Presenting a Novel Evolutionary Method for Reserve Constrained Multi-Area Economic/Emission Dispatch Problem

Round 1

Reviewer 1 Report

An efficient optimization technique Modified grasshopper optimization algorithm (MGO) is introduced in this study to enhance the exploration and exploitation processes of the traditional GO method.

After reading the manuscript I have the following recommendations:

The main contribution of the paper seems to be the formulation of the  Modified grasshopper optimization algorithm (MGO), nevertheless, it is not clear (from the point of view of the mathematical formalism), how to include  mutation in the modified algorithm. In this regard, ¿is it equation 17 related to equation 15 somehow?. Authors should make this point clearer.

Figure 2 makes reference to procedures that are developed in other works. I suggest that the main points of these works have to be outlined, specially those that can be represented using mathematical models, which can be included into Figure 2.

Please explain why to use Fuzzy approach, is it the only one available in this context?

Numeral 4 is used to introduce optimization results. The  way this part of the document is written  is not clear. It is very dificult to understand because of the use of data from other works. I suggest to make a better contextualization of previous works and the use of a Figure that helps readers to have a better understanding of the case of study.

 

 

 

 

 

 

 

 

 

Author Response

Reviewer: 1

 

Comments to the Author

An efficient optimization technique Modified grasshopper optimization algorithm (MGO) is introduced in this study to enhance the exploration and exploitation processes of the traditional GO method.

After reading the manuscript I have the following recommendations:

 

1- The main contribution of the paper seems to be the formulation of the Modified grasshopper optimization algorithm (MGO), nevertheless, it is not clear (from the point of view of the mathematical formalism), how to include mutation in the modified algorithm. In this regard, is it equation 17 related to equation 15 somehow? Authors should make this point clearer.

Authors' reply:

Thanks for your comment, The difference between the proposed MGO algorithm and the original version of the GO algorithm is the provision of two mutation operators in the MGO algorithm, which are presented in equations (17) and (18). These operators are presented in order to improve the performance of the proposed algorithm and avoid premature optimality

(17)

 

 

 

where, R is a random number between [0, 1] and  is a mutation vector. The current search agent is updated related to the optimal position to maximize the utilization of the GO method when there is changeable bandwidth.

 

(18)

where,  is a random number between [0, 1].  is a dynamic bandwidth variable that decreases as follows:

	(19)
	(20)

where,  and  , denote the maximum and minimum bandwidth limitations respectively, T and  represent the current and maximum iteration numbers, respectively.

Regarding the relationship between formulas )15) and (17-18), I can say that these formulas are not related. To clarify the issue, the following explanation about the flowchart of the proposed MGO method and relations (15) and (17-18) helps to explain the matter.

In the proposed flowchart, after updating the factors ,  and PAR, the position of each grasshopper is calculated by equation (15). Next, the step setting condition of the algorithm in equation (21) is compared to the (r₃) random number, then one of the equations (17) or (18), which represent the mutation operator, is used. Finally, the fitness value obtained from one of the mutation operators (17) or (18) is compared with the fitness of the grasshopper position obtained from the equation (15). Finally, either the grasshopper position obtained from the equation (15) or the grasshopper position obtained from the mutation operators (17) or (18) is accepted.

 

2- Figure 2 makes reference to procedures that are developed in other works. I suggest that the main points of these works have to be outlined, especially those that can be represented using mathematical models, which can be included into Figure 2.

Authors' reply:

Thanks for your comment, As answered in the previous question, the difference between the MGO and the original GO algorithm is the provision of mutation operators in the proposed MGO algorithm in order to improve the performance of this algorithm, which is presented in equations (17) and (18). In the flowchart of the proposed MGO algorithm shown in Figure (2), the effect of mutation operators (17) and (18) can be seen. Also, according to the flowchart in Figure (2), before using the mutation operators, equation (15) is used to update the position of each propeller. However, in the original GO algorithm, we don't have mutation operators, and the position of each grasshopper is updated using equation (15).

In the following, the difference between both methods will be determined using a flowchart. In each flowchart, the formulation of each algorithm is presented. But the explanation about the process of using mutation operators in the MGO method in the previous question has been fully answered.

 Figure 2. Diagram of the proposed MGO method.

 

 

 

 

 

 

 

 

 

Figure 10. Diagram of the conventional GO method.

3-Please explain why to use Fuzzy approach, is it the only one available in this context?

Authors' reply:

Thanks for your comment, Considering that the optimization problem in this study is multi-objective and objective functions are not in the same range, therefore fuzzy sets are implemented to substitute each objective function as a value between 0 and 1. A fuzzy set is generally shown by a membership function (μ_i). The ith objective function of F_i is depicted by a membership function μ_i and defined as (22)

 

(22)

 

where,   and  represent the minimum and maximum boundaries of , respectively. The vector of choice variables is called X, and  is the fuzzy set for the ith objective function.

Also, the fuzzy approach is used to control the non-dominated solution repository. In multi-objective optimization, a repository is considered for storing non- dominated solutions. To control the tank size, equation (25) is used to remove some answers with lowest . Also, among the remaining answers, the answer set that has the largest amount of  is selected as a compromise answer in the optimization of several objective functions. In most studies [17-22], a fuzzy method is used to solve multi-objective MADE problem.

(25)

 

The weighting factor for the kth objective function is denoted by k. Number of objective functions and non-dominated solutions are defined by n and m, respectively. Finally,  represents a fuzzy set.

 

4-Numeral 4 is used to introduce optimization results. The way this part of the document is written is not clear. It is very difficult to understand because of the use of data from other works. I suggest to make a better contextualization of previous works and the use of a Figure that helps readers to have a better understanding of the case of study.

Authors' reply:

Thanks for your comment, In the last three lines of section 4 on page 12, explanations about this issue are presented and marked with green color. The introduction of the test system and the optimization results of the study are presented in section 4.In sub-sections 4.1, 4.2 and 4.3, MAED, single-objective RCMAED and multi-objective RCMAEED problems are solved by MGO, GO PSO-SFLA [33], MPSO [32], SFLA [33] and PSO [32] methods, respectively.

In this research, the six evolutionary algorithms mentioned in the above paragraph including MGO, GO, PSO-SFLA, MPSO, SFLA and PSO are simulated and used to solve the optimization problem in single and multi-objective frameworks. The rest of the methods that are presented in Tables 3 and 5 are related to other studies and the relevant references are provided for them in the mentioned tables.

In Table 3, the result of the proposed MGO method is compared with other studies. Tables 4 and 6 compare the results of six algorithms used in this research. In Table 5, the results of six algorithms used in this study are compared with other studies. Figures 4 and 5 show the convergence graph of six evolutionary methods used in this study to solve the MAED and RCMAED problems, respectively. In the figures below, the algorithms used and other algorithms related to other studies to solve the optimization problem in 3 case studies are presented.

 

 

 

 

 

 

Figure 11. The methods used for solving the MAED problem

 

 

 

 

 

 

Figure 12. The methods used for solving the RCMAED problem

 

 

 

 

 

 

Figure 13. The methods used for solving the RCMAED problem

 

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We are looking forward to receiving your final decision on the paper.

Sincerely yours

Authors

Author Response File: Author Response.pdf

Reviewer 2 Report

Title: Presenting a Novel Evolutionary Method for Reserve Constrained Multi-Area Economic/Emission Dispatch problem

Manuscript ID: sustainability-2425319

Thank you for submitting your paper. This paper deals with an interesting topic. However, a few revisions need to be made before publication.

 

1.1. Introduction

Line 52: “The majority of studies on the MAED tackle the problem from an economic standpoint, but doing this ignores other important issues of the power system, such as environ mental impacts, which can have a destructive effect on the environment and increase pollution”

Comment: To support this statement, I recommend that the author include the research papers' references.

 

1.2. Literature Review

Line 105: “However, the pollution objective function is not included in these studies and the problem is solved as a single objective with the fuel cost function of the power plants”

Comment: To strengthen the statement, it would be helpful for the authors to include supporting reference studies. It shouldn't be assumed that readers will automatically think to look for them.

Line 143: “. The advantage of these studies compared to previous studies is to consider the emission function in solving the MAED problem, another feature of these studies is similar to previous studies, providing new exploratory algorithms based on strategies to balance local and global search. However, the spinning reserve constraints in these studies is not considered similar to other previous studies.”

Comment: In order to clarify this statement, it is imperative that it be broken down into 2-3 distinct sentences. Additionally, it is necessary that specific citations be provided for the studies mentioned. We request that the authors specify which studies they are referring to when they use phrases such as "these studies" and "previous studies". Thank you for your cooperation.

Line 163: “However, in these studies, the emission function is not considered in solving the optimization problem, and the problem has been solved as a single objective. Also, the real limitations of the power system in solving the optimization problem, such as VPE, 165 MFO, POZs, are not included in these studies, which makes the obtained results unreliable because the constraints related to a real power system are not considered in these studies.”

Comment: This statement requires clarification. It would be helpful to split it into 2-3 sentences and provide specific citations for the studies mentioned by the authors. For instance, when mentioning "these studies," please indicate which studies they are referring to and when referring to "previous studies," please specify which previous studies are being referred to.

 

1.2. Contribution and 1.4. Paper Organistaion

Comment: My suggestion is for the authors to rearrange the paper. Specifically, they should create a separate main section titled 1.2. Literature Review and place it after the first section titled 1. Introduction. The remaining sections, namely 1.1, 1.3, and 1.4, should be placed under the first main heading of the 1. Introduction section.

 

3         Methodology

Comment: This section is very confusing. To make things crystal clear, it's important to provide a solid justification for why each algorithm was chosen. I would suggest the authors to provide a justified reasoning behind each decision.

 

4. MAED Problem

Comment: This section is acceptable, but I would recommend that the authors rename it as "Findings" or "Discussion" for clarity.

 

5. Conclusion

Comment: This section meets the minimum requirements, but it is important to include recommendations for future researchers.

 

Please note the following minor corrections:

- Line 12: The spelling of "Continuous" is incorrect.

- Line 59: When using abbreviations, such as Multi-Objective Optimization Problem (MOOP), please provide the full form when using it for the first time.

- Line 89: Could you please provide the full form of VPE and POZ?

- Line 169: Please correct "MADE" to "MAED".

 

- Line 613: To maintain consistency with previous usage, please use the term "Chaos Mechanism" instead of "Chaos Theory".

There are minor grammatical errors in the text. It would be beneficial to have it proofread for better accuracy and clarity.

Author Response

Reviewer: 2

 

Comments to the Author

Thank you for submitting your paper. This paper deals with an interesting topic. However, a few revisions need to be made before publication.

 

1.1. Introduction

Line 52: “The majority of studies on the MAED tackle the problem from an economic standpoint, but doing this ignores other important issues of the power system, such as environ mental impacts, which can have a destructive effect on the environment and increase pollution”

Comment: To support this statement, I recommend that the author include the research papers' references.

 Authors' reply:

Thanks for your comment, Reference is given in the text of the article for this sentence and it is marked with purple color.

 

1.2. Literature Review

Line 105: “However, the pollution objective function is not included in these studies and the problem is solved as a single objective with the fuel cost function of the power plants”

Comment: To strengthen the statement, it would be helpful for the authors to include supporting reference studies. It shouldn't be assumed that readers will automatically think to look for them.

Authors' reply:

Thanks for your comment, Reference is given in the text of the article for this sentence and it is marked with purple color.

Line 143: “. The advantage of these studies compared to previous studies is to consider the emission function in solving the MAED problem, another feature of these studies is similar to previous studies, providing new exploratory algorithms based on strategies to balance local and global search. However, the spinning reserve constraints in these studies is not considered similar to other previous studies.”

Comment: In order to clarify this statement, it is imperative that it be broken down into 2-3 distinct sentences. Additionally, it is necessary that specific citations be provided for the studies mentioned. We request that the authors specify which studies they are referring to when they use phrases such as "these studies" and "previous studies". Thank you for your cooperation.

Authors' reply:

Thanks for your comment, This text is broken into 3 sentences and marked with green color. Also, in the text of the article, wherever the terms of these studies and previous studies are mentioned, a reference is given for them and it is marked with purple color.

 

Line 163: “However, in these studies, the emission function is not considered in solving the optimization problem, and the problem has been solved as a single objective. Also, the real limitations of the power system in solving the optimization problem, such as VPE, MFO, POZs, are not included in these studies, which makes the obtained results unreliable because the constraints related to a real power system are not considered in these studies.”

Comment: This statement requires clarification. It would be helpful to split it into 2-3 sentences and provide specific citations for the studies mentioned by the authors. For instance, when mentioning "these studies," please indicate which studies they are referring to and when referring to "previous studies," please specify which previous studies are being referred to.

 Authors' reply:

Thanks for your comment, This text is broken into 2 sentences and marked with green color. Also, in the text of the article, wherever the terms of these studies and previous studies are mentioned, a reference is given for them and it is marked with purple color.

 

1.2. Contribution and 1.4. Paper Organisation

Comment: My suggestion is for the authors to rearrange the paper. Specifically, they should create a separate main section titled 1.2. Literature Review and place it after the first section titled 1. Introduction. The remaining sections, namely 1.1, 1.3, and 1.4, should be placed under the first main heading of the 1. Introduction section.

 Authors' reply:

Thanks for your good suggestion, Considering that the innovations of the study have been presented based on the review of past works. Therefore, it is necessary to review the past works and then present the innovations of the study based on filling the research gap of the previous studies. For this reason, in the introduction, a review of the past works has been done, and then the innovations of this study have been presented.

 

3. Methodology

Comment: This section is very confusing. To make things crystal clear, it's important to provide a solid justification for why each algorithm was chosen. I would suggest the authors to provide a justified reasoning behind each decision.

Authors' reply:

Thanks for your comment,

Mathematical methods [6-8] have been proposed to solve the MAED problem have some counterpoints such as continuity and derivability of the fitness functions. Further, the MAED turns into a non-continuous and non-convex optimization problem by considering all constraints. Therefore, mathematical based optimization methods cannot be efficient to deal with such a multi-constraints and complex problem. Over the past decades different heuristic algorithms have been implemented to solve the complex optimization problems in power systems [9, 10]. Therefore, in this study, we have tried to use a relatively new algorithm to solve the optimization MAED problem. The grasshopper optimization (GO) algorithm was introduced in 2017 by Sarmi et al [31]. This algorithm is modelled on the group life of grasshoppers. Purpose of the grasshoppers is to reach the optimal point. The basic features of this algorithm that made us use it to solve the optimization MAED problem in this study include quick convergence, accuracy in searching for global solutions, simple implementation.

In addition to the advantages of the GO algorithm, this algorithm is similar to other random algorithms due to the random initial population having disadvantages such as being trapped in the local optimum and converging to a global or near-global solution in the long term. Therefore, we have decided to improve the efficiency of the common GO algorithm in this study by presenting new mutation strategy in modified grasshopper optimization (MGO) method. A random mutation of GO is applied in the modified version of the algorithm to improve exploration in order to discover new searching areas and avoid stagnation in the local optima.

Examining the optimization results of this study including table 4, convergence graphs in figures 4 and 5 shows that the MGO algorithm has converged to a more optimal solution compared to the common GO algorithm and other evolutionary algorithms. Therefore, the efficiency of the proposed MGO algorithm is proved in comparison with other evolutionary algorithms including, GO, PSO-SFLA [33], MPSO [32], SFLA [33] and PSO [32].

 

4. MAED Problem

Comment: This section is acceptable, but I would recommend that the authors rename it as "Findings" or "Discussion" for clarity.

 Authors' reply:

Thanks for your comment, Section 4 has been renamed to Results and Discussions.

 

5. Conclusion

Comment: This section meets the minimum requirements, but it is important to include recommendations for future researchers.

 Authors' reply:

Thanks for your comment, The suggestion section for future work is added at the end of the conclusion and marked with green color.

Please note the following minor corrections:

- Line 12: The spelling of "Continuous" is incorrect.

- Line 59: When using abbreviations, such as Multi-Objective Optimization Problem (MOOP), please provide the full form when using it for the first time.

- Line 89: Could you please provide the full form of VPE and POZ?

- Line 169: Please correct "MADE" to "MAED".

- Line 613: To maintain consistency with previous usage, please use the term "Chaos Mechanism" instead of "Chaos Theory".

Authors' reply:

Thanks for your comment, The desired corrections have been applied in the text and are highlighted in yellow in the text.

******************************************************************************************

We are looking forward to receiving your final decision on the paper.

Sincerely yours

Authors

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors took the recommendations into account. The manuscript is in good shape and coherence. It is clearer now.

Minor changes are required.

Author Response

ANSWER TO THE COMMENTS ON THE PAPER:

Presenting a Novel Evolutionary Method for Reserve Constrained Multi-Area Economic/Emission Dispatch problem

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Reviewer: 1

 

Comments to the Author

The authors took the recommendations into account. The manuscript is in good shape and coherence. It is clearer now.

Authors' reply:

Thanks for your positive comment about my paper.

 

Comments on the Quality of English Language

Minor changes are required.

Authors' reply:

Thanks for your comment, In the text of the article, the sections that have been changed in terms of writing are highlighted in yellow.

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We are looking forward to receiving your final decision on the paper.

Sincerely yours

Authors

Author Response File: Author Response.pdf

Reviewer 2 Report

All the recommended changes have been made correctly by the authors, and I believe that the paper is now suitable for publication.

Thank you.

Author Response

ANSWER TO THE COMMENTS ON THE PAPER:

Presenting a Novel Evolutionary Method for Reserve Constrained Multi-Area Economic/Emission Dispatch problem

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Reviewer: 2

 

Comments to the Author

All the recommended changes have been made correctly by the authors, and I believe that the paper is now suitable for publication. 

 Authors' reply:

Thanks for your positive comment about my paper.

*************************************************************************************

We are looking forward to receiving your final decision on the paper.

Sincerely yours

Authors

Author Response File: Author Response.pdf