Hybridizing of Whale and Moth-Flame Optimization Algorithms to Solve Diverse Scales of Optimal Power Flow Problem
, Ali Fatahi 1,2, Hoda Zamani 1,2, Seyedali Mirjalili 3,4,* and Diego Oliva 5Round 1
Reviewer 1 Report
Suggestions
- Plagiarism to be less than 15%. Presently, 21% SIMILARITY INDEX 18% INTERNET SOURCES 18% PUBLICATIONS 4% STUDENT PAPERS
- Clarity in objectives is missing. Standardization of the system is missing
- Can we implement to real power system? If so, please add text in suitable section.
- Ultimate outcome to be highlighted in conclusion section.
- Economic viability and sustainabilityis missing.
- Conclusions to revised in terms of numeric results and not in generics.
- The proposed WMFO takes advantage of WOA’s exploitation ability, while it is profited by the boosted explorative movement of the MFO, simultaneously. Justify it in the results and discussion.
- The obtained results corroborate that the proposed algorithm outperforms the contender algorithms for solving the OPF problem.
- Novelty of research work is missing. Similar type of work is also presented with previous articles as mentioned below.
- Mohammad H. Nadimi-Shahraki, Shokooh Taghian, Seyedali Mirjalili, Laith Abualigah, Mohamed Abd Elaziz, Diego Oliva. "EWOAOPF: Effective Whale Optimization Algorithm to Solve Optimal Power Flow Problem" , Electronics, 2021
- Ghasemi, Mojtaba, Sahand Ghavidel, Mohammad Mehdi Ghanbarian, Hamid Reza Massrur, and Masihallah Gharibzadeh. "Application of imperialist competitive algorithm with its modified techniques for 7 1% 8 <1% 9 <1% 10 <1% 11 <1% multi-objective optimal power flow problem: A comparative study" , Information Sciences, 2014.
- Mojtaba Ghasemi, Sahand Ghavidel, Shima Rahmani, Alireza Roosta, Hasan Falah. "A novel hybrid algorithm of imperialist competitive algorithm and teaching learning algorithm for optimal power flow problem with non-smooth cost functions" , Engineering Applications of Artificial Intelligence, 2014
Author Response
Response to Reviewer 1 Comments
Point 1: Plagiarism to be less than 15%. Presently, 21% SIMILARITY INDEX 18% INTERNET SOURCES 18% PUBLICATIONS 4% STUDENT PAPERS.
Response 1: We thank the reviewer for this comment. We were dismayed to see the word “plagiarism” in the comment as most of such sentences have been properly paraphrased as much as possible and the references have been accurately cited. Plagiarism is not acceptable even 1%, which is an intentional use of contents without proper citations. We think the reviewer is referring to the “overlapping content” here. In most publishers, the international standard is below 25%, but if this is supposed to be less than 20%, we have reduced it further to meet the threshold. We hope this is acceptable now.
Point 2: Clarity in objectives is missing. Standardization of the system is missing
Response 2: We appreciate the reviewer for this comment. In response to this comment, we made the following changes to clarify the objectives and standardize the system:
- Adding lines 89-91 to the Introduction to clearly express the objectives of this paper.
- Adding Subsection 3.2 to comprehensively describe the OPF system.
- Adding load flow calculation method in line 414.
- Inserting references and sentences in lines 458-462, 477, 491-495, 509-510, and 524-525 to determine the values of limitations and coefficients for each IEEE bus test system problem.
Point 3: Can we implement to real power system? If so, please add text in suitable section.
Response 3: We appreciate the reviewer for this comment. In response to this comment, we mentioned some successful implementations of similar approaches on the real power systems in lines 148 and 149.
Point 4: Ultimate outcome to be highlighted in the conclusion section.
Response 4: We thank the reviewer for this comment. To respond to this comment, we made the following changes to highlight the ultimate outcome:
- Adding Section 7 to statistically highlight the superiority of results.
- Adding lines 570-575 in the conclusion section to highlight the ultimate outcome.
Point 5: Economic viability and sustainabilityis missing.
Response 5: We appreciate the reviewer for this comment. In response to this comment, we added lines 577-578 to highlight the economic viability and sustainability of this method. Moreover, Figure (13) is added to show the economic viability and sustainability.
Point 6: Conclusions to revised in terms of numeric results and not in generics.
Response 6: Thank the reviewer and appreciate this comment. To respond to this comment, we revised the conclusion Section in terms of numeric results by adding lines 572-577.
Point 7: The proposed WMFO takes advantage of WOA’s exploitation ability, while it is profited by the boosted explorative movement of the MFO, simultaneously. Justify it in the results and discussion.
Response 7: We appreciate the reviewer for this comment. In response to this comment, first, we added Subsection 6.1 entitled "Impact Analysis of Hybridizing WOA and a modified MFO" to investigate and discuss the cooperation of the two algorithms in WMFO. Then, we replaced the mentioned sentence in the Abstract and added the corresponding sentences to the Conclusion in lines 561-565 based on the finding and impact analysis of Subsection 6.1.
Point 8: The obtained results corroborate that the proposed algorithm outperforms the contender algorithms for solving the OPF problem.
Response 8: We appreciate the reviewer for this comment. In response to this comment, we made the following considerations:
- Adding a radar graph in Section 7 to rank the comparing algorithms in solving different problems of the OPF.
- Adding Figure (13) to graphically illustrate the amount of cost reduction in percentage for each IEEE bus test system.
- Adding lines 572-578 to highlight the obtained results in the conclusion.
Point 9: Novelty of research work is missing. Similar type of work is also presented with previous articles as mentioned below.
- Mohammad H. Nadimi-Shahraki, Shokooh Taghian, Seyedali Mirjalili, Laith Abualigah, Mohamed Abd Elaziz, Diego Oliva. "EWOAOPF: Effective Whale Optimization Algorithm to Solve Optimal Power Flow Problem" , Electronics, 2021
- Ghasemi, Mojtaba, Sahand Ghavidel, Mohammad Mehdi Ghanbarian, Hamid Reza Massrur, and Masihallah Gharibzadeh. "Application of imperialist competitive algorithm with its modified techniques for 7 1% 8 <1% 9 <1% 10 <1% 11 <1% multi-objective optimal power flow problem: A comparative study" , Information Sciences, 2014.
- Mojtaba Ghasemi, Sahand Ghavidel, Shima Rahmani, Alireza Roosta, Hasan Falah. "A novel hybrid algorithm of imperialist competitive algorithm and teaching learning algorithm for optimal power flow problem with non-smooth cost functions" , Engineering Applications of Artificial Intelligence, 2014
Response 9: Thank the reviewer and appreciate this comment. To respond to this comment, we added the contributions in lines 110-121 at the end of the Introduction to highlight the novelty of this research. Also, we added required sentences to lines 159-163, 163-166, and 198-201 to briefly review the mentioned papers. We described that the mentioned papers are different in terms of their methodology comparing to our study. Moreover, the mentioned papers compare a subset of IEEE bus tests systems problems, whereas our study solves diverse scales.
Reviewer 2 Report
The optimal power flow (OPF) is discussed in this paper. The paper is well organized. I suggest following revisions
1) add more pictures in the text
2) the author need to compare each technology for OPF problem and make sufficient discussion (the current disscusion is not clear for readers)
Author Response
Response to Reviewer 2 Comments
Point 1: add more pictures in the text.
Response 1: We appreciate the reviewer for this comment. In response to this comment, we added more pictures in the text as follows:
- Adding Figure (1) containing the convergence curves of the algorithms on some continuous functions. Moreover, the required sentences are added in Section 6.1.
- Adding Figure (12) to illustrate the ranking of algorithms based on their performance in minimizing the cost function of different OPF problems. The related sentences are added in Section 7.
- Adding Figure (13) to depict the percentage of fuel cost reduction obtained by each algorithm in solving OPF problems. Also, the related sentences are added in Section 7.
Point 2: the author need to compare each technology for OPF problem and make sufficient discussion (the current disscusion is not clear for readers).
Response 2: Thank the reviewer and appreciate this comment. To respond to this comment, we compared and discussed each technology for the OPF problem in lines 133-138.
Reviewer 3 Report
This paper proposes a hybridization of whale and moth-flame optimization algorithms, called WMFO, to combine the MFO’s powerful exploring capabilities with the WOA’s efficient exploitation mechanism. The WMFO also integrates a randomized boundary handling mechanism alongside a greedy selection operator to further assure increased performances. The proposed algorithm is then applied for solving the optimal power flow problem on five IEEE bus systems, namely the 14-bus, 30-bus, 39-bus, 57-bus, and 118-bus. For each test system, two cases are considered for the optimization function: 1) single objective for fuel cost minimization and 2) a weighted single objective function for simultaneously minimizing both fuel costs and voltage deviation.
The first part of this paper presents the general context and the state-of-the-art in a clear manner. The mathematical models for the optimal power flow problem, canonic WOA and MFO and the proposed WMFO are presented in a well-organized and clear manner. Finally, the results provided by the WMFO are compared against other seven classical and state-of-the-art meta-heuristic algorithms, highlighting proposed algorithm’s superior performance. Overall, the paper has a good quality, a good organization with well-developed sections and a clear presentation.
The case study is the main strength of this paper, as a the OPF is determined for two cases on each of the 5 test systems by applying 8 different metaheuristic algorithms. Therefore, a significant number of results are supporting the conclusion that WMFO is indeed a high-performance algorithm.
However, there are several parts within the mathematical model that need to be further developed in order to obtain a very good quality paper.
The mathematical model of the optimal power flow problem comprises both equality and inequality constraints which are not mentioned in the text. Please insert a new sub-section in the third section for presenting the equality and inequality constraints.
As a metaheuristic solver is applied, the equality constraints regarding the active and reactive nodal power balance are usually enforced by performing the load flow computation using a method such as Newton-Raphson integrated within the objective function. Please clarify within the paper how is the load flow calculation performed and what method (i.e Newton Raphson) and solver (i.e Matpower or a code developed by the authors) is applied.
Also, meta-heuristic solvers cannot enforce all inequality constraints (such as maintaining all bus voltages within 0.9 – 1.1 p.u) without an additional mechanism such as penalty functions. Please clarify within the paper how the equality constraints are handled.
In order to increase transparency, please specify the values for generation cost coefficients a, b and c and the limits for the control variables for each test system, or the reference where the values are available. For example, for the IEEE 14 bus system no details are provided regarding the upper and lower bounds of the controlled devices while for IEEE 30-bus system the boundaries are provided only for the generator voltage, transformer tap and capacitor bank. Also, no values are provided for the generator active power limits and generation cost coefficients and no reference is cited.
The English is very good, with only a few grammatical or spelling errors to correct, such as:
- Page 2, line 100: “Lev-flight moth-flame optimization”
- Page 3, line 142: “exploitation anility of the GSA.”
- Page 10, table 1, GWO: “is linearly decreases from”
- Page 5, eq (5), at the term bi, i should be a sub-script, etc
The list is not exhaustive, therefore please perform a proofreading for the entire text.
There are some unclear parts of the text, which should be rephrased for a better understanding, such as:
- Page 1, line 100: “while it is profited by the”
- Page 7, line 292: “WOA is profited by”
- Page 15, line 404: “transformers on lines 12-11”, I think it should be “transformers between buses 12-11”
- Page 18, line 420: “shunt reactive power sources are addressed” – maybe located or installed would be more appropriate.
Congratulations for the good quality of the paper!
Author Response
Response to Reviewer 3 Comments
Point 1: The mathematical model of the optimal power flow problem comprises both equality and inequality constraints which are not mentioned in the text. Please insert a new sub-section in the third section for presenting the equality and inequality constraints.
Response 1: We appreciate the reviewer for this comment. In response to this comment, we added a new subsection in the third section (3.2) for presenting the equality and inequality constraints.
Point 2: As a metaheuristic solver is applied, the equality constraints regarding the active and reactive nodal power balance are usually enforced by performing the load flow computation using a method such as Newton-Raphson integrated within the objective function. Please clarify within the paper how is the load flow calculation performed and what method (i.e Newton Raphson) and solver (i.e Matpower or a code developed by the authors) is applied.
Response 2: We appreciate the reviewer for this comment. In response to this comment, we added the required sentence to line 414 to explain that MATPOWER is used to calculate the load flow.
Point 3: Also, meta-heuristic solvers cannot enforce all inequality constraints (such as maintaining all bus voltages within 0.9 – 1.1 p.u) without an additional mechanism such as penalty functions. Please clarify within the paper how the equality constraints are handled.
Response 3: Thank the reviewer and appreciate this comment. To respond to this comment, we added the inequality constraints handling method used in this research in Subsection 3.2.3.
Point 4: In order to increase transparency, please specify the values for generation cost coefficients a, b and c and the limits for the control variables for each test system, or the reference where the values are available. For example, for the IEEE 14 bus system no details are provided regarding the upper and lower bounds of the controlled devices while for IEEE 30-bus system the boundaries are provided only for the generator voltage, transformer tap and capacitor bank. Also, no values are provided for the generator active power limits and generation cost coefficients and no reference is cited.
Response 4: Thank the reviewer for this attention. In response to this comment, we considered the following changes:
- Adding lines 458-462 to provide information on the IEEE 14-bus system and citing a reference for the cost coefficients.
- Citing a refernce for related data to the IEEE 30-bus system in line 477.
- Adding lines 492-495 to provide information on the IEEE 39-bus system and citing a reference for the related data including cost coefficients.
- Citing a reference for related data to the IEEE 57-bus system in line 510.
- Citing a reference for related data to the IEEE 118-bus system in line 525.
Point 5: The English is very good, with only a few grammatical or spelling errors to correct, such as:
Page 2, line 100: “Lev-flight moth-flame optimization”
Page 3, line 142: “exploitation anility of the GSA.”
Page 10, table 1, GWO: “is linearly decreases from”
Page 5, eq (5), at the term bi, i should be a sub-script, etc
The list is not exhaustive, therefore please perform a proofreading for the entire text.
Response 5: Thank the reviewer and appreciate this comment. To respond to this comment, we corrected the mentioned errors and performed proofreading.
Point 6: There are some unclear parts of the text, which should be rephrased for a better understanding, such as:
Page 1, line 100: “while it is profited by the”
Page 7, line 292: “WOA is profited by”
Page 15, line 404: “transformers on lines 12-11”, I think it should be “transformers between buses 12-11”
Page 18, line 420: “shunt reactive power sources are addressed” – maybe located or installed would be more appropriate.
Response 6: We appreciate the reviewer for this comment. In response to this comment:
We revised “while it is profited by the” in lines 23 and 24.
We changed “WOA is profited by” to “WOA benefits from”.
We changed “transformers on lines 12-11” to “transformers between buses 12-11”.
We changed “shunt reactive power sources are addressed” to ” Shunt reactive power sources are located”.
Round 2
Reviewer 3 Report
I appreciate the authors for making the recommended modifications in the revised manuscript.
All the comments are well answered by the authors, therefore I recommend to accept the paper in its current form.
