Improved Seagull Optimization Algorithm Combined with an Unequal Division Method to Solve Dynamic Optimization Problems

Round 1

Reviewer 1 Report

I have some concerns about the article, if I have understood correctly, the main contribution in the article is the "unequal division", basically, if I have followed the explanation right, the idea is to produce a random deviation of the discretization points. But, there are some problems with this approach:

1. Of course, random distributions are, well, random, so actually, how could you be sure that it will always be better than other options? I mean in order to be sure you should run several different cases, and you should use any known random generator and/or specify the seed to provide reproducibility in your experiment.
2. Furthermore, I miss some conjecture about the reason and causality of that behaviour. 
3. Since that reason is missing, could it be possible that any "unequal division" would be an improvement? I mean the origin of the improvement could be the random part or the "unequal division".

There are some other points that, in my opinion, should be improved:

• It is said that there is a relation between these optimization problems and energy consumption, but, none of the examples reflect this relation, I suppose that if the amount of product for a given reaction is improved it is possible to save energy, but the article does not support those comments in any way. Furthermore, if the "objective" is saving energy, why not use the energy as the objective function?
• Finally, I miss some comments on numerical approximation. The numbers for the objective function in the examples are very similar, most of them only differ at 1e-4, so I would say that all methods are finding the same maximum whereas with different numerical exactiness, could those differences be produced by the integration part of the algorithm? I mean, all the process involve a lot of numerical operations, all of them have some degree of approximation so it could be that actually J = 0.5730 is numerically the same number as J = 0.573535, actually they could be the same solution but subject to a different degree of approximation.

 

Author Response

Point 1: Of course, random distributions are, well, random, so actually, how could you be sure that it will always be better than other options? I mean in order to be sure you should run several different cases, and you should use any known random generator and/or specify the seed to provide reproducibility in your experiment.

Response 1: Thank you very much for the review proposal. Yes, we cannot guarantee that our segmentation method will be better than other methods. In fact, each method has its own advantages and disadvantages. We just want to find new and different methods for the segmentation of control variables, and we will continue to focus on it in the future.

Point 2: Furthermore, I miss some conjecture about the reason and causality of that behaviour.

Response 2: Thank you very much for the suggestions of the judges. We propose an unequal division method. The purpose is to divide the control function into a few more copies at the sudden change, and a few fewer copies at the flat part. From the results of our test, it is effective. 

Point 3: Since that reason is missing, could it be possible that any "unequal division" would be an improvement? I mean the origin of the improvement could be the random part or the "unequal division".

Response 3: Thank you very much for the suggestions of the judges. We have not proved this, and we are not sure, but we will work hard in this direction in the future. Our basic idea is mainly based on how to give more points at the sudden change of the control function and less points at the smooth point, and we have also verified it through a few examples. However, a few examples cannot guarantee that all problems will be improved, but we will work hard in the future.

Point 4: It is said that there is a relation between these optimization problems and energy consumption, but, none of the examples reflect this relation, I suppose that if the amount of product for a given reaction is improved it is possible to save energy, but the article does not support those comments in any way. Furthermore, if the "objective" is saving energy, why not use the energy as the objective function?

Response 4: Thank you very much for the suggestions of the judges. We are demonstrating our algorithm based on the classic model as an example, and because there are more people studying the classic example, it is easy to compare the quality of the algorithm, so the objective function of the example is not changed. Of course, we can save energy as the goal. In the future, we will explore the goal of energy saving and conduct demonstration and analysis.

Point 5: Finally, I miss some comments on numerical approximation. The numbers for the objective function in the examples are very similar, most of them only differ at 1e-4, so I would say that all methods are finding the same maximum whereas with different numerical exactiness, could those differences be produced by the integration part of the algorithm? I mean, all the process involve a lot of numerical operations, all of them have some degree of approximation so it could be that actually J = 0.5730 is numerically the same number as J = 0.573535, actually they could be the same solution but subject to a different degree of approximation.

Response 5: Thank you very much for the suggestions of the judges. These objective functions are classic examples, and many people have studied them. At the same time, the solutions listed in the literature are generally the best solutions currently available, and they are already very close to the optimal solution of the model, so the values are very similar. If the values can be improved, the effectiveness and feasibility of the algorithm are explained.

 

 

 

Reviewer 2 Report

In the introduction and literature review of the article, the authors presented a poor study of literature that is connected to the main subject of the paper. In my opinion literature study should be a little bit wider. 

During the pre-review process was also noted below pointed significant editorial disadvantages:
- use capital letters in surname Runge-Kutta (for example line 151, 155 158)
- after the update in May 2020 Windows 10 is only available in architecture 64bit. You should separate the word "windows" and "10" inline 146
- remove space between "(" and "N", for example: ( N = ??) inline 187, 188, 194, 179 and others
- add space between the word "follows" and "[22]" inline 212
- remove space between "B" and "," inline 216

Author Response

Point 1: In the introduction and literature review of the article, the authors presented a poor study of literature that is connected to the main subject of the paper. In my opinion literature study should be a little bit wider.

Response 1: Thank you very much for the suggestions of the judges. Based on your suggestions, we have revised the grammar and format of the introduction part of the article, and supplemented the literature part.

Point 2: During the pre-review process was also noted below pointed significant editorial disadvantages:use capital letters in surname Runge-Kutta (for example line 151, 155 158).

Response 2: Thank you very much for the suggestions of the judges. The “runge-kutta” in the article is modified to “Runge-Kutta”. 

Point 3: After the update in May 2020 Windows 10 is only available in architecture 64bit. You should separate the word "windows" and "10" inline 146.

Response 3: According to the suggestion, we have separated "windows" and "10" inline 146.

Point 4: Remove space between "(" and "N", for example: ( N = ??) inline 187, 188, 194, 179 and others.

Response 4: According to your suggestion, we removed space between "(" and "N".

Point 5: Add space between the word "follows" and "[22]" inline 212.

Response 5: Thank you very much for the suggestions of the judges. We have added space between the word "follows" and "[22]" inline 212.

Point 6: Remove space between "B" and "," inline 216.

Response 6: Thank you very much for the suggestions of the judges. We have removed space between "B" and "," inline 216.

 

 

 

 

 

Reviewer 3 Report

I congratulate the authors on a nicely written and clear paper. Your modification to the Seagull Algorithm is impressive and I would like to see how it compares in terms of efficiency compared to other methods and this is my major concern in the paper as I don’t think this is clearly presented.

 

Here are some specific questions and comments I have:

 

Line 102 if $f_c \tends 0$ then surely so does $A$ and so $CS\tendsto 0$ in equation 4.

 

Line 106 can you explain the term best position

 

Eqn (6) plese explain zbest

 

Eqn (12) I can’t see where r is used. What is its purpose and what exactly is $miu$

 

Line 131 What does “premature phenomenon” mean

 

Section 3: Is it the purpose of the algorithm that a flock of seagulls are deployed simultaneously to search for the optimum. This isn’t clear from the description of the method.

 

Line 139 How do you define the fitness? This is critical to the efficiency of any algorithm that you are investigating.

 

Line 170: Please explain the Batch process, e.g. what is being optimised.

 

Table 3 and 4 I can see that ISOA gives the optimal value but I can’t see how the efficiency compares with other techniques e.g. is N the number of steps required (I think you call it a temperature). If N is a number of steps, then the ISOA is one of the least efficient algorithms compared to IKEA, IKBCA, HIGA, IACA. In the introduction and conclusion you say that your goal is to reduce energy use in the optimisation process, in which case comparing the efficiency of each method is required. This is my main (possibly only) criticism of this paper and feel that it needs to be addressed.

Author Response

Point 1: Line 102 if $f_c \tends 0$ then surely so does $A$ and so $CS\tendsto 0$ in equation 4.

Response 1: Thank you very much for the suggestions of the judges. Yes, if $f_c \tends 0$ then surely so does $A$ and so $CS\tendsto 0$ in equation 4.

Point 2: Line 106 can you explain the term best position.

Response 2: Thanks for the question from the judges. The best position is equivalent to the best solution in a problem.

Point 3: Eqn (6) plese explain zbest.

Response 3: In Eqn (6), zbest represents the best position in the seagull population.

Point 4: Eqn (12) I can’t see where r is used. What is its purpose and what exactly is $miu$.

Response 4: Thanks for the question from the judges. It can be seen from Eqns. (9-11) that we have calculated the values of x, y, and z using r. At the same time, miu is a parameter of the seagull optimization algorithm, its purpose is to enhance the optimization ability of the algorithm.

Point 5: Line 131 What does “premature phenomenon” mean.

Response 5: Thanks for the question from the judges. Premature phenomenon means that the algorithm falls into the local optimum too early, and it is difficult to jump out of the local to the global optimum.

Point 6: Section 3: Is it the purpose of the algorithm that a flock of seagulls are deployed simultaneously to search for the optimum. This isn’t clear from the description of the method.

Response 6: Thank you very much for the suggestions of the judges. We have supplemented the solution steps and details of the seagull optimization algorithm.

Point 7: Line 139 How do you define the fitness? This is critical to the efficiency of any algorithm that you are investigating. 

Response 7: In our paper, the fitness function we define is as follows:

function dxdt = obj(t,x,T) //Batch reactor

    k1 = 4*10^3*exp(-2500/T);

    k2 = 6.2*10^5*exp(-5000/T);

    xa = x(1);

    xb = x(2);

    dxadt = -k1*xa^2;

    dxbdt = k1*xa^2-k2*xb;

dxdt = [dxadt;dxbdt];

function dxdt = obj(t,x,u) //Parallel reaction problem of tubular reactor

x1 = x(1);

x2 = x(2);

dx1dt = -(u + 0.5*u^2)*x1;

dx2dt = u*x1;

dxdt = [dx1dt;dx2dt];

function dxdt = obj(t,x,u)//Tubular reactor

    xa = x(1);

    xb = x(2);

    dxadt = u*(10*xb-xa);

    dxbdt = -u*(10*xb-xa) - (1-u)*xb;

    dxdt = [dxadt;dxbdt];

Point 8: Line 170: Please explain the batch process, e.g. what is being optimised.

Response 8: The optimization process of batch reactor: First, initialize T within the range of (298,398), then use the improved seagull optimization algorithm (ISOA) to iteratively update T, and finally find the best performance index J through the fitness function.

 

Point 9: Table 3 and 4 I can see that ISOA gives the optimal value but I can’t see how the efficiency compares with other techniques e.g. is N the number of steps required (I think you call it a temperature). If N is a number of steps, then the ISOA is one of the least efficient algorithms compared to IKEA, IKBCA, HIGA, IACA. In the introduction and conclusion you say that your goal is to reduce energy use in the optimisation process, in which case comparing the efficiency of each method is required. This is my main (possibly only) criticism of this paper and feel that it needs to be addressed.

Response 9: Thank you very much for the advice of the judges. Regarding the solution of the chemical engineering case in this article, most scholars are currently concerned about the accuracy of the solution, but there are few related studies on the efficiency of the algorithm. But we now increase the use ISOA to solve chemical problems by combining the equal division method and the unequal division method respectively, and finally compare their execution efficiency. The experimental results show that the efficiency of the unequal division method is better than that of the equal division method.

Reviewer 4 Report

See attached. 

Comments for author File: Comments.pdf

Author Response

Point 1: In line 12 “automatic control of chemical process” should include in the title.

Response 1: Thank you very much for the review proposal. We changed the title to “Improved seagull optimization algorithm combined with unequal division method to solve automatic control of chemical process”.

Point 2: In line 27 be more specific: what process?

Response 2: Thank you very much for the review proposal. Therefore, the optimization control of chemical process such as batch chemical process, tubular reaction process, which has become a research hotspot.

Point 3: In line 28 delete “scholars at home and abroad”.

Response 3: As suggested, we have deleted “scholars at home and abroad”.

Point 4: In line 31 “Nonlinearity and low stability” should be more specific.

Response 4: Thank you very much for the review proposal. However, as the chemical engineering model becomes more and more complex and the number of control variables increases, the stability of the model becomes lower, and the input and output are not proportional.

Point 5: In line 33 “, it”.

Response 5:  We changed to “.It”.

Point 6: In line 35 rephrase “Among them, use direct method [1] and indirect method [2] to solve chemical problems which is the most common”. 

Response 6: Thank you very much for the review proposal. We changed it to “direct methods [1] and indirect methods [2] are often used to solve chemical problems”.

Point 7: In line 36 rephrase “infinite-dimensional”. 

Response 7: We changed “infinite-dimensional” to “continuous”.

Point 8: In line 38 rephrase “But the indirect method mainly solves the optimality condition (necessary condition) of the original problem”. 

Response 8: But indirect methods mainly solve the optimality condition (necessary condition) of the original problem.

Point 9: Delete ‘, etc’ in line42.

Response 9: Deleted.

Point 10: Modify “Literature” in line 51,55.

Response 10: We changed “Literature” to “Reference”.

Point 11: What does “good” mean in line 61.

Response 11: Thank you very much for the review proposal, “good” means each chemical case has achieved good performance index values.

Point 12: Introduction is too generic and this hard to follow.

Response 12: Based on your suggestions, we have revised the grammar and format of the introduction part of the article, and supplemented the literature part to expand its scope.

Point 12: What is “them” referring to? In line 65.

Response 12: We changed “Among them” to “At the same time”.

Point 13: Explain what these variables represent in line 67.

Response 13: Thank you very much for the review proposal. Where  shows performance index;  is terminal value function; and  represents integral function.

Point 14: Modify “In the above formula” in line 69. 

Response 14: Thank you very much for the review proposal. We changed it to “In Eqns. (1-2)”.

Point 15: Modify “that is” in line 79. 

Response 15: Thank you very much for the review proposal. We changed it to “i.e.”.

Point 16: Capitalize paper names, such as “runge-kutta”. 

Response 16: Thank you very much for the review proposal. We changed it to “Runge-Kutta” in the paper.

Point 17: Be consistent: t is used for time above in section 3.

Response 17: Thank you very much for the review proposal. We changed the “t” in the third section to “iter”.

Point 18: Line 101 “Among them”.

Response 18: Thank you very much for the review proposal. We have deleted it.

Point 19: Modify the “miu” of formula 12.

Response 19: Thank you very much for the review proposal. We changed “miu” to “”.

Point 20: Move Figure 1. closer to where it is cited in the text.

Response 20: Thank you very much for the review proposal. We moved Figure 1. to the top of "3.1 Migration behavior".

Point 21: Explain the algorithm in more details. The current description is difficult to follow and leaves the reader guessing for many steps and equations given.

Response 21: In the third section, we added an introduction to the seagull optimization algorithm and the solution steps for adding the seagull optimization algorithm.

Point 22: I don't understand how this improves the existing algorithm? be more specific in section 4.

Response 22: Thank you very much for the review proposal. We have added the details of the improved seagull optimization algorithm in section 4.

Point 23: In line 131 premature phenomenon？

Response 23:Thanks for the question from the judges. Premature phenomenon means that the algorithm falls into the local optimum too early, and it is difficult to jump out of the local to the global optimum.

Point 24: In line 135 what text?

Response 24: We changed “what text” to “in this paper”.

Point 25: Modify “the” in line 137. 

Response 25: We changed “the” to “this”.

Point 26: Modify “windows10” in line 146. 

Response 26: Thank you very much for the review proposal. We changed “windows10” to “Windows 10”.

Point 27: Avoid using imperative tense in line 148.

Response 27: We deleted devide and replaced it with other statements. “First assume that the number of segments in the time domain is , and use Eqn. (3) for unequal division”

Point 28: “Eqns” not “formulas” .

Response 28: According to your suggestion, we have modified the formula in the article.

Point 29: The formatting of this psoudocode can be improved using flow chart,bullet pts,e.g .

Response 29: Thank you very much for the review proposal. We have modified the pseudocode.

Point 30: Explain in more details providing an example or two for batch reactor.

Response 30: Thank you very much for the review proposal. We have added details to it.

Point 31: Unit problems and figure problems in batch reactors.

Response 31: Thank you very much for the review proposal. We modified these questions, where the units of C_A, C_B and J are mol/L, and the unit of T is K. At the same time, according to your suggestions, Figure 2.-Figure 5. have been modified, and we adjusted page margin.

Point 32: For Table 3, does J have units?

Response 32: Thank you very much for the review proposal. We added a unit to J (mol/L).

Point 33: For Table 3, does J have units?

Response 33:Thank you very much for the review proposal. We added a unit to J (mol/L).

Point 34: Explain in more details providing an example or two for parallel reaction problem of tubular reactor.

Response 34: Thank you very much for the review proposal. We have added some details to it.

Point 35: Unit problems and figure problems in parallel reaction problem of tubular reactor.

Response 35: Thank you very much for the review proposal. We modified these questions, where the units of x₁, x₂ and J are mol/L, and the unit of u(t) is 10⁶. At the same time, according to your suggestions, Figure 6.-Figure 9. have been modified, and we adjusted page margin.

Point 36: Is it fair to compare methods that used a smaller a or where N is unknown? about all examples.

Response 36: Thank you very much for the review proposal. Regarding the solution of the chemical engineering case in this article, most scholars are currently concerned about the accuracy of the solution. But in this article, we compare and analyze the efficiency.

Point 37: Unit problems and figure problems in tubular reactor.

Response 37: Thank you very much for the review proposal. We modified these questions, where the units of x_A, x_B and J are mol/L, and the unit of u(z) is %. At the same time, according to your suggestions, Figure 10.-Figure 13. have been modified, and we adjusted page margin.