A Novel Optimization Algorithm Combing Gbest-Guided Artificial Bee Colony Algorithm with Variable Gradients

Round 1

Reviewer 1 Report

In this paper, an enhanced version of the global artificial bee colony algorithm (GABC) is presented. The paper introduces a gradient-based technique to steer the search towards the minima. The gradient is computed with the help of numerical approximation.

I have some major and minor comments to the manuscript.

Major comments:

1. There is not only discussion or describtion on the effect of algorithm hyperparameters on the convergence speed and accuracy. For example, the size of the population is quite an important parameter, of which effect on the results should always be tested. In addition, the experiments should be made with different bee configurations (employer, seekers and scouts). A preferable implementation of these experiments would include a careful Design of Experiments (For example full factorial design).
2. There seems to be no pseudo code (other than the flow chart) for the algorithm given in the manuscript. As it takes thousands of generations for the algorithm to converge, the analysis of the complexity of each iteration rounds would clarify the computational effciency of the strategy.
3. It would be more interesting to see the algorithm compared to other more famous metaheuristic strategies as well, namely to Genetic Algorithms, Particle Swarm Optimization and Differential Evolution. At the current version, the comparison is only made to other ABC algorithms.
4. The algorithm is tested with 10 well-known test functions. However, it is by far well-known that there are a plethora of metaheuristic algorithms (I bet there are tens or even hundreds of them) that can solve these toy problems. Therefore, I would like to see the algorithm applied to real problems as well. For example, in optimizing a real world systems, processes etc.
5. There seems to be no practical difference ebetween GABC and the GABCG in solving these toy problems, other than the preciseness of the solution, which however is in order of 10^-2 to 10^-15, depending on the problem under study. Therefore, I would like to see the algorithm in action for example in training of neural networks, as in that problem the benefit achieved with the gradient is more obvious
6. The drawn conclusions are not supported with the actual findings, as the convergence graphs are given only for single test runs. The benefit of the gradient is obvious for the latter stage, but the middle stage convergence can be only coincidental, as the initial guess is random. Please add more proofs for this issue, for example by recording the number of iterations needed for convergence for each of the algorithms. These can be given in the form of table, bar chart etc.

Minor comments:

1. The texts in the boxes of figure 2 (Flow chart) do not fit in the boxes. Please, fix this issue.

2.

Author Response

Dear reviewer:

The paper has been revised in accordance with your last comments:

Major comments:

1．The effect of algorithm colony size on the convergence speed and accuracy has been discussed in Section 4.3. It should be noted that there are some requirements for the numbers of different bees. Since both the numbers of employed bees and onlookers are equal to the number of food sources, the number of these two bees is always the same. The production of scout is controlled by a threshold judgment. If the nectar amount of a food source has not increased more than “limit” times, a scout search randomly. So in ABCs algorithm, the number of scout is always one.

2. The pseudo code has been added to the manuscript. Compared with ABC and GABC algorithms, the innermost loop body of the new algorithm has not changed, only the execution command is modified. Although discrete gradient calculation for the best solution still takes up some computing resources, the complexity of each iteration does not increase greatly.
3. As illustrated in the manuscript: “Karaboga’s previous researches [8, 9] show that ABC algorithm outperforms other stochastic algorithms, such as Genetic Algorithm (GA), Particle Swarm Algorithm (PSO) and Particle Swarm Inspired Evolutionary Algorithm (PS-EA).” In Karaboga’s researches, it can be found that ABC algorithm has a greater advantage than other stochastic algorithms. Since GABCG algorithm is better than ABC algorithm, its advantage is more obvious.

[8] Karaboga, D.; Basturk, B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of global optimization. 2007, 39, pp. 459–471.

[9] Karaboga, D.; Akay, B. A comparative study of artificial bee colony algorithm. Applied mathematics and computation. 2009, 214, pp. 108–132.

4. In fluid calculation, the gradient relationship between design parameters and objective performance can be calculated by the adjoint method. We are studying an adjoint-based ABC algorithm approach for shape optimization of blood centrifugal pump impeller. Thus, the application of our new algorithm will be presented in the optimization of fluid machinery.
5. It is a very good suggestion. We plan to apply the algorithm to the training of neural networks. The research results will be presented in our following study.
6. It should be noted that the convergence curves are given not only for single test runs, but for average of 30 test runs. We have revised the manuscript to make the expression of curves clearer. Due to the algorithm’s random search, the results at the first and middle periods of each test run may be quite different. Therefore, in order to ensure the universality of the conclusion, we modify the statement, only highlighting the advantage of GABCG algorithm in the latter stage.

Minor comments:

1. The size of boxes in Figure 2 has been adjusted.

THANKS FOR YOUR REVIEW.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is concerned with using Gbest-guided artificial bee colony algorithm to enhance the exploitation through optimizing the search domain.

1. The title must be revised for the scientific soundness.
2. please revise the abstract for better presenting the problem statement. Currently the aim is not clear.
3. please use standard keywords.
4. Mamy claims in the first paragraph of the abstract is not cited. Problem statement and application domain is not given. The Research gap is not presented well. The motivation and contribution are not clear in the introduction section. Please answer these questions: why using the proposed method? Why not using machine learning methods, or other novel methods? what not hybrid methods? contribution of the paper must satisfy all these questions.
5. The manuscript is very difficult to follow due to the use of long sentences. Native English proofreading is essential. 
6. The abbreviations must be explained when first appear. Please insert an Acronyms table.
7. Please elaborate more on the data and the figures.
8. The model used is not cited. The evaluation metrics are not cited. The former models with these methods are not cited.
9. The result of the paper must be briefly reported in the abstract, and also in the conclusions.
10. What are the suggested for future research, Please elaborate, and advice readers. 
11. With respect to the results and the methods used what are the future research direction?
12. comparative analysis for validation of the results is essential.
13. please use updated and more relevant references.

Author Response

Dear reviewer:

The paper has been revised in accordance with your last comments:

1. The title has been revised for the scientific soundness.
2. The Abstract has been revised for better presenting the problem statement.
3. Keywords have been modified.
4. The introduction has been revised for clearly presenting the motivation and contribution
5. Some long sentences have been modified.
6. All abbreviations have been explained when first appear.
7. The descriptions of data and figures has been elaborated more clearly.
8. The former model and the evaluation metrics have been cited.
9. The result of the paper has been reported both in the abstract and the conclusions.
10. The suggested for future research has been elaborated in last part of Conclusion.
11. The future research direction has been illustrated in last part of Section 4.6 Discussion.
12. More comparative analysis for validation of the results has been presented.
13. The references have been updated.

THANKS FOR YOUR REVIEW.

Round 2

Reviewer 1 Report

The authors have responded to the questions properly, and in addition they have improved the manuscript.

However, I have still one concern concerning the Table 1 (describing the pseudocode):

1. Please add the annotation to the table (Table 1. Pseudo code....)
2. Remove the initialization, so the focus is in the algorithm loops
3. Remove the grey color, in my opinion the novelty is not needed to be highlighted
4. Use indentations for loop sections, conditional statements etc.... Example below the dashed line

--------------------------------------

### This is an algorithm to greet elements in a 2 dimensional table ###

print("Hello world!")

for i from 1 to n:

     print("Hello new row!")

     for j from 1 to k:

          if j == 2:

               print( "Hello element in the 2nd column on the %dth row", i )

          end

     end

end

Author Response

Dear reviewer:

The paper has been revised in accordance with your last comments:

1. The annotation has been added to Table 1.
2. The initialization part of pseudo code has been removed,
3. The grey color has been removed.
4. Necessary supplements and indentations have been added for loop sections.

THANKS FOR YOUR REVIEW.

Reviewer 2 Report

Dear Authors,

Please consider all the former comments and highlight your changes in the revised version. Please provide higher quality figures. Please answer comment four. and elaborate on in the paper. 

Author Response

Dear reviewer:

The paper has been revised in accordance with your last comments:

1. We have reconsidered your former comments, and highlighted the changes in the revised version.
2. Higher quality figures have been updated.
3. Thanks for your suggestions in Comment four, we have reorganized the abstract and introduction to clarify the problem statement, motivation and contribution. I hope the modification might satisfy the questions you mentioned.

THANKS FOR YOUR REVIEW.

Round 3

Reviewer 2 Report

Thank you for providing the revised version. The manuscript is recommended for publication.