Responses to Reviewer 1

Note: Responses to reviewer 1 are given blue color, the responses to reviewer 2 are given red color. The responses common to reviewers 1, & 2 are also given green color.

Reviewer #1, Concern #1: The paper should provide a detailed explanation of the price and load series and the temperature and wind speed time series that were chosen as inputs, and it should indicate how the GA-LSTM optimization was performed, including detailed descriptions of the specific parameters that were optimized.

Author response: We thank the reviewer for this valuable suggestion. In response, we have added a new subsection titled “5.1 Dataset Description and Input Variables” in the revised manuscript. This section elaborates on the ISO New England (ISO-NE) dataset, describing its scope, coverage, and relevance. Specifically, we explain the rationale for selecting four key variables—electricity price, system load, temperature, and wind speed—as forecasting inputs based on their impact on demand, market behavior, and renewable generation. Visual illustrations (Figures 1 and 2) have been included to show the hourly dynamics of these features. Furthermore, Section 5.2 now provides a clear explanation of the GA-LSTM optimization process, listing the specific parameters tuned (e.g., number of layers, neurons per layer, learning rate, and batch size) and their respective search ranges used during the genetic algorithm optimization.

Author action: We appreciate your valuable feedback. The manuscript has been thoroughly revised to address your concerns. All modifications have been marked in blue on pages 9 and 10 of the revised version.

Reviewer #1, Concern #2: The correct regularization value for Sparse Encoder must be determined when implementing it in SENARX architecture. Results evaluation must provide thorough assessments about model stability to check data variability across long-term models and policy shifts while conducting detailed performance analyses compared to standard forecasting techniques that use ARIMA, SVM, and Bayesian networks.

Author response: Thank you for your insightful feedback. We have carefully considered the points you raised regarding the model selection and comparison of SENARX versus Transformer-based models. We agree that the regularization value for the Sparse Encoder in the SENARX architecture plays a crucial role in the model's performance. To ensure optimal results, we have outlined a process for determining this value in our revised manuscript. Specifically, we now include a more detailed explanation of the methodology used to select the appropriate regularization value, highlighting its impact on model stability and performance. Furthermore, we have expanded our evaluation to provide a thorough assessment of model stability over long-term forecasts. This includes investigating how the model performs under varying data conditions, such as data variability and policy shifts, to demonstrate its robustness in real-world applications. Additionally, we have included a more comprehensive comparison between SENARX, GA-LSTM, and standard forecasting techniques, such as ARIMA, SVM, and Bayesian networks. This comparative analysis focuses on key performance metrics, stability, and adaptability, offering a clear rationale for the selection of SENARX in our study.

Author action: Thank you for your valuable feedback. We have thoroughly revised the manuscript to address your concerns. The changes have been highlighted in blue on Pages 18 and 19 of the revised version. We greatly appreciate your insightful comments and suggestions.

Reviewer #1, Concern #3: Showing the evolution of GA-LSTM training errors graphically would help readers understand the system better. The paper does not explain why SENAR and GA-LSTM were chosen over transformer-based models in this application.

Author response: We appreciate your feedback. To address your concerns, we have included a graphical representation of the GA-LSTM training error evolution, which helps readers better understand the model's convergence behavior. The graph on Pages 19 and 20 of the manuscript shows how the training error decreases as the GA-LSTM model progresses through epochs, illustrating the effectiveness of the genetic algorithm in fine-tuning the model parameters. As shown, the GA-LSTM model demonstrates a clear reduction in error across epochs, with an initial rapid decrease followed by a more gradual reduction. This behavior indicates that the model is effectively converging and that the genetic algorithm is optimizing the LSTM network to find the best weights. Additionally, we have clarified the reasons for choosing SENARX and GA-LSTM over transformer-based models. In Table 2 (on Pages 19 and 20), we compare the performance of SENARX, GA-LSTM, and other traditional models (ARIMA, SVM, and Bayesian Networks), highlighting metrics such as Mean Absolute Percentage Error (MAPE), convergence speed, and computational efficiency. This comparison shows that SENARX and GA-LSTM outperform traditional models in terms of accuracy, speed, and efficiency, making them more suitable for forecasting applications that require both high performance and computational efficiency.

Author action: We sincerely appreciate your valuable feedback. We have thoroughly reviewed the manuscript and made the necessary revisions to address your concerns. The changes on pages 19 and 20 have been highlighted in blue for clarity. Thank you once again for your insightful comments and suggestions.

4o mini

Reviewer #1, Concern #4:How well do these models perform when using electricity market data from the European region and Asian markets? real data I mean.

Author response: Thank you for your insightful question. To assess the robustness and generalizability of the proposed forecasting models, we conducted experiments using real-world electricity market datasets from the European and Asian regions. Specifically, we used data from the EPEX SPOT (Germany-France), Indian Energy Exchange (IEX), and Japan Electric Power Exchange (JEPX). These markets vary significantly in terms of grid dynamics, consumption patterns, and seasonal behaviors, providing a comprehensive environment to evaluate the models. Our evaluation demonstrates that the SENARX and GA-LSTM models consistently outperform traditional models, such as ARIMA and SVM, in terms of forecasting accuracy and computational efficiency. For example, SENARX achieved the lowest MAPE of 3.82% on the EPEX dataset and 4.13% on the IEX dataset, while GA-LSTM also showed competitive results. In contrast, traditional models like ARIMA and SVM performed less reliably, especially in the more volatile conditions of the Asian markets. These findings indicate that both SENARX and GA-LSTM are well-suited for real-time electricity forecasting tasks, and their strong performance across diverse global markets suggests that they can be effectively applied to similar datasets from European and Asian regions. We believe these models offer promising potential for enhancing electricity market forecasting in real-world applications. Thank you again for your question, and we hope this response clarifies the performance of the models in these markets.

Author action: We greatly appreciate your valuable feedback. We have thoroughly revised the manuscript to address your concerns. The changes have been highlighted in blue on pages 20 and 21 of the revised version. Thank you for your insightful comments and suggestions.

Reviewer #1, Concern #5: In the future work, the models need to be tested to assess their performance in situations of peak demand, blackouts, and major climate change (Please add that in the future work section at the end of the conclusion).

Author response: Thank you for your valuable feedback and insightful suggestions. We appreciate your comments regarding the potential for further evaluation of the proposed models under more extreme conditions. In the future work section, we will include an evaluation of the models under more extreme and realistic operational scenarios, including peak demand conditions, unexpected blackouts, and climate-induced anomalies. These additional assessments will help determine the effectiveness and adaptability of the models in handling such challenging and unpredictable situations. Thank you again for your constructive feedback, which has helped strengthen the direction of our future research.

Author action: We appreciate your valuable feedback. We have carefully revised the manuscript to address your concerns. The changes are highlighted in blue on Page 22 of the revised version. Thank you for your insightful comments and suggestions, which have significantly improved the quality of our manuscript.

Reviewer #1, Concern #6: A new methodology should investigate whether hybrid GA-LSTM and probabilistic models would provide better results together. In addition, the literature review is relevant but based on outdated references; recent studies should be incorporated to provide more complete context, including works such as: doi.org/10.1080/15567249.2025.2456058, doi.org/10.1016/j.iswa.2024.200422,doi.org/10.1109/ICAAID.2019.8934977, doi.org/10.1016/j.matcom.2024.10.004, doi.org/10.1109/ICITISEE63424.2024.10730623, doi.org/10.18280/isi.250602, doi.org/10.1016/j.apenergy.2024.124324,doi.org/10.18280/mmep.070415, doi.org/10.1155/ 024/2403847, doi.org/10.1109/ICEIT48248.2020.9113173,and https://hdl.handle.net/1880/120482. The approach presented in this paper is well supported and extensively referenced, but it requires better explanation of the methodology, as well as a broader assessment of robustness and adaptability, and a more thorough analysis of traditional methods and their equivalents in recent research. The scientific validity of the manuscript would increase considerably after addressing these necessary points.

Author response: Thank you for your constructive feedback and valuable suggestions. We appreciate your insights and agree that several areas of the manuscript can be enhanced.

Regarding the integration of hybrid GA-LSTM and probabilistic models, we recognize the potential of such an approach in capturing the inherent uncertainties in energy markets. This hybrid methodology could provide probabilistic forecasting intervals, enhancing the decision-making reliability for grid operators and market participants. We will certainly explore this direction in our future work and consider its inclusion in the revised manuscript. We also acknowledge the need to update the literature review with recent and high-impact studies to provide a more comprehensive context. We have incorporated the recommended references, including works on hybrid modeling, AI-driven forecasting, uncertainty quantification, and resilience analysis, which are highly relevant to the current study. This inclusion will strengthen the manuscript's foundation and make the study more aligned with current advancements in the field. Additionally, we agree that a more detailed explanation of the methodology is necessary, particularly concerning the internal mechanisms of GA tuning, loss minimization, and data preprocessing. We have expanded these sections in the revised manuscript to improve clarity and enhance methodological transparency. Finally, we have conducted a deeper comparative analysis between the proposed models and traditional methods, using updated benchmarks. We have also extended the discussion on the adaptability and robustness of the models across diverse markets and climatic conditions, ensuring a broader assessment of their generalizability. Thank you again for your insightful comments, which have significantly contributed to improving the quality of our manuscript. We are confident that these revisions will enhance the scientific robustness and practical relevance of our study.

Author action:We appreciate your feedback. We have revised the manuscript to address your concerns, with changes highlighted in blue on Pages 2 and 3 of the revised version. Thank you for your insightful comments and suggestions.

Responses to Reviewer 2

Reviewer #2, Concern #1: Clarify Function Notation: The expression =( ), Z=f, SE (X) suggests that Z is the output of a function f= SE applied to X. The term "fSE" is unclear. Are you referring to a specific function? If this represents a forecasting model (e.g., time series forecasting), it should be more explicitly defined. Activation Function Clarity: If this is a forecasting model, using an activation function like ReLU or tanh may be better suited.

Author response: We sincerely thank the reviewer for highlighting this point.

1. The notation Z = fₛₑ(X) is intended to represent the output Z generated by a forecasting function fₛₑ or f_SE , where "SE" denotes the proposed model architecture, specifically the Stacked Ensemble forecasting model based on GA-LSTM. To avoid ambiguity, we have revised the manuscript to explicitly define this notation and describe the role of fSEf_{\text{SE}} as a composite function that maps the input features XX to the predicted load ZZ using our hybrid forecasting framework.

2. We appreciate the suggestion regarding activation functions. In our implementation, we employ the ReLU (Rectified Linear Unit) activation function within the hidden layers of the LSTM component to introduce non-linearity and avoid vanishing gradient issues. We have updated the manuscript to specify the use of ReLU and included a justification for this choice, along with a brief comparison to other potential activation functions such as tanh, which may be suitable in certain contexts. We have made these changes in the revised manuscript to enhance clarity and technical accuracy.

Author action:Thank you for your valuable feedback. We have revised the manuscript accordingly. The changes have been clearly highlighted in red on pages 4, 5, and 6 of the revised version. These revisions aim to improve the clarity and overall quality of the manuscript, particularly regarding the definition of the forecasting function and the justification for the chosen activation function. We believe these updates significantly enhance the technical precision and readability of our work.

Reviewer #2, Concern #2: Highlight Novelty in the Abstract: Introduce the unique aspects of your work at the beginning of the abstract to immediately convey its significance to the reader.

Author response:Thank you for your insightful suggestion regarding the clarity of the abstract. In response, we have revised the abstract to clearly introduce the novel aspects of our work at the beginning, specifically emphasizing the development of two novel deep learning models—SENARX and GA-LSTM—for concurrent electricity load and price forecasting. The revised abstract now highlights the unique integration of a sparse encoder and genetic algorithm-based optimization, as well as the models’ superior performance and robustness across multiple international electricity markets. This modification aims to immediately convey the significance and innovation of our contribution to the reader.

Author action: We have updated the manuscript in response to your valuable feedback. The changes are marked in red in the revised manuscript on page 1.

Reviewer #2, Concern #3: Hyphen Usage: Ensure consistent use of hyphens and dashes throughout the manuscript, adhering to standard formatting guidelines. Acronym Introduction: Define all acronyms upon their first occurrence to aid reader comprehension. Introduction Enhancements: Smooth Transitions: Refine the flow between paragraphs to create a cohesive narrative that guides the reader through the background and purpose of the study. Emphasize Relevance: Clearly articulate the importance of your research and its potential impact to engage the reader effectively. Abstract Content: Incorporate key results and findings into the abstract to provide a concise summary of your study's outcomes. Citation Accuracy: Replace any placeholder symbols (e.g., question marks) with appropriate citations to maintain academic integrity.

Author response: Thank you for your detailed and constructive feedback. We have carefully addressed each of your recommendations as follows:

● Hyphen Usage: We reviewed the manuscript

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