Operational Scheduling of Household Appliances by Using Triple-Objective Optimization Algorithm Integrated with Multi-Criteria Decision Making

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper suggested Triple-objective optimal scheduling of household appliances for smart grid integrated with multi-criteria decision making. This version is not acceptable. It should be resubmitted after considering the overall following comments:

 

1.     Title Revision: The authors are advised to refine the paper's title, ensuring it accurately reflects its content while being concise and captivating.

2.     Abstract Clarity: The abstract should succinctly outline the significant findings and maintain a clear and structured format. This will aid readers in comprehending the research.

3.     Introduction Enhancement: The introduction should establish a coherent framework for the research, allowing for seamless transitions between paragraphs. Additionally, the authors should emphasize the research's contributions, clearly stating its purpose, articulating the research question, and highlighting its significance.

4.     Figures and Captions: Figures should be presented with clarity and brevity, accompanied by captions that offer ample information to aid reader comprehension.

5.     Clear Research Problem Statement: The research problem should be articulated clearly and concisely to enhance readability.

6.     Methodology Clarification: The authors are encouraged to elucidate the connections between the forecasting and Data Augmentation methods, along with explaining the chosen solution method and its effectiveness in detail.

7.     Visual Presentation: Figures and charts should be of high quality, easy to interpret, visually appealing, and should effectively convey the research findings. It is recommended to enrich Figure 1 with additional data or more detailed information.

8.     Managerial Insights: The authors should provide more profound and actionable managerial insights derived from the research findings. They should also explicitly state the practical implications for managers and organizations.

 

9.     Proofreading and Editing: The authors should meticulously proofread and edit the paper to rectify any typos or grammatical errors. It is advisable to have a second set of eyes review the paper for any overlooked mistakes.

10. Please explain more Step-9: Dominance rank. It should be clarified more. and should apply the MDPI structure and subsections in all parts. 

Comments on the Quality of English Language

English is very difficult to understand/incomprehensible

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valuable comments and feedback which enriched the article. We have revised our manuscript according to the reviewers’ comments. Below are our detailed responses to the received comments. Please note that the comments of the reviewers are colored black, while the authors’ responses are colored red. Moreover, the modified or added parts to the manuscript are colored red except for the language corrections.

 

Best regards

Dhiaa Halboot Muhsen

 

Reviewer-1:

This paper suggested Triple-objective optimal scheduling of household appliances for smart grid integrated with multi-criteria decision making. This version is not acceptable. It should be resubmitted after considering the overall following comments:

Thank you for your comment and comprehensive understanding, we appreciate the time you have given in reviewing our article and we hope that we have addressed all of your concerns in the revised version. 

1. Title Revision: The authors are advised to refine the paper's title, ensuring it accurately reflects its content while being concise and captivating.

Thank you for your comments. We have amended the title to be “Operational scheduling of household appliances using triple-objective optimization algorithm integrated with multi-criteria decision making “.

 

2. Abstract Clarity: The abstract should succinctly outline the significant findings and maintain a clear and structured format. This will aid readers in comprehending the research.

Thank you for your comments. We have revised the abstract and has been modified to be as follows. It is worth mentioning that, we have explained the significant findings as numerical results in the last two lines in the abstract section.

"Load scheduling is the key factor for demand side management (DSM) that manages the available generation capacity with regards to the required demand. In this paper, a triple-objective load scheduling optimization problem (LSOP) is formulated to realize optimal cost, peak, and inconvenience. A Henry gas solubility optimization (HGSO) algorithm-based multiobjective is used for solving LSOP. The proposed HGSO offers a set of optimal solutions that represent the tradeoff between the triple objectives. The set of all optimal solutions of the dominate Pareto front are covered and then ranked using MCDM to sort these solutions. The entropy weighting method (EWM) is used for computing the weights of various criteria that dominate the LSOP and is provided for ordering preferences by similarity to achieve the ideal solution while (TOPSIS) is adapted to rank the solutions. Two types of working users are considered, non-cooperative and cooperative to show the effect of the proposed LSOP. The results of the proposed load scheduling method indicate the significance of the presented work for non-cooperative users as well as for cooperative work. The proposed LSOP provides R50.62 as the total cost of non-cooperative of four users, while for cooperative was R47.39. Thus, the cost saving was around 5.5 %. The peak value is reduced from 10.3 for non-cooperative to 9.3 kW of cooperative work, which accordingly is about 9.7 % peak saving.”

3. Introduction Enhancement: The introduction should establish a coherent framework for the research, allowing for seamless transitions between paragraphs. Additionally, the authors should emphasize the research's contributions, clearly stating its purpose, articulating the research question, and highlighting its significance.

Thank you for your helpful comments. According to your suggestions, the introduction is revised and is divided into two sections as follows.

1. “Introduction

The rapid growth and development of information and communication technologies (ICT) and pricing schemes (PS) have provided large opportunity for residential end user and to support energy saving [1]. The energy demands of residential sector have increased (globally with 30-40 % of the total energy consumption) for different reasons; increasing of population, wide range of urbanization, and adding more appliances [2]. To meet these energy demands, more generation capacity is required. However, building traditional power plants is not recommended in order to tackle greenhouse gases increase and to limit global worming crises [3]. Therefore, managing the available generation to meet the required demand is the critical aspect of demand side management (DSM). DSM tries to initiate the contribution of end user by using the ICT and PS to manage the energy consumption and mitigating the needs for more generation capacity. Load scheduling (LS) is one of the most active tools for DSM to manage household appliances for a given price rate, and so decreasing the energy bill of users and reduces the peak power load for utility company [4].

Flexible pricing scheme is another key factor of demand side management to encourage users in participating with demand response programs [5]. There are two types of pricing scheme, the first type is price-based such as real time pricing (RTP), Time-of-Use (ToU), critical-peak-pricing (CPP) and day-ahead-pricing (DAP). In price-based, the pricing rate changes based on the required demand, so that users can adjust their load based according to a given rate [6]. Meanwhile, with the incentive-based, the users are motivated to minimize their energy consumption with regards to the request offers or based to a contractual agreement. Accordingly, the program administrator will gain a degree of authority to directly reduce, disconnect, and schedule in order to save cost. This can be achieved through applying an agreement between the utility company and the user. Lately, such programs have included residential users besides to the large commercial and industrial users. The centralized controllers are utilized to provide decision and control action to manage operating state and instantaneous demand of individual devices. Some program cases based in this scheme offer interruptible tariffs, direct-load controls (DLCs), emergency programs and demand-bidding programs. Depending on these DR techniques, the user load can be changed according to incentive offers, price change, or an emergency case that jeopardizes the grid operation. The outcomes of DR with regards to the users and utility can be realized through reducing both user energy and cost, minimizing air pollution, dropping peak-energy prices, and reducing the need for new generation capacity [7].

Despite the available earlier studies that have focused on presenting mutual outcomes from supply and demand side, the earlier contributions lack to the following points: First, majority of the previous studies have relied on only one price-based rate, that in turn could be incompatible with other pricing rate. Second, commercial software packages have been used to solve most of the proposed multi-objective’s algorithms, which are not adaptable to modification and could not support global optimization. Moreover, combining multi-objective into single objective is widely dependent on the aggregated weighted sum model. Finally, it has been noticed that sorting all possible solutions process is rarely dependent on multi-criteria decision-making method.

According to the aforementioned, the contributions of this paper for load scheduling optimization problem (LSOP) are listed as follows:

• Propose a multi-objectives LSOP that relies on dominant rank and utilizes the Henry gas solubility optimization (HGSO) approach to achieve an optimal cost, peak and user inconvenience concurrently. These objectives are devised according to HGSO for attaining all solutions’ set.
• A hybrid multi-criteria decision-making method is utilized to candidate the compromise solutions, entropy weighting method (EWM). It is adapted to compute the weights of various criteria which dominate the LSOP and is considered as a technique to order preferences by similarity to ideal solution (TOPSIS) for ranking the solutions. The multi-objectives HGSO will produce sets of solutions for scheduling user’s load to realize energy saving and optimal cost while ensuring lower inconvenience level. Merging EWM-TOPSIS with multi-objective HGSO aids the realization of the compromise solutions that are based to predefined criteria among the entire optimal solution sets.
• Two types of pricing scheme namely the ACLPS and ToU are utilized to validate the results via comparing the performance with other various pricing techniques. “

 

2. “Related works

There are many studies that addressed load scheduling for cost and energy saving. In [8], a mixed-integer nonlinear optimization technique that is based on the ToU pricing program is presented to schedule actual user load types. The outcomes showed approximately 25% cost reduction. A dynamic residential load management scheme has been presented in [9]. Based on a given allowance, the users are motivated to manage their devices to optimal saving for cost and energy. The performance of ToU demonstrated about 35% and 31% for energy and cost saving, respectively. Load scheduling system in residential area has been proposed by authors in [10] which addresses end-user’s preferences. In addition, based on ToU electricity tariff, a multi-objective linear programming is utilized to reduce the peak power load. This paper addressed the reduction of coordinated peak load within a multiple-household context. The presented approach seeks to reduce three objectives: the scheduling inconvenience, the electricity cost, and the peak load. Depending on the three objectives, both utility companies and consumers will have the facility to adjust their priority in minimizing one over other. In this study, three multi-objective optimization approaches are applied: preemptive optimization, compromise optimization and normalized weighted-sum approach. The outcomes of the study revealed an outstanding performance as analyzed with regards to three techniques in literature and the end-suer’s preferred schedule. Home energy management scheme that is based on IoT context is provided in [11]. Seeking to improve the system efficiency in terms of energy consumption cost and end-user’s satisfaction, an enhanced butterfly optimization technique version is adapted. This approach is studied on a designed house and the outcomes have been compared with a normal consuming method. In [12], a multi-objective (cost and incontinence) algorithm is presented and is depending on a multi-objective optimization differential evolution (MODE) scheme to achieve optimal energy and cost saving. In order to obtain all set of solutions, the objectives are formulated using MODE. Next, the compromise solutions are designated using analytic hierarchy process (AHP), and technique for order preferences by similarity to ideal solution (TOPSIS) as a hybrid multi-criterion decision-making method. The analyses highlight how the approach managed to save more than 32% of customer energy cost for time of use. On the other hand, and regarding the baseline operation, the peak load of customer is minimized by 41%. In [13], an optimal scheduling method has been proposed for household devices. The proposed approach has addressed electricity cost, incentive, and end-users’ inconvenience under ToU electricity charge. Moreover, a study of inconvenience weighting parameter effect on the total costs has been carried out. Next, the impact of incentive on optimization performance is evaluated. The simulation results illustrated that 34.71% saving in end-user’s total costs has achieved. Authors in [14] have proposed a flexible demand management scheme to schedule residential load efficiently and the load operating time window has been addressed as the constraint. The target of this contribution is to emphasize constraints affecting the operation schedule of devices while contributing demand response events. Accordingly, an innovative crossover approach of genetic algorithms has been adapted in this work. The presented method has addressed dynamic pricing, distributed generation and load shifting to reduce both energy costs and electricity bill. Real household workload data is presented as a case study by which four devices are scheduled for five days, and three various scenarios have been examined. The adapted genetic model has managed to realize up to 15% in bill reduction for multiple scenarios as compared to business as usual. Operation management of residential appliances is provided in [15] through a demand-side management model. In order to reduce user dissatisfaction and electricity cost, A multi-objective optimization problem is presented, where residents’ tolerance to discomfort has been addressed. Non-inferior solution sorting genetic algorithm (NSGA-II) and the hybrid multi-objective particle swarm optimization (MOPSO) are presented to determine the scheduling issue. Next, selecting the most compromising solution within the Pareto solution set is achieved via the TOPSIS method. The study demonstrated that the hybrid algorithm can achieve higher efficiency and have validated the effectiveness of the optimization algorithm. Finally, determining the efficacy of the scheduling approach is demonstrated through providing a case study in this work. Authors in [16] have proposed an optimal schedule model for resident devices. An improved genetic algorithm (GA) is used to solve the optimization problem by which the scheduling is formulated. The entropy method has been adapted to perform chromosomes selection process in this improved GA while the mutation and blended crossover is been carried though correlation coefficient. The simulation is based on the Python programming and considered a set of appliances regarding single resident load profile. The outcomes of the simulations indicated a decrease in the electricity cost as the original. The execution time is minimized by 2.76 s where the iterations number that considered by the enhanced GA is comparatively lower than the standard GA. Authors in [17] have proposed a demand response (DR) scheduling model that targeted four classes of residential building loads: non-interruptible and deferrable loads, interruptible and deferrable loads, air conditioning loads and non-interruptible and nondeferrable loads. In order to find minimal inconvenience index and minimal electricity cost, a multi-objective optimization algorithm that based on nondominated sorting genetic algorithm II is utilized. The adopted multi-objective optimization model was NSGA-II while the minimal inconvenience index and minimal electricity cost were the optimization objectives. The AC load flexibility is tested on Dymola platform, where two kinds of DR strategies have been developed for AC. About 25% of nocturnal peak load saving can approximately be realized while 10% of the daily electricity charge can be reduced. Other efforts in [18] have been directed to explore the potential variations in peak-to-valley electricity consumption and electricity charges that are considered under smart home context. This has been achieved by proposing a multi-objective smart home integrated management approach while considering the behavioral heterogeneity of appliances and household electricity consumption. The analysis indicated that smart home which are involved in power demand response could minimize peak load by 29.3% - 49.3%. Meanwhile, the peak-to-valley difference can be reduced by 37.5% - 78.2%. In [19], the authors have proposed a non-cooperative Stackelberg model-based game theory that take into account the impact of both users’ dissatisfaction with electricity consumption and load fluctuations in power grid. In this approach, the users are firstly categorized into various kinds through induction and classification to comprehend an insight consideration of different electricity users’ categories. Next, two utility functions will be set up in this approach. The power supply’s utility function will be set to indicate the outcomes gained form the process of power supply regarding the power company. On the other hand, the utility function regarding power demand side will set to show the degree of dissatisfaction for the electricity users. The NSGA-II algorithm is used to solve the developed model in this work. Finally, the proposed algorithm is used for the actual case while the sensitivity analysis of related parameters is considered to validate the effectiveness.”

4. Figures and Captions:Figures should be presented with clarity and brevity, accompanied by captions that offer ample information to aid reader comprehension.

Thank you for your comment on improving our manuscript. We have revised the captions of the most figures to be accessible, as well as the clarity of the figures is enhanced.

5. Clear Research Problem Statement:The research problem should be articulated clearly and concisely to enhance readability.

Thank you for your important comment. According to your suggestion, the problem statement has been clearly stated at the end of revised version of section 1 (introduction) as follows:

” Despite the available earlier studies have focused on presenting mutual outcomes from supply and demand side, the earlier contributions lack to the following missing points: First, majority of the previous studies have relied on only one price-based rate, that in turn could be incompatible with other pricing rate. Second, commercial software packages have been used to solve most of the proposed multi-objective’s algorithms, which are not adaptable to modification and could not support global optimization. Moreover, combining multi-objective into single objective is widely dependent on the aggregated weighted sum model. Finally, it has been noticed that sorting all possible solutions process has been rarely dependent on multi-criteria decision-making method.”

6. Methodology Clarification:The authors are encouraged to elucidate the connections between the forecasting and Data Augmentation methods, along with explaining the chosen solution method and its effectiveness in detail.

Thanks for the opportunity to address this point. Nonetheless, our discussion may have been unclear; thus, we hope we have enhanced our explanation of this issue. The proposed LSOP considers that the data given of the available household to be as a real consumption profile. The covered data consider four users for two types of operations, cooperative and non-cooperative work. Most recent contributions in this field covered only one user for very little numbers of household users. We can expand the number of users but unfortunately the paper becomes very long.

7. Visual Presentation:Figures and charts should be of high quality, easy to interpret, visually appealing, and should effectively convey the research findings. It is recommended to enrich Figure 1 with additional data or more detailed information.

Thank you for your comment. The quality of the figures is improved. Figure 1 illustrates the steps of the proposed method for solving LSOP. The steps were discussed in detail before presenting Figure 1. We believe that Figure 1 reflects the methodology of the manuscript exactly.

 

8. Managerial Insights:The authors should provide more profound and actionable managerial insights derived from the research findings. They should also explicitly state the practical implications for managers and organizations.

Thanks for the opportunity to address this point. Nonetheless, our discussion may have been unclear; thus, we hope we have enhanced our explanation of this issue. The proposed solutions for scheduling the users’ load profile provides saving for cost, peak and lowering the user incontinence. These contributions led to manage the available generation capacity to overcome the needs for new generation capacity. Users are getting lower energy bill with little deferment (within user margins) for the operation time of household appliance, while utilities company get valuable outcomes by reducing the peak load so that, there will be no need for additional capacity. Therefore, both users and utility companies get benefited. In addition, managing the available generation reduces the emission of GHG and minimizes the global warming.

According to your comment, the conclusion is revised to highlight this issue, as follow:

“Triple objectives load scheduling system is proposed to achieve optimal cost, peak and inconvenience. All sets of Pareto front for domain solutions are presented then these solutions are ranked using MCDM according to predetermine weight of EWM method. The proposed system is applied for two cases of work for users, cooperative and non-cooperative mode to support the effect of cooperation work on these objectives. The cost saving for cooperative work of all users is about 5.5% while the peak saving is 9.7%. The results confirmed that the cooperative work is more beneficial for users to save cost. In accordance, the utility also gets benefited by reducing the peak and minimizes the required generation capacity to support the demand. The advantages of managing the available generation capacity that benefit the users and utility company led to reduce the GHG and tackle the effect of weather worming and blackout crises.”  

9. Proofreading and Editing:The authors should meticulously proofread and edit the paper to rectify any typos or grammatical errors. It is advisable to have a second set of eyes review the paper for any overlooked mistakes.

We sincerely appreciate the reviewer’s comments. As it has been suggested, we have gone through the revised version of manuscript and corrected any existed typing mistakes and grammatical errors.

 

10. Please explain more Step-9: Dominance rank. It should be clarified more. and should apply the MDPI structure and subsections in all parts. 

Thank you for your comment. We have added the following paragraph and Algorithm 1 for addressing your concern about “step -9: Dominance rank” in subsection 3.1: “Algorithm 1 illustrates the steps of dominance rank concept that utilized for initiating the new population of the next generation in the proposed HGSO algorithm.

Algorithm 1. Pseudo code of the proposed dominance rank in HGSO algorithm

Combine the parent solutions and their updated ones to construct .

Initiate 1 vector () to represent the dominance rank value of each solution in .

Set the  elements of  equal to zero.

For  to  do

For  to () do

If solution () is dominated by solution () where  then .

End for

End for

Sorting the elements of vector in ascending form.

Sorting the solutions in based on.

Choose the first  solutions from  to construct the new population for the next generation.”

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Demonstrate why the chosen method (TOPISS and EWM) is suitable for this study but not others?
The discussion section was poor written. The authors must show practical and theoretical implications of the paper.

Comments on the Quality of English Language

No

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valued comments and feedback which enriched the article. We have revised our manuscript according to the reviewers’ comments. Below are our detailed responses to the received comments. Please note that the comments of the reviewers are colored black, while the authors’ responses are colored red. Moreover, the modified or added parts to the manuscript are colored red except the language corrections.

 

Best regards

Dhiaa Halboot Muhsen

 

Reviewer-2:

• Demonstrate why the chosen method (TOPISS and EWM) is suitable for this study but not others?
  
  

Thank you for this valuable comment. The EWM is an objective weighting method, the weights of criteria are computed utilizing specific computational steps based on information gathered from the decision matrix without any consideration of the decision maker’s intervention [R1]. In contrast, in other weighting methods (Subjective weighting methods), the preferences among the criteria are a mental task (expert opinion) that is achieved by the decision maker; thus, the increasing of criteria leads to inaccuracy preferences among them. However, subjective criteria weight determination is often time-consuming especially when there is no agreement between decision makers of the problem under consideration. It is worth mentioning that, the no agreement between the experts leads to inconsistency problems in the computed weights. Thus, the EWM was used to overcome the aforementioned drawbacks in other weighting methods.

 

The TOPSIS method is represented as one of the most common effective MCDM method that used for ranking alternatives (solutions) based on predefined weights for criteria, which dominate the problem. The main advantages of TOPSIS method are the following [R2, R3]:

• Simple, rational, comprehensible, and understandable concept,
• Intuitive, internal consistency and logical soundness that represent the rationale of human choice,
• Ease of computation and reliability (good computational efficiency).
• A scalar value that accounts for both the best and worst alternative’s ability to measure the relative performance for each alternative in a simple mathematical form,
• Possibility for visualization.

 

[R1] Aldian, A; Taylor, M.A.P. (2005). A consistent method to determine flexible criteria weights for multicriteria transport project evaluation in developing countries. J.  East. Asia Soc. Transport. Stud. 6: 3948-3963.

[R2] Roszkowska, Ewa. "Multi-criteria decision making models by applying the TOPSIS method to crisp and interval data." Multiple Criteria Decision Making/University of Economics in Katowice 6, no. 1 (2011): 200-230.

[R3] Hung, Chia-Chang, and Liang-Hsuan Chen. "A fuzzy TOPSIS decision making model with entropy weight under intuitionistic fuzzy environment." In Proceedings of the international multiconference of engineers and computer scientists, vol. 1, pp. 13-16. IMECS Hong Kong, 2009.

 

• The discussion section was poor written.

Thank you for your important comment. According to your comment, the discussion is revised as follows:

“According to Table 7, the user load consumption profile for non-cooperative of the first rank solutions that based on different number of users are presented in Figures 7 to 10. Figure 7 shows the consumption of first user before and after applying the proposed load scheduling method. According the to the load distribution of the first user, the total cost was reduced from R25.37 before load scheduling to R20.78 after applying the proposed load scheduling. The peak load reduced from 9.8 to 6.135 kW while the incontinence become 31 slots as shown in Table 8. Thus, the saving becomes 18% for cost and about 37.3% for peak load. These savings of the first rank solution clearly reflect the importance of the given weights and are tabulated in table 6 for the covered objectives. The results indicate high saving for peak and inconvenience because they offer high weights while the cost for this solution offers lower weight. The second rank of the first user provides significant reduction for peak to become 5600 kW, while third rank solutions of the first user show superior reduction in energy cost to be about R17.05, as shown in table 7. These solutions show the importance of weights regarding the covered objectives. Figurers 8 to 10 show the profiles consumption of other users. The cost and peak saving for second, third and fourth user are (1.4% and 38.18%), (9.2% and 0%), and (4.5% and 24.9) respectively.”

 

• The authors must show practical and theoretical implications of the paper.

Thanks for the opportunity to address this point. Nonetheless, our discussion may have been unclear; thus, we hope we have enhanced our explanation of this issue. The proposed solutions for scheduling the users’ profile load provide saving for cost, peak and lowering the user inconvenience. These contributions led to manage the available generation capacity to overcome the need for new generation capacity. Users are getting lower energy bill with little deferment (within user margins) for operation time of household appliance, while utilities company get valuable outcomes by reducing the peak load, so that no need for additional capacity. Therefore, both users and utility companies get benefited. In addition, managing the available generation reduces the emission of GHG and minimizes the global warming.

According to your suggestion, the conclusion is revised to highlight this issue as follow:

“Triple objectives load scheduling system is proposed to achieve optimal cost, peak and inconvenience. All sets of Pareto front for domain solutions are presented then these solutions are ranked using MCDM according to predetermine weight of EWM method. The proposed system is applied for two cases of work for users, cooperative and non-cooperative mode to support the effect of cooperation work on these objectives. The cost saving for cooperative work of all users is about 5.5% while the peak saving is 9.7%. The results confirmed that the cooperative work is more beneficial for users to save cost. In accordance, the utility also gets benefited by reducing the peak and minimizes the required generation capacity to support the demand. The advantages of managing the available generation capacity that benefit the users and utility company led to reduce the GHG and tackle the effect of weather worming and blackout crises.”  

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors are advised to avoid tables and instead use Microsoft Power BI or Matlab to generate robust metrics for the proposed scheduling model.

 

On the other hand, it is suggested that the authors order the document.

1.- Introduction (Generalities of the problem - 15 references between 2024-2020), 2.- Related Works (Specific works with punctual solutions, summary table of state of the art of other proposals against the current work - 15 references between 2024-2020), 3.- Problem Formulation and Methodology (Table of variables of the mathematical model, mathematical model, pseudocode, methodology flowchart, Big Oh Notation of the algorithm - Forecasting), 4. - Analysis of Results (Metrics performed in Matlab in PDF format or directly from Overleaf), 5.- Conclusions (Direct relation between the objective stated in the abstract vs. the metrics found), 6.-References 2024-2020 (All documents with DOI from ScienceDirect, MDPI, Wiley, PLOS, Taylor & Francis, Springer, Hindawi, IEEE Xplore [transactions, magazines, journals]).

 

 

Comments on the Quality of English Language

There are no suggestions for significant corrections in the grammar.

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valued comments and feedback which enriched the manuscript. We have revised our manuscript according to the reviewers’ comments. Below are our detailed responses to the received comments. Please note that the comments of the reviewers are colored black, while the authors’ responses are colored red. Moreover, the modified or added parts to the manuscript are colored red except the language corrections.

 

Best regards

Dhiaa Halboot Muhsen

 

The authors are advised to avoid tables and instead use Microsoft Power BI or Matlab to generate robust metrics for the proposed scheduling model.

Thank you for your comment. As a matter of fact, we have used tables to illustrate the detailed data that have been utilized in the presented LSOP.

 

On the other hand, it is suggested that the authors order the document.

1.- Introduction (Generalities of the problem - 15 references between 2024-2020), 2.- Related Works (Specific works with punctual solutions, summary table of state of the art of other proposals against the current work - 15 references between 2024-2020), 3.- Problem Formulation and Methodology (Table of variables of the mathematical model, mathematical model, pseudocode, methodology flowchart, Big Oh Notation of the algorithm - Forecasting), 4. - Analysis of Results (Metrics performed in Matlab in PDF format or directly from Overleaf), 5.- Conclusions (Direct relation between the objective stated in the abstract vs. the metrics found), 6.-References 2024-2020 (All documents with DOI from ScienceDirect, MDPI, Wiley, PLOS, Taylor & Francis, Springer, Hindawi, IEEE Xplore [transactions, magazines, journals]).

Thank you for your comment. We appreciate your suggestions and opinions. We have revised our manuscript by initiating a new section called “Related works” and revising other sections. The variables of the mathematical model are tabulated in the “Nomenclature” table. The pseudo-codes of algorithms used in the proposed mathematical model are illustrated in “Algorithm 1” and “Algorithm 2”. The results of the proposed MHGSO-AHP-TOPSIS methods are discussed in section 4 of the old version of the manuscript. Furthermore, the results are validated by comparing them with other related research works published in literature in section 5 of the original version of the manuscript. Finally, we have written the DOI of all references.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In this paper, a multi-objective scheduling optimization problem is proposed to optimize the cost, peak and inconvenience, so as to give a reasonable power plant load schedule.

 

There is a small comment for this manuscript. Hopefully, this comment can improve the paper's readability and quality.

 

 

Can the existing commercial scheduling solvers such as GAMS solve the scheduling optimization problem mentioned in the paper? A comparative study should be conducted.

 

Using the proposed method to solve the scheduling problem in the paper, will there be more than one solution?

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valued comments and feedback which enriched the manuscript. We have revised our manuscript according to the reviewers’ comments. Below are our detailed responses to the received comments. Please note that the comments of the reviewers are colored black, while the authors’ responses are colored red. Moreover, the modified or added parts to the manuscript are colored red except the language corrections.

 

Best regards

Dhiaa Halboot Muhsen

 

Reviewer-4:

In this paper, a multi-objective scheduling optimization problem is proposed to optimize the cost, peak and inconvenience, so as to give a reasonable power plant load schedule.

There is a small comment for this manuscript. Hopefully, this comment can improve the paper's readability and quality.

Thank you for your comment and valuable suggestions, we appreciate the time you have given in reviewing our article and we hope that we have addressed all of your concerns in the revised version. 

 

1. Can the existing commercial scheduling solvers such as GAMS solve the scheduling optimization problem mentioned in the paper? A comparative study should be conducted.

Thank you for your comment and suggestion. GAMS solver can be used for solving the load scheduling problem, but using GAMS is difficult when dealing with multiobjective optimization problem. In the current research work, MATLAB is used for coding the HGSO algorithm based on triple objectives in order to optimally schedule the domestic load. Defining a problem in MATLAB is relatively easier than in GAMS and gives us more flexibility to deal with an optimization problem. In our research work, we focused on how to solve the load scheduling problem for multiusers based on multiobjective rather than the type of solver. The results of the manuscript were validated by comparing them with other related works as well as to data of users before scheduling.

As a matter of fact, we are currently working on a new research paper for solving the load scheduling problem for multiusers by using an multiobjective artificial hummingbird algorithm and a new pricing scheme, which may validate the proposed solver with GAMS.

 

2. Using the proposed method to solve the scheduling problem in the paper, will there be more than one solution?

Thank you for your comment. The proposed multiobjective HGSO algorithm, which was used for solving load scheduling optimization problem (LSOP), produces a set of optimal solutions that have a Pareto front in objective space as illustrated in Figures 3-6. After that, the hybrid multicriteria decision-making (HMCDM) methods are used for ranking the superior solutions, which belong to the Pareto front of load scheduling optimization problem (LSOP).

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Please consider the structure of your paper at the end of introduction.

Comments on the Quality of English Language

Minor spelling check required.

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valued comments and feedback which enriched the article. We have revised our manuscript according to the reviewers’ comments. Below are our detailed responses to the received comments. Please note that the comments of the reviewers are colored black, while the authors’ responses are colored red. Moreover, the modified or added parts to the manuscript are colored red except for the language corrections.

 

Best regards

Dhiaa Halboot Muhsen

 

Reviewer-1:

Thank you for your comment and comprehensive understanding, we appreciate the time you have given in reviewing our article and we hope that we have addressed all of your concerns in the revised version. 

1. Please consider the structure of your paper at the end of introduction.

We sincerely appreciate the reviewer’s comments. We have added the following paragraph at the end of the “Introduction” section to address your concern: “The rest of the paper is organized as follows. Section 2 reviews the related works. Section 3 describes the mathematical model of LSOP. The proposed multi-objective HGSO algorithm and EWM-TOPSIS multicriteria decision making methods are presented in section 4. The performance evaluation of the proposed load scheduling method is presented in section 5. Section 6 discusses the validation of results. The conclusion is drawn in section 7. “

 

2. Minor spelling check required.

Thank you for your comment and notice. we have gone through the revised version of the manuscript and corrected any existing typing mistakes and grammatical errors.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Congratulation!

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valuable comments and feedback which enriched the article.

 

Best regards

Dhiaa Halboot Muhsen

 

Reviewer-2:

Thank you for your comment and comprehensive understanding, we appreciate the time you have given in reviewing our article.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The author has answered all my questions and I have no more questions

Author Response

Dear Editor of Sustainability,

The authors of the manuscript would like to thank the Sustainability’s editorial office members as well as the reviewers for their valuable comments and feedback which enriched the article.

 

Best regards

Dhiaa Halboot Muhsen

 

Reviewer-4:

Thank you for your comment and comprehensive understanding, we appreciate the time you have given in reviewing our article.

Author Response File: Author Response.pdf