Optimization of Fuel Consumption for an Offshore Supply Tug Using a Backtracking Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. I think the abstract needs to be reconsidered and rewritten. The part of the abstract that starts with "In this study..." seems like a repetition of the previous one.
2. In the introduction, the importance of the method used and why it was preferred should be explained in detail. It is also necessary to emphasize the study's contributions to the literature. Generally, the outline of the paper should be included at the end of the introduction.
3. In the literature review, the study's contributions to the literature and the gap it fills in the literature should be explained more clearly.
4. Section 3.1: It would be more descriptive to give a separate notation list explaining the parameters in the mathematical model.
5. The main numerical results of the study are reported in Figure 6-Figure 10. Although these figures visually explain the basic results, the inferences derived from the numerical results should be explained more clearly. Figures or tables are not always a substitute for textual explanations.
6. Section 4: This section is treated more like a conclusion. There is no conclusion section in the study anyway. The discussion is the section where the results of the study are reported by comparing them with the literature results. For this reason, a scientifically written conclusion section should be added to the study and future studies should be expanded.
7. Tables such as Table 6 should not be divided into two when they do not fit on one page. Usually, the table description is continued by adding the expression "continued".
8. There are no references to Figure 5, Figure 10, and Table 5 in the main text.
9. Explanations of abbreviations such as IMO and PSV should be given in the text.
10. Equation 3.1: The -> symbol in the equation is confusing and its meaning is not clearly understood.

Author Response

I express my gratitude to the editor and reviewer for granting us the opportunity to revise the manuscript ID sustainability-2657265. Taking into considerations the comments, I have made the needed changes to the manuscript. The comments and revision have significantly improved the quality of the paper. In this document, I have provided responses to the comments  and highlighted the corresponding changes made to the main manuscript .

1)     I think the abstract needs to be reconsidered and rewritten. The part of the abstract that starts with "In this study..." seems like a repetition of the previous one.

Thank you to the reviewer for this comment. We have reconsidered the abstract paying attention on the formulation. This changes can be found in the reviewed manuscript at line 11-21, pg.1

2)     In the introduction, the importance of the method used and why it was preferred should be explained in detail. It is also necessary to emphasize the study's contributions to the literature. Generally, the outline of the paper should be included at the end of the introduction.

The choice of the backtracking algorithm in our study stems from its unique adaptability and precision. Unlike traditional methods, backtracking offers a dynamic approach, efficiently navigating through multiple paths to optimize fuel consumption, making it particularly apt for the complexities of maritime voyage planning. This study aims to enrich the maritime optimization literature by introducing this novel method, especially emphasizing its applicability to older vessels, which often remain overlooked. Our research not only showcases the potential of the backtracking algorithm but also empirically validates its effectiveness. Concluding the introduction, we'll provide a clear roadmap for our readers: delving into the existing methodologies, detailing our approach, presenting our findings, and wrapping up with key insights and future research directions. We aim to offer both depth and clarity, ensuring our research resonates with and contributes meaningfully to the academic community. For this reason I have updated the Introduction and included the sugegsted changes at  lines 57 – 73, pg.2.

3)     In the literature review, the study's contributions to the literature and the gap it fills in the literature should be explained more clearly.

      Thank you for this observation. In the maritime optimization landscape, our study carves a unique niche by harnessing the backtracking algorithm's adaptability for voyage planning, an approach less explored in current literature. Additionally, while most studies focus on modern vessels, we prioritize older ships, addressing a notable gap. Through this dual emphasis, we present both a novel methodological approach and cater to an underserved segment of the maritime industry, thus enriching the academic discourse.Modifications where done at lines 136 – 159, pg.3.

4)     Section 3.1: It would be more descriptive to give a separate notation list explaining the parameters in the mathematical model.

Many thanks to the reviewer for this comment. The section was updated and changed to 3.2. We have updated the manuscript and created a notation list for the mathematical model variables.This can be seen between lines 197-210 at pg.5.

5)     The main numerical results of the study are reported in Figure 6-Figure 10. Although these figures visually explain the basic results, the inferences derived from the numerical results should be explained more clearly. Figures or tables are not always a substitute for textual explanations.

Thank you for highlighting the importance of textual explanations alongside visual data. We recognize that figures, while illustrative, may not capture the nuances and in-depth interpretations of our findings. In the revised version, we provided a comprehensive narrative accompanying Figures 6 through 10, ensuring that the insights derived from the numerical results are clearly articulated and contextualized, offering readers a more holistic understanding of our study's outcomes.The change can be seen partly in section 4 – Results and section 5 - Disussion.

6)     Section 4: This section is treated more like a conclusion. There is no conclusion section in the study anyway. The discussion is the section where the results of the study are reported by comparing them with the literature results. For this reason, a scientifically written conclusion section should be added to the study and future studies should be expanded.

We appreciate your keen observation regarding Section 4. You're right; the section inadvertently took on a concluding tone. In the revised manuscript, we' differentiated the discussion from the conclusion. Additionally, a dedicated conclusion section was incorporated to succinctly highlight the study's key takeaways and suggest possibilities for future research, providing a well-rounded closure to the paper.The Conclusion paragraph – Section 6 can be found at pg.17.

7) Tables such as Table 6 should not be divided into two when they do not fit on one page. Usually, the table description is continued by adding the expression "continued".

Thank you for the comment. The Table decription was updated .

8) There are no references to Figure 5, Figure 10, and Table 5 in the main text.

Thank you for the correct observation.We have included a detailed description at pg.12, lines 391 – 394 for Figure 5 and Table 5. Figure 10 was renumbered as Figure 8 and the description and meaning was added at pg.17, lines 448-453.

9) Explanations of abbreviations such as IMO and PSV should be given in the text.

Thank you for the suggestions. Explanation for the abbreviations added at pg.1,3,4.

10) Equation 3.1: The -> symbol in the equation is confusing and its meaning is not clearly understood.

Thank you for the suggestion. The mathematical model formulation was rewrittend to be more clear.The change can be seen below line 201 at equation 3.1

Reviewer 2 Report

Comments and Suggestions for Authors

In Line 74: Full name of PSV should be addressed here.  

In Line 140: Authors claimed that complete algorithms include backtracking and dynamic programming were widely used in the maritime industry. Thus, reletive studies should be addressed, and explain how the proposed algorithm is different from the existing studies.

In Line 207: Other studies about backtracking algorithms should be cited in the paragraph.

In Line 232: It is better to utilize the MDPI template, and explain it as an algorithm.

In Line 384: Results should be analyzed. Each figure and table should be explained.

In Line 420: Conclusion should be added here.

 

Author Response

I express my gratitude to the editor and reviewer for granting us the opportunity to revise the manuscript ID sustainability-2657265. Taking into considerations the comments, I have made the needed changes to the manuscript. The comments and revision have significantly improved the quality of the paper. In this document, I have provided responses to the comments  and highlighted the corresponding changes made to the main manuscript .

In Line 74: Full name of PSV should be addressed here.  

Thank you for the suggestion.The update was done and is currently visible at line 52.

In Line 140: Authors claimed that complete algorithms include backtracking and dynamic programming were widely used in the maritime industry. Thus, reletive studies should be addressed, and explain how the proposed algorithm is different from the existing studies.

Thank you for your valuable feedback. We acknowledge the importance of providing a comprehensive description to our methodological choices, especially when asserting the prevalence of certain algorithms in the maritime industry. To address this reference for dynamic programming, research articles have been included at lines 80 – 87 , pg.2. The use of bactracking algorithms is referenced at lines 134-148 , pg.3 and explanation about the differences included at lines 140-146, pg.3.

In Line 207: Other studies about backtracking algorithms should be cited in the paragraph.

Thank you for the suggestion. A description of the bactracking algorithm was added and description was referenced to other sources.This can be seen at lines 234 – 239. Pg.6.

In Line 232: It is better to utilize the MDPI template, and explain it as an algorithm.

Thank you for the accurate observation.The algorithm description was updated to match MDPI template. An explanation for the algorithm was added at lines 275 – 281. The algorithm aims to optimize speed to minimize fuel consumption by exploring all possible speeds/actions at each decision point. It uses recursion to examine potential paths, discarding those that surpass consumption or time limits. By the conclusion, the algorithm determines the least consumption under set constraints using the backtracking method, ensuring optimal speed selection.

In Line 384: Results should be analyzed. Each figure and table should be explained.

Figures and Tables description from the Results section  has been updated and explained in detail. This can be seen at lines 427-431,438-440,448-451. The analysis of the results was continued in the new section 5 – Discussion.

In Line 420: Conclusion should be added here.

Thank you for the suggestions. A Conclusion paragraph (6) at pg.17, was added which emphasize that the backtracking algorithm offers ship operators, particularly in the offshore sector, a refined approach to voyage planning, aiding in fuel efficiency and cost reduction. Its ability to provide a structured and efficient approach to voyage planning makes it invaluable in the quest to optimize fuel consumption, reduce costs, and minimize environmental impact.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper addresses an important topic in sustainability, of reducing the consumption of fossil fuels for old transport means; they are widely used and cannot be easily upgraded or not easy replaced, from various reasons. An example, analysed in the article, are the tugboats servicing off shore extraction rigs.

The introduction from section 1 makes a concise but sufficient presentation of the global dimension of the problem.

The literature review in section 2 presents the research status in the field. Although this part presents examples for all aspects of optimising the fuel consumption, it doesn’t focus on similar solutions and optimisation algorithms.  Consequently, the article lacks a state of the art and a basis for presenting the originality and the contributions of the authors.

Section 3 needs improvement at both content and formal level.  Generally, it should be better understandable which parts are original contributions, like the algorithm, and what and how was taken from the literature.

As the problem is obviously in the Travelling Salesman Problem family, a discussion about the algorithm complexity is mandatory. In order to have the discussion, a subsection specifying the dimension of the problem (mainly the number of stops) is necessary. Some sort of analysis on similar specific configurations (port rigs) using similar transports could advocate for the use of the method on a larger scale.

The complexity analysis should be used to justify why the backtracking and not another method is proposed.

 After the algorithm is proposed, the optimality of the solution should also be discussed even if only by mentioning that it is an exact algorithm or a heuristically/approximative algorithm.

The materials and methods part has no section dedicated to the practical implementation of the algorithm. At least the modality of obtaining the results must be presented in the article with some consideration of its particularities.  The significance of the paper can be improved by presenting and discussing a practical implementation (even only at the conceptual level).

The mathematical part of section should be thoroughly rewritten. Many of the formulas lack some terms or explanations for other terms. Some letters are used in different contexts for different terms.

The following sections should be renumbered as 4 Results and 5 Disscussion. The content of section 5 should be moved to Section 6 Conclusion. Section 5 should include discussion about the obtained solution in the line of first sentences in section 4 Results.  Figures 7-10 needs explanation in section 4 and discussion in section 5. A complete approach would include some sort of verification of the results through practice or simulation methods.

The discussion section should also include discussions about the proposed method with comparison to similar approaches and an evaluation of the impact of using the method (costs vs fuel economy) based on all previous considerations.

The conclusions must be rewritten and should present the advantages of the proposed method compared to similar approaches and the original contributions of the authors.  

Comments on the Quality of English Language

Minor editings to English language are needed to correct some sentences like the first in the abstract.

“This paper introduces backtracking algorithm for fuel optimization of a tugboat “ could be corrected as  “This paper introduces a backtracking algorithm for the fuel optimization of a tugboat“

Author Response

I express my gratitude to the editor and reviewer for granting us the opportunity to revise the manuscript ID sustainability-2657265. Taking into considerations the comments, I have made the needed changes to the manuscript. The comments and revision have significantly improved the quality of the paper. In this document, I have provided responses to the comments  and highlighted the corresponding changes made to the main manuscript .

The paper addresses an important topic in sustainability, of reducing the consumption of fossil fuels for old transport means; they are widely used and cannot be easily upgraded or not easy replaced, from various reasons. An example, analysed in the article, are the tugboats servicing off shore extraction rigs.

The introduction from section 1 makes a concise but sufficient presentation of the global dimension of the problem.

Thank you for the comment.

The literature review in section 2 presents the research status in the field. Although this part presents examples for all aspects of optimising the fuel consumption, it doesn’t focus on similar solutions and optimisation algorithms.  Consequently, the article lacks a state of the art and a basis for presenting the originality and the contributions of the authors.

Thank you for pointing out the oversight in the literature review. We recognize the importance of comparing our approach with similar solutions and optimization algorithms to highlight our unique contributions and to position our work within the existing body of knowledge. To address this we expanded Section 2 to include a comprehensive review of similar solutions and optimization algorithms in the domain of fuel consumption optimization. The incorporated state of the art , references different studies and algorithms used for fuel conumption optimization of ships, including dynamic programming, mix integer problem,calculus of variations, dicrete optimization methods based on genetic algorithms (lines 81-111 and 126-131). Post the expanded review, we clearly delineate our novel contributions, by the use of bactracking algorithm as pioneer solution for fuel optimization in case of short,coastal voyages at lines 140-148.

Section 3 needs improvement at both content and formal level.  Generally, it should be better understandable which parts are original contributions, like the algorithm, and what and how was taken from the literature.

Thank you for your comment. Section 3 was rewritten and specifications about the contributions of the authors added, which include algorithm formulation and model proposal.The weather impact model was taken from the specific literature.The model used is Kwon model, which gives an empirical solution to accurately calculate the speed losses due to specifci weather conditions and vessel displacement.

As the problem is obviously in the Travelling Salesman Problem family, a discussion about the algorithm complexity is mandatory. In order to have the discussion, a subsection specifying the dimension of the problem (mainly the number of stops) is necessary. Some sort of analysis on similar specific configurations (port rigs) using similar transports could advocate for the use of the method on a larger scale.The complexity analysis should be used to justify why the backtracking and not another method is proposed.After the algorithm is proposed, the optimality of the solution should also be discussed even if only by mentioning that it is an exact algorithm or a heuristically/approximative algorithm.

The proposed algorithm is part of the Travelling Salesman Problem (TSP) family which is one of the most studied and iconic problems in the field of operations research and computer science. Our objective is to determine the optimal speed for a particular voyage, given a set of stops(oil rigs) and the distances between each pair of stops. The difficulty of the issue grows factorially with the number of visits. The number of stops and other journey characteristics will heavily influence the algorithms used.

Using the backtracking algorithm looks to be a reasonable option when thinking about the specifics of our application, which prioritizes quick coastal voyages with few stops within a limited time constraint.

At its essence, backtracking is an exhaustive search for the optimal solution configuration.The solution space for fuel optimization includes a wide variety of possible inter-segment speeds. By going backwards, you may test out different permutations of speed and see how they affect fuel consumption. Backtracking seeks to identify the precise best solution, as opposed to heuristic approaches which yield approximations. This guarantees the optimum time and energy saving route and speed setup between segments.

However, it's important to note that as the number of segments increases, the solution space grows exponentially. While backtracking does eliminate many non-optimal paths, for a large number of segments, the computational time can become prohibitive and this can limit the applicative domain.

This modifications can be found in the newly added Section 3.1 – Suitability analysis.

The materials and methods part has no section dedicated to the practical implementation of the algorithm. At least the modality of obtaining the results must be presented in the article with some consideration of its particularities.  The significance of the paper can be improved by presenting and discussing a practical implementation (even only at the conceptual level).

To implement an optimized speed strategy for platform supply vessel (PSV) operations, a systematic framework is essential and was added in Section 3.4. The process starts with pre-voyage planning, where the voyage route is segmented based on ports, stops, and known time restrictions. Using the back-tracking algorithm, the optimal speed for each segment is calculated, factoring in weather conditions and other constraints.  Fuel consumption predictions are made using mathematical models, based on the ship consumption curve and characteristics of energy requirements, which can be found in the vessels manuals.

   Once the voyage is underway, real-time monitoring becomes crucial. Onboard systems must be established to monitor the vessel's real-time speed and fuel consumption. As the voyage progresses, weather updates should be continually tracked, adjusting planned speeds using Kwon's formula when significant weather changes are detected.

After the voyage, a post-voyage analysis is conducted. Data on the actual speed pro-file and fuel consumption are gathered and compared with pre-voyage predictions.

To ensure the long-term success of this strategy, a focus on continuous improvement is necessary. After several voyages, accumulated data should be analyzed to discern pat-terns and trends.

Some major challenges and limitations  include : accurately segmenting the route and the unpredictability of weather forecasts, real time voyage monitoring and dunamic weather conditions, ensuring accurate data collection for post-voyage analysis and bal-ancing the need for optimization with operational and business constraints.

The mathematical part of section should be thoroughly rewritten. Many of the formulas lack some terms or explanations for other terms. Some letters are used in different contexts for different terms.

Thank you for the constructive feedback on the mathematical section of the paper. The mathematical equations underwent a comprehensive revision for enhanced clarity. We re-evaluated the mathematical model, streamlining its expression to more aptly fit the application's scope. A consistent notation system was employed throughout, ensuring that common variables retained the same symbolic representation across all formulas. Additionally, detailed clarifications were provided for the Admiralty Coefficient, emphasizing its connection to speed and fuel consumption. The algorithm was reformatted in alignment with the journal's guidelines. Supplementary insights into the algorithm's workings, including the computations executed and initial values, were also incorporated.This can be found in Section 3.2.

The following sections should be renumbered as 4 Results and 5 Disscussion. The content of section 5 should be moved to Section 6 Conclusion. Section 5 should include discussion about the obtained solution in the line of first sentences in section 4 Results.

Thank you for the suggestiosn ,we appreciate your guidance on the structure of the sections. Based on your recommendations, we adjusted the layout of the document. Section 4 is dedicated to 'Results'. The subsequent Section 5 was titled 'Discussion', wherein we further explore the implications and insights derived from our results, particularly emphasizing the initial observations from the original Section 4. The content that was previously in Section 5 was relocated to a new 'Section 6: Conclusion'.

  Figures 7-10 needs explanation in section 4 and discussion in section 5. A complete approach would include some sort of verification of the results through practice or simulation methods.

Thank you for pointing out this area that require more explanation.Figures discussion was included in section 5 and more detailed explanation given in section 4.Based on the sugestion , used data was obtained from a real voyage in calm waters and for the development of the application in different environmental conditions a tested and reviewd speed loss calculation method was used.By using the real paramateres of the ship and collected spees/fuel consumption data as depicted in Table 6, we have tested the model results for the calm water conditions.

The discussion section should also include discussions about the proposed method with comparison to similar approaches and an evaluation of the impact of using the method (costs vs fuel economy) based on all previous considerations.

Thank you for your valuable feedback.The section was updated to include a comparison with other used methods . Numerous studies have explored the issue of speed optimization for ships engaged in long voyages. A vessel's speed at sea is influenced by various factors, both voluntarly and in-voluntarly. Unlike other methods, our model provides a cost-effective solution tailored for short coastal journeys, such as those in the offshore supply context. Here, the primary factors affecting speed are typically weather conditions and constrained timeframes.The newly added discussion can be found in Section 5.

The conclusions must be rewritten and should present the advantages of the proposed method compared to similar approaches and the original contributions of the authors.

Thank you for your insightful feedback. In revising our conclusions, we aim to emphasize the distinctiveness and advantages of our backtracking algorithm based method for speed optimization, especially in the context of offshore supply vessels. When considering short coastal voyages, which are typical of offshore environments, our strategy emerges as both an affordable and robust solution, adeptly balancing fuel economy with travel duration. Moreover, our research fills a significant gap in the maritime literature. While speed optimization is extensively researched, the application of the backtracking algorithm to offshore supply vessels remains underexplored, making our study both innovative and of practical significance to industry stakeholders. We believe these emphasized points will underscore the value of our research and differentiate it from existing studies in the field. The Conclusion section was updated accordingly.

Reviewer 4 Report

Comments and Suggestions for Authors

1	The research study is indeed very interesting, and the highlight is that it is updated till recent years.
2	For the readers to understand easily, an excellent diagram with blocks has been included.
3	Tabulations and comparative graphs have been explicitly included and is appreciable.
4	A better clarity image could be added instead of Figure 2.
5	Future scope for the research work could be carried out by comparing the results with few more algorithms.
6	Conclusion and abstract are in well sync.
7	What are the limitations of proposed method? If any
8	Overall, the paper has been elaborated in a very good manner.
9	The literature review carried out is appreciable, but could be improved by including few more papers which gives an idea about the existing system and the future scopes.
8	Few papers could be like https://doi.org/10.1002/jnm.2993 ,  could be included where in different algorithms are used for comparison.

Author Response

I express my gratitude to the editor and reviewer for granting us the opportunity to revise the manuscript ID sustainability-2657265. Taking into considerations the comments, I have made the needed changes to the manuscript. The comments and revision have significantly improved the quality of the paper. In this document, I have provided responses to the comments  and highlighted the corresponding changes made to the main manuscript .

1.The research study is indeed very interesting, and the highlight is that it is updated till recent years.

Thank you for the appreciation.

2. For the readers to understand easily, an excellent diagram with blocks has been included.

Thanks to the reviewer for this comment.

Tabulations and comparative graphs have been explicitly included and is appreciable.

Thank you for the appreciation.

A better clarity image could be added instead of Figure 2.

Thank you for the suggestion. Indeed Figure 2 was replaced with a more clear one which emphasize the activity of the vessel types similar to the one used in the paper.

Future scope for the research work could be carried out by comparing the results with few more algorithms.

The application of the backtracking algorithm in the maritime industry offers numerous promising avenues for future research. Expanding its use to different vessel types, such as container ships and bulk carriers, can provide insights into unique optimization challenges. Integrating real-time weather forecasting can dynamically adjust routes and speeds, while multi-objective optimizations could balance factors like fuel consumption, voyage time, and crew comfort. As the industry shifts toward autonomous ships, the algorithm's role in navigation systems becomes pivotal, ensuring optimal speeds and safe decisions. Furthermore, a comparative study with other optimization techniques, real-time algorithm applications, and evaluations of its environmental impact, particularly with alternative fuels, can present a holistic view of its potential. This newly added information can be found in Section 6, Conclusions.

Conclusion and abstract are in well sync.

Thank you for the comment.

What are the limitations of proposed method? If any

Thank you for the comment.The limmitations are in terms of voyage length and data points such as number of stops due to the nature of the offshore vessel. It's important to note that as the number of segments increases, the solution space grows exponentially. While backtracking does eliminate many non-optimal paths, for a large number of segments, the computational time can become prohibitive and this can limit the applicative domain.This was mentioned in the article at newly adde section 3.1

Overall, the paper has been elaborated in a very good manner.

Thank you for the comment.

The literature review carried out is appreciable, but could be improved by including few more papers which gives an idea about the existing system and the future scopes.

Thanks to the reviewer for this comment and the excellent paper suggestion. The literature review was updated and included aditional analysis on several papers disucssing other algorithms used for the optimization of fuel consumption, inlcuding the suggested https://doi.org/10.1002/jnm.2993  (point 20) and other references that can be found at point no.22,23,24,26 and 27 from the refence list.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This version of the paper is suitable for publishing in Sustainability. I would like to thank the authors for their interest.

Reviewer 2 Report

Comments and Suggestions for Authors

This study demonstrates an application of the backtracking algorithm for optimizing fuel consumption in platform supply vessels (PSVs) which transport goods and personnel from a port to different offshore structures. This reviewer believes that all previous comments have been appropriately incorporated in the manuscript. Thank you for your effort.

Reviewer 3 Report

Comments and Suggestions for Authors

The signaled issues where adreesed with great attention   so that the  qua;ity of the article was significantly improved. Perhaps more generalisation and more experimental or simulation work  to verify and validate the results could improve  the contribution to scholarship.

Comments on the Quality of English Language

The english language was improved and signaled faults where corrected