Dual-Population Adaptive Differential Evolution Algorithm L-NTADE
Round 1
Reviewer 1 Report
The current manuscript presents a DE variant that aimed to solve numerical optimization problems. The paper is well-written in general and can be accepted after a minor review as follows:
1-Please, provide a flow chart of the proposed algorithm.
2- The Mann-Whitney test is a famous non-parametric rand test. The results provided are satisfactory but the authors should have highlighted the parametric statistical test more clearly to compare their method.
3- A suggestion can be given to authors to increase the population sizes rather than the considered values. The CEC 2017 is usually a complex benchmark set and needs a higher population size.
4- In line 175, the authors wrote that the CEC 2017 benchmark consists of 30 test functions with dimensions 10, 30, 50, and 100, and the computational resource is set to 10000D function evaluations. The original test has implemented the overall number of evaluations for each dimension to be set as 100000, 300000, 500000, and 1000000 evaluations, respectively. Please correct!
5-The abstract and introduction are very brief. Further efforts should be paid to improve these two sections. In this regard, the authors can refer to the recent algorithm that used the CEC 2017 which is the novel oppositional unified particle swarm gradient-based optimizer, and the combined social engineering particle swarm optimization where they both implemented useful comparative studies.
6- The conclusion section should be improved. Further highlights about the major achievements, drawbacks, and future scope can be added.
Author Response
The current manuscript presents a DE variant that aimed to solve numerical optimization problems. The paper is well-written in general and can be accepted after a minor review as follows:
Answer: Thank you for a good evaluation of our work. We tried our best to address all the questions.
1-Please, provide a flow chart of the proposed algorithm.
Answer: The flow chart of the proposed algorithm is added in Figure 1.
2- The Mann-Whitney test is a famous non-parametric rand test. The results provided are satisfactory but the authors should have highlighted the parametric statistical test more clearly to compare their method.
Answer: The settings we used for running the non-parametric Mann-Whitney U tests are described in section 4.2, where it is mentioned that the normal approximation for the U statistics is applied due to sufficient sample sizes. The only parameter of the non-parametric test is the significance level, equal to 0.01 in our tests. A possible alternative for Mann-Whitney U test, which compares the probability distribution functions of two samples, could be the parametric Student’s t-test, which compares mean values. However, the application of t-test requires that both samples are normally distributed, which should be additionally checked before application to every two samples. Moreover, Mann-Whitney U-test is known to be more powerful compared to Student’s t-test, hence we do not believe that it would be useful for comparison. Nevertheless, if you insist that t-test or any other specific statistical test should be performed for efficiency comparison, please indicate it, and we will include it in the next revision of the manuscript.
3- A suggestion can be given to authors to increase the population sizes rather than the considered values. The CEC 2017 is usually a complex benchmark set and needs a higher population size.
Answer: The population size depended on the problem dimension, so for 25D and 100-dimensional problem this resulted in 2500 individuals at the beginning. The experiments with larger population sizes have shown that the algorithm efficiency dropped. We added the following part for clarity: “which resulted in 150 to 250 individuals for $D=10$ and 1500 to 2500 individuals for $D=100$ Further increase of population size parameter resulted in performance deterioration in most cases”
4- In line 175, the authors wrote that the CEC 2017 benchmark consists of 30 test functions with dimensions 10, 30, 50, and 100, and the computational resource is set to 10000D function evaluations. The original test has implemented the overall number of evaluations for each dimension to be set as 100000, 300000, 500000, and 1000000 evaluations, respectively. Please correct!
Answer: The number of function evaluations depended on the problem dimension and was equal to 10000*D, which resulted in 100, 300000, 500000, and 1000000 evaluations. We added the following part for clarity: “the computational resource is set to 10000D function evaluations 100000, 300000, 500000 and 1000000 correspondingly)”
5-The abstract and introduction are very brief. Further efforts should be paid to improve these two sections. In this regard, the authors can refer to the recent algorithm that used the CEC 2017 which is the novel oppositional unified particle swarm gradient-based optimizer, and the combined social engineering particle swarm optimization where they both implemented useful comparative studies.
Answer: We have expanded the introduction section by mentioning many other alternative approaches.
6- The conclusion section should be improved. Further highlights about the major achievements, drawbacks, and future scope can be added.
Answer: The conclusion section was expanded by mentioning the replacement scheme in L-NTADE, possible drawbacks and directions of further studies.
Reviewer 2 Report
Comments to the Author
This paper proposes a dual-population algorithmic scheme for differential evolution and specific mutation strategy.
Weakness:
1. Abstract: L-NTADE was introduced without any definition. Please define all the terms introduced/used by this article, otherwise, it would be meaningless for the readers.
2. This paper must be checked for grammar and typos. For example, the first sentence of the abstract (Line 13) has typos.
3. What is the SI method?
3. Algorithm 1: Define inputs and output in the beginning of the algorithm.
4. Refer to each line of the Algorithm 1 and explain it clearly for reproducibility.
5. Table 4 and Table 5: Please include one row for the proposed algorithm.
6. The requirement of a new algorithm is not clear. Please compare the algorithm runtime with the state-of-the-arts.
Author Response
This paper proposes a dual-population algorithmic scheme for differential evolution and specific mutation strategy.
Answer: Thank you for a good evaluation of our work. We tried our best to address all the questions.
Weakness:
- Abstract: L-NTADE was introduced without any definition. Please define all the terms introduced/used by this article, otherwise, it would be meaningless for the readers.
Answer: The algorithm name is explained in the introduction part, where it is first mentioned: “L-NTADE algorithm (Linear population size reduction Newest and Top Adaptive Differential Evolution)”. We have added the definition in the abstract.
- This paper must be checked for grammar and typos. For example, the first sentence of the abstract (Line 13) has typos.
Answer: We have checked the manuscript with a native speaker.
- What is the SI method?
Answer: SI stands for Swarm Intelligence, it is mentioned in the first paragraph of the Introduction section.
- Algorithm 1: Define inputs and output in the beginning of the algorithm.
Answer: Two lines were added in Algorithm 1. The algorithm requires goal function, problem dimension, total computational resource and initial population size to run, and returns best solution alongside with its value.
- Refer to each line of the Algorithm 1 and explain it clearly for reproducibility.
Answer: The description of every line of the algorithm was added after it.
- Table 4 and Table 5: Please include one row for the proposed algorithm.
Answer: We have added new lines in Tables 4 and 5, however, as they present the comparison of L-NTADE with other approaches, the statistical tests of comparing with itself are non-informative. Please inform us if you believe that they should be kept or removed.
- The requirement of a new algorithm is not clear. Please compare the algorithm runtime with the state-of-the-arts.
Answer: We have added Table 6 comparing the computational complexity of L-NTADE with two alternative approaches on CEC 2022 benchmark.
Round 2
Reviewer 2 Report
The authors addressed the reviewer's previous concerns adequately. Thank you.
