An Enhanced Particle Swarm Optimization (PSO) Algorithm Employing Quasi-Random Numbers
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
This paper introduced an innovative Particle Swarm Optimization (PSO) Algorithm incorporating Sobol and Halton Random number samplings，and assessed it with nine benchmark problems and TSP problem. This research is interesting but it has some aspects that need to be improved:
1. The literature review section of this paper is relatively weak. New PSO variants are not presented and reviewed at all. The state-of-the-art of PSO are not given.
2. This paper lacks innovation and contribution because it only propose to introduce
Sobol and Halton Random number samplings. I don’t know the purpose of doing this, and it is used in the particle swarm initialization to make the particles uniformly distributed? This samplings have no help to improve the search mechanism in the iteration process after initialization, and they don’t involve the modification the cruicial position and velocity updating rule.
3. This paper assessed the proposed algorithm with nine benchmark problems and compared with the conventional PSO , which is not so convincing. The newest CEC benchmark and PSO variants should be taken as the comparison and the strict test, for example rank sum test etc, should be adopted to statistically verify the proposed algorithm’s performance . There are no much meaning to compare with the original algorithm.
4. This paper also takes the TSP problem as another test case. As I know, the TSP problem is a discrete optimization problem. The conventional PSO algorithm previously introduced by this paper is the continuous optimization algorithm. But how this paper use PSO to optimize the TSP is not presented.
Comments on the Quality of English Language
Moderate editing of English language are required.
Author Response
Please find attached.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for Authors
This paper introduces an innovative PSO Algorithm with Sobol and Halton samplings, showing marked improvements over traditional PSO, especially in solving the Travelling Salesman Problem, underscoring the efficacy of these methods in enhancing algorithm efficiency.
First, the authors' research represents an improvement in parameter generation methods, within the domain of parameter enhancements for metaheuristic algorithms, particularly in terms of parameter adaptiveness. It is apparent that the authors' improvements are mutually exclusive with adaptive parameter enhancement methods; therefore, it is hoped that the authors can provide a more detailed description of the proposed technique to highlight its advantages.
Secondly, while the use of Sobol and Halton sampling has increased the traversability of parameters, it evidently requires additional computational resources. Hence, a comparison of computation times is necessary to demonstrate that the performance benefits of the proposed method can outweigh the time costs.
Thirdly, the improved PSO by the authors has not been compared with other algorithms, such as Grey Wolf Optimization, Differential Evolution, and other metaheuristic algorithms, nor has it been compared with improved versions of PSO. This lack of comparison diminishes the persuasiveness of the technique's effectiveness. If time permits, it is recommended to at least compare it with other algorithms.
Lastly, the layout of the tables in the paper is very inconvenient for reading. Please reformat them.
Author Response
Please find attached.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
The two comments are not contrapuntally responded:
1. The newest CEC benchmark and PSO variants should be taken as the comparison and the strict test, for example rank sum test etc should be adopted to statistically verify the proposed algorithm’s performance . There are no much meaning to compare with the original algorithm.
2. The TSP problem is a discrete optimization problem. The conventional PSO algorithm previously introduced by this paper is a continuous optimization algorithm. But how this paper use PSO to optimize the discrete TSP is not presented.
Comments on the Quality of English Language
The English writing need further improved.
Author Response
The newest CEC benchmark and PSO variants should be taken as the comparison and the strict test, for example rank sum test etc should be adopted to statistically verify the proposed algorithm’s performance . There are no much meaning to compare with the original algorithm.
We have compared with two different new variants in the revised file.
- The TSP problem is a discrete optimization problem. The conventional PSO algorithm previously introduced by this paper is a continuous optimization algorithm. But how this paper use PSO to optimize the discrete TSP is not presented.
The algorithm is applicable to both continous and mixed variables including TSP. This is explained in the manuscript.
Reviewer 2 Report
Comments and Suggestions for Authors
The author answered my questions very well.
Author Response
The reviewer is satisfied with our changes. Thanks.
