appropriate place. We have carefully reviewed the content and layout to ensure the accuracy and coherence of our manuscript.
(Point 11) I would recommend avoiding citation of e.g. [3], [4], [5], 50 [6], [7], [8], [9], [10], [11], [12], [13], with no explanation…
Response 11: Thank you for your valuable feedback on our manuscript. We appreciate your suggestion regarding the citation of references [3], [4], [5], 50 [6], [7], [8], [9], [10], [11], [12], [13]. In response to your comment, we have included an additional sentence in the revisited manuscript, lines 48-49 to provide further clarification on the relevance and significance of these citations. We hope that this revised explanation adequately addresses your concerns while avoiding excessive elaboration. We remain committed to improving the clarity and quality of our manuscript based on your insightful input.
Reviewer 2 Report
Major Revision:
This article primarily investigates a large number of phosphate ores of varying qualities and optimizes all process parameters that influence industrial-scale phosphate production. Sensitivity analysis was conducted by simulating ten different phosphate salts with 18 parameters being modified. Multi-objective optimization was performed using artificial neural networks and genetic algorithms to find suitable parameters. Finally, the study predicted the impact of process parameters on acid quality produced and minimized losses during production. Overall, the topic of this study is of great importance to production. However, some technical issues need to be clarified before publication:
1. This article describes the optimization design of phosphate production and uses artificial neural networks and genetic algorithms for multi-objective optimization of phosphate production process parameters, analyzing less-researched filter parameters, which has some innovative significance. The study simulated the production process of phosphate using Matlab, SciLab, and Aspen Plus. The necessary filter parameters were experimentally determined to ensure the accuracy of the simulation process. To achieve the generality of the predictive process parameter algorithm and to maximize the recovery of H3PO4 from raw materials, an ANN model with a determination coefficient of 96% was established. The article's logic is clear and innovative. However, some issues still need to be addressed, such as unclear sentence expressions and graph representation that can cause misunderstandings.
2. This article studies the filtering and reaction processes in phosphate production by establishing an ANN model. Please explain why an ANN model was adopted and what advantages ANN models have in predicting production process parameters.
3. The results and discussions in this article are too lengthy. Can more systematic and efficient expression be used?
4. This article provides insufficient introduction to ANN models and genetic algorithms. Please provide more detailed explanation on how neural networks are combined with the process of optimizing process parameters, and what problem the introduction of neural networks solves in the process of parameter optimization.
The article is well written, smooth and natural, with almost no confusing expressions.
Author Response
(Point 1) This article describes the optimization design of phosphate production and uses artificial neural networks and genetic algorithms for multi-objective optimization of phosphate production process parameters, analyzing less-researched filter parameters, which has some innovative significance. The study simulated the production process of phosphate using Matlab, SciLab, and Aspen Plus. The necessary filter parameters were experimentally determined to ensure the accuracy of the simulation process. To achieve the generality of the predictive process parameter algorithm and to maximize the recovery of H3PO4 from raw materials, an ANN model with a determination coefficient of 96% was established. The article's logic is clear and innovative. However, some issues still need to be addressed, such as unclear sentence expressions and graph representation that can cause misunderstandings.
Response 1: We are pleased to learn that you found our article to be clear and innovative in terms of the optimization design of phosphate production. We agree that there are some areas where sentence expressions could be clarified, and we apologize for any confusion caused by the graph representations. We will carefully revise these sections to ensure they effectively convey the intended information and minimize the potential for misunderstandings. Furthermore, we appreciate your acknowledgment of the innovative significance of our study, particularly in analyzing less-researched filter parameters and establishing an ANN model with a determination coefficient of 96% for predicting process parameters and maximizing H3PO4 recovery. We believe these findings contribute to the broader understanding of phosphate production and optimization techniques. Once again, we sincerely thank you for your constructive feedback and for recognizing the strengths of our work.
(Point 2) This article studies the filtering and reaction processes in phosphate production by establishing an ANN model. Please explain why an ANN model was adopted and what advantages ANN models have in predicting production process parameters.
Response 2: Thank you for your valuable comment. We appreciate the opportunity to further clarify why we adopted an Artificial Neural Network (ANN) model in our study. The use of an ANN model provides distinct advantages over traditional statistical and regression models. Its advanced capabilities lie in its adaptivity and ability to capture nonlinearity. Given the complexity of parameter changes in the production of phosphoric acid, tracking these changes during regular production becomes challenging. It is noteworthy that altering a single parameter may affect some but not all outlet parameters, while changing multiple input parameters simultaneously may influence other output parameters, without affecting the previously modified parameter.
To establish a model capable of learning and predicting these intricate relationships, we deemed it necessary to employ an ANN model. By leveraging its adaptive and nonlinear properties, we can effectively uncover the connections amidst these changes. We have taken your suggestion into consideration and incorporated this explanation in the revised manuscript at the designated location (P 6, lines 193-205): “The use of an ANN model provides distinct advantages over traditional statistical and regression models. Its advanced capabilities lie in its adaptivity and ability to capture non-linearity. Given the complexity of parameter changes in the production of phosphoric acid, tracking these changes during regular production becomes challenging. It is noteworthy that altering a single parameter may affect some but not all outlet parameters, while changing multiple input parameters simultaneously may influence other output parameters, without affecting the previously modified parameter. To establish a model capable of learning and predicting these intricate relationships, it was deemed necessary to employ an ANN model. By leveraging its adaptive and nonlinear properties, it was effectively discovered the connections amidst these changes. Number of samples that are used for Training, Validation, Testing, are 70%, 15%, 15% respectively, type of fitting neural network is fitnet, type of training algorithm is Levenberg-Marquardt.” Thank you once again for your valuable feedback, which has contributed to the improvement of our manuscript.
(Point 3) The results and discussions in this article are too lengthy. Can more systematic and efficient expression be used?
Response 3: Thank you for your valuable feedback on our manuscript. We appreciate your thoughtful consideration of the length of our results and discussions section. We understand your suggestion for a more systematic and efficient expression. While we acknowledge the importance of conciseness, we believe that our current approach provides readers with a comprehensive understanding of the workings of our model. Our intention was to ensure that the paper contains detailed explanations to aid readers in replicating and building upon our research. We are concerned that significantly shortening the paper might deprive readers of the necessary insights and nuances that are crucial for the complete comprehension of our finding. With your comment in mind, we will carefully revisit the results and discussions section to identify areas where we can streamline the content without compromising clarity. Our goal is to provide a more efficient expression while still conveying the key details and insights.
(Point 4) This article provides insufficient introduction to ANN models and genetic algorithms. Please provide more detailed explanation on how neural networks are combined with the process of optimizing process parameters, and what problem the introduction of neural networks solves in the process of parameter optimization.
Response 4: Authors thanks for this comment. Authors add more detailed information on how results from sensitivity analysis are used to create and train ANN, number of samples that are used for Training, Validation, Testing, type of fitting neural network, type of training algorithm, description why Pseudo-code is within function “gamultiobj”, and search space in the revisited manuscript at the lines 203-205, 231-232 and 543-550.
Added text in lines 203-205: “Number of samples that are used for Training, Validation, Testing, are 70%, 15%, 15% respectively, type of fitting neural network is fitnet, type of training algorithm is Leven-berg-Marquardt.”
Added text in lines 231-232: “After creating ANN model, it is possible to do Code generation in form of MATLAB Matrix-Only function, which is later used in Genetic algorithm.”
Added text in lines 543-550: “For filtration section, it was established lower bounds search space of [70 65 45 0.45 4e-05 3 60] while the corresponding upper bounds are [90 80 60 0.6 7e-05 5 110]. These bounds ensure that the algorithm's search is confined within a reasonable and meaningful range.
Similarly, for the reaction section, the lower bounds search space we have set are [70 65 240 55 60 8 70], while the upper bounds are [90 80 270 78 100 9.5 100]. These bounds are carefully chosen to maintain the feasibility and practicality of the algorithm's exploration in the reaction domain.”
Additionally, we provide a clearer description of the number of samples used for Training, Validation, and Testing, as well as the specific type of fitting neural network employed, and the training algorithm utilized. Furthermore, we have considered to provide a description of why the Pseudo-code is integrated within the function "gamultiobj.” lines 236-240: “The gamultiobj function in MATLAB utilizes a variation of the traditional GA called the non-dominated sorting genetic algorithm II (NSGA-II). NSGA-II is an elitist algorithm that uses a combination of genetic operators such as selection, crossover, and mutation to evolve a population of candidate solutions.”
We hope that these revisions adequately address your concerns and provide the necessary clarity and detail. We greatly appreciate your input and believe that these changes enhance the overall quality of the manuscript.
Reviewer 3 Report
The paper presents an interesting work. However, there are some concerns as below:
1- In the abstract and other related sections (Introduction and Results Sections), more details of the results are needed to justify how the proposed model is superior to other models and based on what evaluation metrics.
2- In Section1, Introduction, interesting information has been given on the production of phosphate rocks and its challenging conditions. However, there are no details on the limitations of existing techniques to minimize the loss of its production. Also, there is no statement in terms of justifying the novelty of the proposed work in terms of finding the limitations of existing techniques that are similar to what is being proposed (e.g. other artificial intelligence models employed for the same aim). Including such information is very important to justify the novelty of the proposed work.
3- In Section 2.1.5, although it is mentioned that multi-objective optimization is performed via a genetic algorithm, it is not clear what genetic algorithm is used; is it the original one or a variation of it?
4- In addition, it is not clear how the genetic algorithm is used. How the algorithm pseudo-code is employed? What is the search space on which the algorithm functions to optimize the obtained solution?
5- Also, why the genetic algorithm is used for the optimization? there are several other algorithms used for optimization including those recent swarm intelligence algorithms. Those algorithms could be used and they prove to be much more effective than the genetic algorithm.
The overall quality of the English language looks good.
Author Response
(Point 1) In the abstract and other related sections (Introduction and Results Sections), more details of the results are needed to justify how the proposed model is superior to other models and based on what evaluation metrics.
Response 1: Thank you for your valuable feedback on our manuscript. We appreciate your thoughtful comments and suggestions. In response to your specific questions and concerns, we would like to provide the following clarifications and additional information: Our proposed model for the UCEGO filter in phosphoric acid production offers several key advantages over existing models. Firstly, unlike previous models that treat the filter as a single entity, our model takes into consideration all sections of the filtration process, including the strong acid section, recycle acid section, weak acid section, and gypsum section. This holistic approach allows us to capture the intricate interplay and coordination among these sections, which is crucial for achieving high-quality phosphoric acid production. To justify the superiority of our model, we have employed advanced techniques and methodologies. We have utilized AspenTech, a widely recognized process simulation software, to accurately model the UCEGO filter and its various sections. Additionally, we have implemented an Artificial Neural Network (ANN) in combination with a Multi-Objective Optimization Genetic Algorithm (MOOGA) to optimize the performance of the filter. The evaluation metrics we have utilized to demonstrate the superiority of our model include:
- Filtration efficiency: We measure the overall efficiency of the filtration process, considering factors such as filtrate clarity, solid separation, and filtration rate. By comparing the performance of our model with existing models, we can showcase the enhanced filtration efficiency achieved by our approach.
- Product quality: We assess the quality of the phosphoric acid produced using our model. Parameters such as impurity levels, acid concentration, and acid purity are considered to evaluate the superiority of our model in achieving higher-quality phosphoric acid.
- Operational stability: We evaluate the stability and robustness of our model under different operating conditions and disturbances. By simulating various scenarios and assessing the model's performance, we can highlight its superior stability compared to alternative approaches.
(Point 2) In Section1, Introduction, interesting information has been given on the production of phosphate rocks and its challenging conditions. However, there are no details on the limitations of existing techniques to minimize the loss of its production. Also, there is no statement in terms of justifying the novelty of the proposed work in terms of finding the limitations of existing techniques that are similar to what is being proposed (e.g. other artificial intelligence models employed for the same aim). Including such information is very important to justify the novelty of the proposed work.
Response 2: Thank you for your valuable feedback on our manuscript regarding phosphoric acid production and the development of a model for the UCEGO filter. We appreciate your comments and would like to address your concerns regarding the limitations of existing techniques and the novelty of our proposed work. The following text is added (lines 111-117): “To the best of researchers’ knowledge, existing techniques often overlook the intricate interplay and coordination among the various sections of the UCEGO filter. They tend to focus on individual sections in isolation, without recognizing the potential cross-effects and interferences that can occur. This manuscript seeks to bridge this gap by analyzing and tracking changes in each part of the filter and establishing connections between them. Conventional approach of considering the filter as a single entity is not sufficient to address the challenges posed by inconsistent filtration quality across different sections.”
The following text is added (lines 214-222): “By employing advanced artificial neural network techniques and employing a multi-objective optimization genetic algorithm, manuscript aim to optimize the filtration performance across all sections simultaneously, thereby minimizing loss and improving the overall production efficiency. The novelty of this approach lies in its comprehensive nature and the integration of advanced artificial intelligence techniques to address the challenges associated with filtration in phosphoric acid production. To the best of authors’ knowledge, no previous studies have specifically focused on developing a model for the UCEGO filter those accounts for the individual sections and their coordination.”
By providing a detailed analysis of the limitations of existing techniques and highlighting the uniqueness of our proposed work, we aim to contribute to the advancement of the field and provide valuable insights for both operators and engineers in the phosphoric acid production industry. Thank you once again for your insightful comments, which will undoubtedly strengthen our manuscript.
(Point 3) In Section 2.1.5, although it is mentioned that multi-objective optimization is performed via a genetic algorithm, it is not clear what genetic algorithm is used; is it the original one or a variation of it?
Response 3: Thank you for your suggestion. NSGA-II genetic algorithm was used. We added following sentence in the revisited manuscript (lines 236-240): “The gamultiobj function in MATLAB utilizes a variation of the traditional GA called the non-dominated sorting genetic algorithm II (NSGA-II). NSGA-II is an elitist algorithm that uses a combination of genetic operators such as selection, crossover, and mutation to evolve a population of candidate solutions.”
(Point 4) In addition, it is not clear how the genetic algorithm is used. How the algorithm pseudo-code is employed? What is the search space on which the algorithm functions to optimize the obtained solution?
Response 4: The GA is implemented in the Matlab function “gamultiobj” and was used for multi-objective optimization problems in the section 3.5 on the pages 15-20. Pseudo-code is within function “gamultiobj”. For the search space we added sentences regarding search space in the revisited manuscript (lines 543-550): “For filtration section, it was established lower bounds search space of [70 65 45 0.45 4e-05 3 60] while the corresponding upper bounds are [90 80 60 0.6 7e-05 5 110]. These bounds ensure that the algorithm's search is confined within a reasonable and meaningful range.
Similarly, for the reaction section, the lower bounds search space we have set are [70 65 240 55 60 8 70], while the upper bounds are [90 80 270 78 100 9.5 100]. These bounds are carefully chosen to maintain the feasibility and practicality of the algorithm's exploration in the reaction domain.”
(Point 5) Also, why the genetic algorithm is used for the optimization? there are several other algorithms used for optimization including those recent swarm intelligence algorithms. Those algorithms could be used and they prove to be much more effective than the genetic algorithm.
Response 5: This is a good remark. We have tried both types of nature-inspired optimization techniques that have been widely used in solving complex problems. Although swarm intelligence algorithms have advantages over GA, in our study GA was better and faster algorithm. It can be because genetic algorithms have a better balance between exploration and exploitation of the search space. GA use mechanisms such as selection, crossover, and mutation to explore different regions of the search space while gradually converging towards optimal solutions. This property helps GA in escaping local optima and searching for globally optimal solutions. On the other hand, swarm intelligence algorithms, such as particle swarm optimization (PSO), tend to focus more on exploitation and in our study in few iterations was stacked in local optima.
Round 2
Reviewer 1 Report
Thanks the authors for the very detailed and comprehensive replies to all my comments. In fact, it is not normal answering the reviewers’ comment to lead to another one article to be written… However, I truly believe that addressing my comments the paper has achieved better level of understanding. Once again I would like to point the focus to the impressive amount of information given in the paper and then to be evaluated the authors efforts to present their idea as clear as possible. That faced the authors to a quite hard task which they succeeded to solve in an acceptable level. Although very hard, they convinced me that their investigation deserves to be presented to the wider audience. For the future work I would suggest authors to try to treat their paper as a reader, rather than as an author, that will help them to present their achievements in more acceptable manner.
I would suggest careful reading of the manuscript - minor editing of English language required.
Reviewer 3 Report
The authors addressed most of my concerns, except for the point where they justified the usage of the GA algorithm. The authors were correct in their response :"Although swarm intelligence algorithms have advantages over GA, in our study GA was better and faster algorithm." as GA is more efficient than several other swarm intelligence algorithms. However, GA can still suffer from several problems in being stuck in local optima compared to very recent swarm intelligence algorithms. Also, some recent algorithms are more efficient than the older ones. This is why it is very interesting for authors to explore in the future the usage of more recent swarm intelligence algorithms and it is important that they highlight this point in their paper's future work.
The English writing is good.
