An Energy-Saving Clustering Algorithm for Wireless Sensor Networks Based on Multi-Objective Walrus Optimization
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsMy comments are in a separate file.
Comments for author File: 
Comments.pdf
Author Response
Thank you very much the comments about our paper. We have checked the manuscript and revised it according to the comments. We submit here the revised manuscript as well as a list of changes. Although we try our best to modify it, there must be many deficiencies. We very much hope to get your further guidance, thank you!
Commants 1: There is an inconsistent method of reviewing the literature. The authors of some references are awarded the title ”Scholar”. This is an irregular way of doing citations
Response 1: We take this comment from the reviewers very seriously. We have optimized this translation.
Commants 2: Line 32: ”is that” → ”is to”
Response 2:
We take this comment from the reviewers very seriously. Grammar error has been corrected.
Commants 3: Line 37: There is a wild statement about ”deploying humans by unmanned vehicles”. Is there a citation to this innovative application of WSN? I thought WSN was mainly for sensing data not moving humans around
Response 3:
We take this comment from the reviewers very seriously. We have made revisions to this. It should be through drones to send sensor nodes to some areas that have been modified.
Commants 4: Line 41: Incomplete sentence (missing verb) ”.During the process of network [7]”
Response 4:
We take this comment from the reviewers very seriously. An error occurred during editing and has been corrected.
Commants 5: Line 42: The sentence mentions three key technologies without mentioning what they are or at least saying these technologies will be explained in the following paragraphs
Response 5:
We take this comment from the reviewers very seriously. We have added content to the paper. The three technologies are explained in the following three paragraphs respectively.
Commants 6: Line 45: Sentence unusual citation of a reference ”Scholar Wendi Rabinar Heinzelman” and the reference is not cited. There is a reference [9] after 4 lines.
Response 6:
We take this comment from the reviewers very seriously. We have made modifications to this.
Commants 7: Line 48: Same unusual citation by spelling out the full name of the researcher.
Response 7:
We take this comment from the reviewers very seriously. The names cited throughout the text have been modified.
Commants 8: Line 50: Why Jonnalagadda Suman is preceded with the epithet ”Scholar”? Is he a non-researcher or a graduate student? I hope this is just a slip.
Response 8:
We take this comment from the reviewers very seriously. This has been modified.
Commants 9: Figure 1 is described as having a geographic extent of T ×T. But this geography is actually in Fig. 2.
Response 9:
We take this comment from the reviewers very seriously. This has been modified.
Commants 10: Figure 1 is hardly discussed in the text. I see some nodes not within the circles. Are these nodes unconnected? The factor K refers to packet size. But traffic intensity is not present.
Response 10:
We take this comment from the reviewers very seriously. Here are only two clusters listed briefly, and in real scenarios, all nodes need to be connected to the cluster head or base station. The K in formulas (1) and (3) has been changed to lowercase k, which is a k-bit data packet. In formulas (18) - (26), K is the number of clusters in the network.
Commants 11: Figure 2 is hardly discussed too. What is the significance of blue and red circles? I infer that this is shown in Fig. 3 but the paper does not mention that.
Response 11:
We take this comment from the reviewers very seriously. Annotate the sensor and base station in the bottom left corner of Figure 2. The color of the circle has no special meaning, it is just for differentiation.
Commants 12: Equation 1: Energy consumed depends not only on distance but on traffic intensity. This depends on the activity of the ordinary nodes and on how many ordinary nodes are served by the cluster head. I do not see such discussion.
Response 12:
We take this comment from the reviewers very seriously. We have added corresponding content for discussion: Energy consumption depends not only on distance, but also on data transmission, reception, and data fusion. Equations (18)-(23) calculate the energy consumption of nodes.
Commants 13: Fig. 4 & 8 : The flowchart is hardly readable. It is not discussed in the text.
Response 13:
We take this comment from the reviewers very seriously. We have added content to the paper to enhance the interpretation of the Figures. Figure 4 is a simple description of 3.1.3. Figure 8 is a flowchart of the entire experimental process, which is briefly described above.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper proposes an energy-saving clustering and routing algorithm (CM-WaOA) for wireless sensor networks, combining K-means++ initialization, Chaotic Mapping Walrus Optimization, and Sparrow Search Algorithm for efficient cluster head selection and routing. The simulation results show improvements over existing benchmarks in terms of energy consumption, node survival, and latency. Please see my detailed comments below.
1. In the Introduction, I would recommend the authors to strengthen the motivation by highlighting the relevance of their work in emerging scenarios such as the IoT and UAV swarm networks, where energy consumption and communication efficiency are critical bottlenecks. In such contexts, the proposed energy-saving clustering and routing strategy could have significant practical value. To this end, it would be useful to explicitly discuss these scenarios and include some related work (e.g., [R1]) to better position the contribution within the broader research landscape.
[R1] 10.1109/TSP.2022.3158759
2. Some sentences in Section 1 are grammatically incorrect or difficult to read. For example, “whose main function is that monitor the information of the target area and transmits the information” should be revised to “whose main function is to monitor the target area and transmit the information.” The authors are encouraged to polish the language for better readability.
3. The introduction focuses primarily on WSN energy efficiency, but it would be useful to also mention other critical factors in IoT/WSN applications, such as reliability, scalability, and latency, which are indeed evaluated later in the paper.
4. In Equations (4) and (5), the meaning of variables $X_m$ and $Y_m$ is not clearly explained. Please define them explicitly before presenting the equations.
5. The derivation of the optimal number of cluster heads $K$ in Equation (25) is too brief. Please show intermediate steps or provide an appendix with details, since this formula is critical for the algorithm.
6. The pseudocode in Algorithm 1 is incomplete (e.g., input/output specifications missing). Please follow a consistent pseudocode format throughout the paper.
7. The simulation setup in Section 5 is somewhat limited. For example, the number of nodes is fixed at 100 in an 800×800 m² area. It would strengthen the paper if the authors could provide more detailed justification for parameter choices (e.g., why 100 nodes, why initial energy 4 J) and also evaluate the scalability of the proposed algorithm under different network densities or larger-scale scenarios.
Author Response
Thank you very much the comments about our paper. We have checked the manuscript and revised it according to the comments. We submit here the revised manuscript as well as a list of changes. Although we try our best to modify it, there must be many deficiencies. We very much hope to get your further guidance, thank you!
Comments 1: In the Introduction, I would recommend the authors to strengthen the motivation by highlighting the relevance of their work in emerging scenarios such as the IoT and UAV swarm networks, where energy consumption and communication efficiency are critical bottlenecks. In such contexts, the proposed energy-saving clustering and routing strategy could have significant practical value. To this end, it would be useful to explicitly discuss these scenarios and include some related work (e.g., [R1]) to better position the contribution within the broader research landscape.
[R1] 10.1109/TSP.2022.3158759
Response 1:
We take this comment from the reviewers very seriously. We have updated the introduction section. And reference 1 is the modified content.
Comments 2: Some sentences in Section 1 are grammatically incorrect or difficult to read. For example, “whose main function is that monitor the information of the target area and transmits the information” should be revised to “whose main function is to monitor the target area and transmit the information.” The authors are encouraged to polish the language for better readability.
Response 2:
We take this comment from the reviewers very seriously. We have made corrections to the grammar errors.
Comments 3: The introduction focuses primarily on WSN energy efficiency, but it would be useful to also mention other critical factors in IoT/WSN applications, such as reliability, scalability, and latency, which are indeed evaluated later in the paper.
Response 3:
We take this comment from the reviewers very seriously. We have added relevant content, including other key factors in wireless sensor network applications such as reliability, scalability, and latency.
Comments 4: In Equations (4) and (5), the meaning of variables and is not clearly explained. Please define them explicitly before presenting the equations.
Response 4:
We take this comment from the reviewers very seriously. We have added content to the paper to explain the variables and meanings in the formulas. and represent the horizontal and vertical coordinates of the initial clustering center, respectively.
Comments 5: The derivation of the optimal number of cluster heads K in Equation (25) is too brief. Please show intermediate steps or provide an appendix with details, since this formula is critical for the algorithm.
Response 5:
We take this comment from the reviewers very seriously. It has been modified. We have summarized the energy consumption formula and explained its impact on the k value, as well as how the k value is calculated.
Comments 6: The pseudocode in Algorithm 1 is incomplete (e.g., input/output specifications missing). Please follow a consistent pseudocode format throughout the paper.
Response 6:
We take this comment from the reviewers very seriously. We have improved the situation where the pseudocode in Algorithm 1 is incomplete. Meanwhile, we examined the entire paper to ensure adherence to a consistent pseudocode format.
Comments 7: The simulation setup in Section 5 is somewhat limited. For example, the number of nodes is fixed at 100 in an 800×800 m² area. It would strengthen the paper if the authors could provide more detailed justification for parameter choices (e.g., why 100 nodes, why initial energy 4 J) and also evaluate the scalability of the proposed algorithm under different network densities or larger-scale scenarios
Response 7:
We take this comment from the reviewers very seriously. In order to strengthen the research of the paper, we have updated and optimized the relevant content. As explained in section 5.1, an 800 * 800 simulation environment is established based on the Euclidean distance and hop count between nodes, cluster heads, and base stations. One hundred nodes is the standard experimental quantity. The experimental parameter settings here are in accordance with the design. When tested in the same environment, both the environment and parameter effects are the same, so they can be ignored.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe idea of a CM-WaOA + SSA hybrid is interesting and consistent with the trend of optimization research in WSN, but the article in its current version has significant methodological limitations: lack of realistic validation, strong simplifying assumptions, incomplete cost analysis, and lack of repetitions/statistics. In order for the work to be competitive with the best global publications, experiments in a more realistic environment, analysis of computational/communication overhead, and improved reproducibility are needed. Sources and excerpts from the work on which I based my comments: abstract and introduction; simulation parameters; experimental section; conclusions and future work.
Below, I present the weaknesses of the reviewed article:
1. No validation in realistic environments / lack of testbed or network emulation.
The paper relies exclusively on MATLAB simulations with simplified radio/PHY models. There are no experiments on a real testbed nor emulations in NS-3/OMNeT++, and no radio measurements (packet loss, retransmissions, collisions). Contemporary works increasingly demand at least NS-3 validation or small testbed results because simple path-loss→energy models do not capture lower-layer behavior. This limits confidence that results will hold in real deployments.
2. Unrealistic / simplifying network assumptions.
Assumptions include identical, static nodes, absence of interference, an unconstrained base station, and unrestricted transmit-power adaptation. Such assumptions are rarely met in practice (heterogeneous batteries, mobile elements, regulatory power limits). These simplifications can make reported gains overly optimistic.
3. No computational-cost and communication-overhead analysis.
The CM-WaOA and SSA descriptions lack an accounting of computational complexity and the communication overhead required (e.g., exchanging candidate positions, energy levels). In WSNs the algorithm overhead can erase any transmission savings.
4. Potentially inconsistent or incomplete baseline comparisons.
The paper compares against LEACH, EEUC, CGWOA and EBPT-CRA, but omits recent, widely cited methods (including learning-based or other hybrid approaches) and does not state whether baselines used official implementations or matched parameter settings. Without consistent baseline implementation details, comparisons risk being unfair.
5. Simplified energy model and unclear units.
Simulation parameters list energy coefficients as “10 Pj/bit/m2” and “0.0013 Pj/bit/m2” — the notation looks unusual (likely pJ vs Pj) and may be a typographical error. The model also omits receiver costs, retransmission energy and protocol overhead, which affect real energy consumption. This undermines reproducibility and realism.
6. No statistical analysis or reporting of uncertainty.
Results are shown without specifying number of repeated runs, standard deviations, confidence intervals, or statistical tests. Comparative claims require reporting variance and significance testing.
7. Limited scale and no scalability analysis.
Experiments are limited (100 nodes, three area sizes). Large-scale WSN/IoT deployments may involve far more nodes — the paper lacks analysis of algorithmic scalability in computation, memory and communication.
8. No sensitivity analysis of algorithm parameters.
Metaheuristics have many hyperparameters (population size, iteration count, chaotic map parameters, SSA parameters). The manuscript does not analyze sensitivity or explain how parameters were chosen, making reproducibility and stability assessment difficult.
9. Omission of security, reliability and QoS discussion.
Although "future work" briefly mentions topics like 3D models, the manuscript does not consider security (e.g., sinkhole, spoofing), reliability, or QoS (priority for critical traffic). For many practical WSN applications these aspects are crucial.
10. Reproducibility — no public code or configuration.
I could not find a link to source code or simulation scripts. Current best practice expects authors to release code (e.g., GitHub) so others can reproduce results.
Author Response
Thank you very much the comments about our paper. We have checked the manuscript and revised it according to the comments. We submit here the revised manuscript as well as a list of changes. Although we try our best to modify it, there must be many deficiencies. We very much hope to get your further guidance, thank you!
Comments 1: No validation in realistic environments / lack of testbed or network emulation.
The paper relies exclusively on MATLAB simulations with simplified radio/PHY models. There are no experiments on a real testbed nor emulations in NS-3/OMNeT++, and no radio measurements (packet loss, retransmissions, collisions). Contemporary works increasingly demand at least NS-3 validation or small testbed results because simple path-loss→energy models do not capture lower-layer behavior. This limits confidence that results will hold in real deployments.
Response 1:
We appreciate the valuable feedback from the reviewers, which highlights the importance of real-world validation. After proposing our algorithm ideas, we actively validated them through software. Verification methods include Matlab and other forms. In future research, we will enrich the validation methods, such as NS-3/OMNeT++. Experimental verification is a systematic work, and we have been striving to improve the effectiveness of our work.
Comments 2: Unrealistic / simplifying network assumptions.
Assumptions include identical, static nodes, absence of interference, an unconstrained base station, and unrestricted transmit-power adaptation. Such assumptions are rarely met in practice (heterogeneous batteries, mobile elements, regulatory power limits). These simplifications can make reported gains overly optimistic.
Response 2:
We appreciate the valuable feedback from the reviewers. Due to testing in the same environment, the impact of parameter settings and environmental conditions on the experimental comparison of these five algorithms is the same.
Comments 3: No computational-cost and communication-overhead analysis.
The CM-WaOA and SSA descriptions lack an accounting of computational complexity and the communication overhead required (e.g., exchanging candidate positions, energy levels). In WSNs the algorithm overhead can erase any transmission savings.
Response 3:
We appreciate the valuable feedback from the reviewers. We have improved the discussion of the experimental section and added relevant content. We added the time complexity of CM-WaOA and SSA algorithms at the end of 4.1 and 4.3 respectively based on the information of the nodes.
Comments 4: Potentially inconsistent or incomplete baseline comparisons.
The paper compares against LEACH, EEUC, CGWOA and EBPT-CRA, but omits recent, widely cited methods (including learning-based or other hybrid approaches) and does not state whether baselines used official implementations or matched parameter settings. Without consistent baseline implementation details, comparisons risk being unfair.
Response 4:
We appreciate the valuable feedback from the reviewers. We have improved the discussion of experimental details to ensure fairness in the experiment. Added explanations for these four comparative experiments in 5.1, which were reproduced based on the original idea.
Comments 5: Simplified energy model and unclear units.
Simulation parameters list energy coefficients as “10 Pj/bit/m2” and “0.0013 Pj/bit/m2” — the notation looks unusual (likely pJ vs Pj) and may be a typographical error. The model also omits receiver costs, retransmission energy and protocol overhead, which affect real energy consumption. This undermines reproducibility and realism.
Response 5:
We appreciate the valuable feedback from the reviewers. The formatting error has been corrected. Due to the consistent environment used, the ignored cost has little impact on the comparison results of the five algorithms.
Comments 6: No statistical analysis or reporting of uncertainty.
Results are shown without specifying number of repeated runs, standard deviations, confidence intervals, or statistical tests. Comparative claims require reporting variance and significance testing.
Response 6:
We appreciate the valuable feedback from the reviewers. We have improved the relevant content and optimized the statistical analysis. At the end of 5.1, it is added that multiple experiments were conducted and one of them was selected for subsequent comparison and presentation.
Comments 7: Limited scale and no scalability analysis.
Experiments are limited (100 nodes, three area sizes). Large-scale WSN/IoT deployments may involve far more nodes — the paper lacks analysis of algorithmic scalability in computation, memory and communication.
Response 7:
We appreciate the valuable feedback from the reviewers. We have added content to the paper and conducted scalability analysis. In Section 5.6, analysis of experimental results from three different regions has been added.
Comments 8: No sensitivity analysis of algorithm parameters.
Metaheuristics have many hyperparameters (population size, iteration count, chaotic map parameters, SSA parameters). The manuscript does not analyze sensitivity or explain how parameters were chosen, making reproducibility and stability assessment difficult.
Response 8:
We appreciate the valuable feedback from the reviewers. We appreciate the valuable feedback from the reviewers. We have made modifications to this and strengthened the analysis of algorithm parameters. Added explanations of parameters in sections 4.1.3 and 4.2. added explanation in 4.1.4. The iteration count is the standard value for the experiment.
Comments 9: Omission of security, reliability and QoS discussion.
Although "future work" briefly mentions topics like 3D models, the manuscript does not consider security (e.g., sinkhole, spoofing), reliability, or QoS (priority for critical traffic). For many practical WSN applications these aspects are crucial.
Response 9:
We agree that these omissions could impact the algorithm’s applicability in real-world scenarios. To address this, we have revised the “Future Work” section to explicitly include plans to integrate these aspects. Due to the lack of analysis on security, reliability, and QoS, further research will be conducted in this area in the future to increase the comprehensiveness of experiments. We appreciate the reviewer's emphasis on this gap and look forward to further guidance.
Comments 10: Reproducibility — no public code or configuration.
I could not find a link to source code or simulation scripts. Current best practice expects authors to release code (e.g., GitHub) so others can reproduce results.
Response 10:
We appreciate the valuable feedback from the reviewers. The code has been uploaded to the journal system. If necessary, please contact the corresponding author.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have properly addressed my previous comments. The paper can be accepted in its present form.
Reviewer 3 Report
Comments and Suggestions for AuthorsThank you for responding to my suggestions and comments and for incorporating the reviewers' comments into the revised version of the article. I have no further critical comments.
