Review Reports - A Tuning-Free Constrained Team-Oriented Swarm Optimizer (CTOSO) for Engineering Problems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors propose the Constrained Team-Oriented Swarm Optimizer (CTOSO), a tuning-free metaheuristic that adapts the ETOSO framework by replacing linear exploiter movement with spiral search and integrating Deb's feasibility rule.

Questions:

1. The technical contribution of the new algorithm is not entirely clear. It is a modification of an existing algorithm. What are the weaknesses of the traditional, existing algorithm? What do the authors intend to improve?

2. A step-by-step algorithm and/or flowchart of the proposed algorithm is missing. The reader and researcher should be able to understand the proposed metaheuristic and know how to implement it without difficulty.

3. Section 4.2: Provide references for each of the metaheuristics used in the case studies.

4. Are the optimization problems described in Sections 4.1.1 to 4.1.12 minimization or maximization problems?

5. Why didn't the authors perform a comparative analysis with the traditional Team-Oriented Swarm Optimizer in the case studies? The algorithm proposed by the authors is a modification of the Team-Oriented Swarm Optimizer. A comparative analysis would have allowed them to assess how effective the modification proposed by the authors was.

6. The literature review is weak. Few articles are cited and there is little discussion of existing metaheuristics.

7. What was the number of individuals and the number of iterations defined for the simulations? Were these values ??fixed for all case studies?

8. The authors proposed modifications to the traditional Team-Oriented Swarm Optimizer. Are there other articles that have also proposed modifications to the traditional Team-Oriented Swarm Optimizer? It would be interesting to present a literature review of the articles already published.

Author Response

Please find attached the response to the comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1) In the abstract, the problem statement seems not clear. Please add the issues or problems of existing swarm optimizers such that it motivates the author to propose the CTOSO.

2) At the end of the abstract, please add the numerical performance index results to justify the effectiveness of the proposed CTOSO in comparison with other algorithms.

3) The organization and content of Section 1 and Section 2 can be improved as follows:

(i) It is preferable to put the equations in the next methodology section with proper definitions and equation numbers.

(ii) The motivation of using the term "tuning-free" should be clearly highlighted with proper survey and gap.

(iii) Section 2, should firstly introduce several classes or types of optimizer. Then, please state the difference and similarity of CTOSO with other swarm optimizers.

(iv) Please consider several recent swarm optimizers such as random average marine predators algorithm (RAMPA), improved tunicate swarm algorithm (ImTSA), competitive swarm optimizer and many more.

(v) Please discuss the computational time perspective of the CTOSO, while some researchers are preferable to use the single-agent based optimizer that manipulates either several elements or the whole elements of design parameter of single agent such as game theoretic approaches and gradient stochastic approximation approaches. As a result, those algorithms can produce less computational burden.

(vi) Please add the list of main contributions at the end of Section 1.

4) The written symbols and notations should be further improved. Only symbols are italic and not the bracket. Please put numbers for all stated equations.

5) In Section 3.3, some of the updated equations in CTOSO already imitate other recently published algorithms such as spiral dynamic algorithm (SDA). Please discuss the difference between the proposed updated equations and the existing SDA.

6) The pseudocode in Figure 1 should be improved. Please add some indentations and bold. Also, please use the same symbols that have been defined previously. Please do not directly put the software code here since it is difficult to understand.

7) Please add another Section before Section 4 that discusses the applications of CTOSO to the standard CEC benchmark functions. Here, please compare the performance of the algorithms with the algorithms such as PSO, GA, L-SHADE and many more.

8) The presented results in Section 5 are rather comprehensive and acceptable. However, in each case study, if the results are compared with other optimizers, please put appropriate reference and please consider to put the same results from the cited paper.

Author Response

Please refer to the attached response to the comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The article has been improved, the contribution is good and all questions have been effectively answered.

Author Response

No further comments from the reviewer.

Reviewer 2 Report

Comments and Suggestions for Authors

The author has carefully addressed most of the comments except:
(i) Please discuss the computational time perspective of the CTOSO, while some researchers are preferable to use the single-agent based optimizer that manipulates either several elements or the whole elements of design parameter of single agent such as game theoretic approaches and improved smoothed functional algorithm approaches. As a result, those algorithms can produce less computational burden. Please discuss it in the manuscript by referring to recent related articles.

(ii) In Section 3.3, some of the updated equations in CTOSO already imitate other recently published algorithms such as spiral dynamic algorithm (SDA). Please discuss the difference between the proposed updated equations and the existing SDA. Please discuss it in the manuscript by referring to recent related articles.

Author Response

We thank the reviewer for the careful second-round assessment and for the constructive comments. The manuscript has been revised accordingly, as detailed below.

Reviewer Comment (i)

“Please discuss the computational time perspective of the CTOSO, while some researchers are preferable to use the single-agent based optimizer that manipulates either several elements or the whole elements of design parameter of single agent such as game theoretic approaches and improved smoothed functional algorithm approaches. As a result, those algorithms can produce less computational burden.”

Response:
This comment has been addressed by revising Section 7.5 (Computational Complexity) to explicitly discuss single-agent based optimization frameworks from a computational-time perspective. The revised manuscript acknowledges that single-trajectory derivative-free methods such as improved smoothed functional and stochastic-approximation-based approaches, as well as formulations discussed in connection with game-theoretic learning may exhibit lower internal computational burden due to the absence of population-level operations. This discussion is supported by the following recent studies:

E. Gorbunov, S. Hanzely, and P. Richtárik, An accelerated method for derivative-free smooth stochastic optimization, SIAM Journal on Optimization, vol. 32, no. 2, pp. 1210–1238, 2022.
J. Zhu, L. Wang, and J. C. Spall, Efficient implementation of second-order stochastic approximation algorithms in high-dimensional problems, IEEE Transactions on Automatic Control, vol. 65, no. 10, pp. 4232–4247, 2020.
S. Pachalyl and S. Bhatnagar, Generalized simultaneous perturbation-based gradient search with reduced estimator bias, IEEE Transactions on Automatic Control, 2025 (early access).

Location in manuscript: Section 7.5, following Table 20.

Reviewer Comment (ii)

“In Section 3.3, some of the updated equations in CTOSO already imitate other recently published algorithms such as spiral dynamic algorithm (SDA). Please discuss the difference between the proposed updated equations and the existing SDA.”

Response:
This point has been addressed through a restructuring of the manuscript. The paragraph previously located at the end of Section 3.5 has been removed, and a focused discussion distinguishing CTOSO from the Spiral Dynamic Algorithm (SDA) has been added to Section 3.3, where the mathematical formulation of CTOSO is presented. The distinction is made with explicit reference to established spiral-based optimization literature:

K. Tamura and K. Yasuda, Spiral dynamics inspired optimization, Journal of Advanced Computational Intelligence and Intelligent Informatics, 2011.
K. Tamura and K. Yasuda, Primary study of spiral dynamics inspired optimization, Proceedings of the IEEE Congress on Evolutionary Computation, 2015.

Location in manuscript: Section 3.3.

We believe that these revisions satisfactorily address the reviewer’s remaining concerns and improve the clarity and organization of the manuscript. We appreciate the reviewer’s careful reading and valuable feedback.