Multi-Objective Optimization of Electric–Gas–Thermal Systems via the Hippo Optimization Algorithm: Low-Carbon and Cost-Effective Solutions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors This study introduced the hippopotamus optimization algorithm into the integrated energy system and compared it with the Pigeon-Inspired Optimization (PIO) algorithm and the Particle Swarm Optimization (PSO) algorithm to highlight its advantages. The author has done a lot of work. 1. The formatting of images within the article requires standardisation. 2. Compared to other published related materials, the Hippopotamus Optimisation Algorithm (HOA) introduced in this paper can effectively prevent getting stuck in local optima. However, in the model, to simplify the model, self-consumed energy sources such as compressors have been ignored. Do the results obtained closely reflect actual conditions? 3. When the search becomes trapped in local optima or encounters suboptimal ‘predator-like’ solutions, HOA employs a large-step escape method to exit local regions. Please elaborate on this approach. 4. It is recommended to include a discussion on the limitations of the proposed method. 5. The conclusion section should be further refined. Comments on the Quality of English Language

The language could be further refined.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

Here are some comments.

1. The study adopts simplified models for key subsystems, such as the DC power flow model and the steady-state natural gas pipeline model. While such simplifications enhance computational tractability, their potential impact on optimization results remains insufficiently validated. Please compare these simplified models with the unsimplified models, such as the models in 10.1109/TSG.2025.3578271. Or at least, compare these work in Introduction and discuss on their applicability.
2. Please expand the algorithmic comparison to include 2–3 state-of-the-art multi-objective optimizers widely used in IES research.
3. Please provide a detailed parameter sensitivity analysis and use some statistical metrics to confirm that HOA’s superiority is not due to randomness.
4. Please revise the payback period calculation by (1) clarifying the composition of investment cost, (2) verifying the annual operational cost saving via a line-item breakdown, and (3) reconciling the 1.15% vs. 1.5% cost reduction discrepancy.
5. Please add a “Limitations” subsection in Conclusion to discuss HOA’s scalability and computational complexity in large-scale IES.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

Major Comments:

1.The authors repeatedly emphasize in the abstract and introduction that traditional algorithms struggle with renewable energy uncertainties, using this as a key motivation for introducing the HOA. However, the core simulations in the case study do not explicitly or substantively incorporate the variability and uncertainty of renewable energy sources. Consequently, the claim that HOA holds a distinct advantage over traditional algorithms in this critical aspect remains unsubstantiated and lacks persuasive power.

2.The problem is oversimplified. Reducing a fundamentally "stochastic optimization problem" to a "deterministic optimization problem" significantly diminishes the problem's difficulty and real-world relevance. Traditional algorithms like PSO often perform adequately in deterministic settings; their true limitations typically emerge in complex, dynamic, and uncertain environments. The "exploration" and "escaping" mechanisms of HOA are ostensibly designed for such complex search spaces, yet their potential advantages may not be fully demonstrated or necessary within a deterministic model.

3.The conclusion that "HOA outperforms PSO and PIO" is valid only for the specific, simplified deterministic scenario presented. It remains uncertain whether this advantage persists in more realistic scenarios incorporating wind/PV fluctuations and forecast errors. Furthermore, the rationale for selecting PIO and PSO as benchmark algorithms is not sufficiently justified, leaving questions about the comprehensiveness and representativeness of the comparative analysis.

4.The attribution of system performance improvements (e.g., 1.5% cost reduction, 16.3% energy efficiency increase) directly to the superiority of the HOA algorithm presents a unclear causal relationship. System optimization results from the combined effect of the algorithm and the model. The HOA may have simply identified a more aggressive operational strategy (e.g., utilizing P2G and natural gas more intensively), whose feasibility might be highly dependent on the specific model parameters and assumptions (e.g., energy prices, device efficiencies, network constraints). In other words, it is unclear if HOA is genuinely "smarter," or if it merely found a specialized solution tailored to this particular setup. The lack of sensitivity analysis across different system configurations or parameters casts doubt on the generalizability of its claimed advantages.

5.The manuscript highlights the benefits of HOA (reduced cost and emissions) but overlooks the analysis of potential drawbacks. The HOA strategy results in greater fluctuations in P2G output and gas-fired unit cycling (Figs. 8, 11). The paper does not discuss whether these more frequent and intense operational shifts could accelerate equipment wear and tear, thereby increasing maintenance costs.

6.The payback period calculation uses the formula T = ΔI / ΔC_annual, where ΔI is the increased investment cost (~¥19.2 million) for the HOA-based solution, and ΔC_annual is the annual operational cost saving (~¥485 million) attributed to HOA. This calculation relies on a strong implicit assumption – that the additional ¥19.2 million investment is the direct cause of the ¥485 million annual savings. However, the paper does not demonstrate this causality. Where exactly is this additional investment allocated? Is it for larger P2G capacity or more energy storage? More critically, if the same ¥19.2 million investment were applied to system configurations optimized by PSO or PIO, could similar or even greater operational savings be achieved? The analysis lacks a crucial "equal investment comparison," making the conclusion that the HOA solution is economically superior appear presumptuous.

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This manuscript presents a well-structured and innovative study on the multi-objective optimization of IEGHES using the Hippopotamus HOA. Howeve there are still some shortcomings:

1. The manuscript notes that HOA’s population size was set to 20 to balance accuracy and efficiency. Adding a brief supplementary analysis (e.g., a small table or plot showing how convergence speed/solution quality varied with population size) would make this parameter choice more transparent.
2.  While the study focuses on deterministic optimization, real-world IES face significant uncertainties. A short discussion in the conclusions or future work section about how HOA could be adapted for stochastic or robust optimization （10.1038/s41598-025-92601-9） would broaden the study’s impact. 
3. The cost optimization results show HOA’s higher investment cost but lower annual operational cost, yet the manuscript does not break down how investment costs are allocated across system components.
4. In comparative analysis does not quantify the specific amount of surplus wind power absorbed via P2G technology.
5. The study’s optimization model relies on several implicit assumptions that are not explicitly summarized.

Author Response

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Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The author has addressed the reviewers' comments, and I recommend accepting the paper.