A Microcirculation Optimization Model for Public Transportation Networks in Low-Density Areas Considering Equity—A Case of Lanzhou

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The abstract contains some overly long and complex sentences (such as those involving the "Logit model"), which may affect readability. It is recommended to use the full standardized term when technical terms first appear (for example, change "Logit" to "Logit discrete choice model").
2. Punctuation marks need to be unified throughout the paper.
3. The meaning of fairness in public transport networks needs to be emphasized and clarified. Currently, the definition of fairness is relatively vague. The authors are advised to strengthen the description.
4. The keyword "Two-tier planning model" needs to be verified - whether it should be "two-layer planning".
5. The abbreviation "OD" should be explained when it first appears. In the explanation of formula notation, parameters should be italicized (for example, in the explanations of Formulas 2 and 3). Please check this throughout the entire paper.
6. It is recommended to add a flowchart in section 2.3 to illustrate the algorithm steps and factors considered in the optimization process. This would help readers better understand the author's optimization approach.
7. In section 3.2, regarding the source of model parameter values, if there are reference bases, relevant literature should be cited.
8. The authors are advised to add comparisons with optimization results from other methods in the discussion section. The current model treats OD demand as static data, but travel demand in low-density areas exhibits spatiotemporal heterogeneity.
9. The case study does not validate the model's adaptability in dynamic demand scenarios. It is recommended to: add discussion of this limitation in the discussion section; or supplement with dynamic demand sensitivity testing to enhance model extensibility.

Author Response

Dear Reviewer,

Thank you for your comments concerning our manuscript entitled “A microcirculation optimization model for public transportation networks in low-density areas considering equity--A case of Lanzhou” (sustainability-3687306). These comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections which we hope meet with approval. Revised portions are marked in red on the paper. The primary corrections in the paper and the responses to the reviewer’s comments are as follows:

 

 

Response to Reviewer 1 Comments:

Reviewer 1.

Comment : The abstract contains some overly long and complex sentences (such as those involving the "Logit model"), which may affect readability. It is recommended to use the full standardized term when technical terms first appear (for example, change "Logit" to "Logit discrete choice model").

Response： Thank you very much for your comments. In the revision, we have reworked the standardized terminology to make it easier to read, as shown below.Logit discrete choice model Modify to Logit discrete choice model. (21)

 

Comment : Punctuation marks need to be unified throughout the paper.

Response： We apologize for our misspelling, which we have corrected in our revisions.

 

Comment : The meaning of fairness in public transport networks needs to be emphasized and clarified. Currently, the definition of fairness is relatively vague. The authors are advised to strengthen the description.

Response： Thank you very much for your comments. Based on your comments, we have added and described the meaning of fairness in public transportation in our article. It is shown below:

As an important foundation for social activities, the transportation field necessarily needs to reflect the concept of social equity. The connotation of equity varies from field to field, and in the field of transportation, the definition of equity is closely related to the core function of the field. The problem of limited spatial displacement capacity due to the imbalance in the distribution of transportation resources is the core embodiment of the problem of transportation fairness, and transportation fairness is mainly embodied in the following three dimensions: firstly, the social benefits generated by transportation need to be equitably distributed among all members of the society. Secondly, the rights and obligations of users of different transportation modes need to be balanced. Finally, the transportation system as an important support for social equity, its resource allocation and service provision should be committed to creating equal conditions for all members of society to participate in economic activities and market competition.（48-59）

 

Comment : The keyword "Two-tier planning model" needs to be verified - whether it should be "two-layer planning".

Response： Thank you very much for your comments. In the revision, we have reworked the standardized terminology to make it easier to read, as shown below：“Two-tier planning model” revised to “two-layer planning”.

 

Comment : The abbreviation "OD" should be explained when it first appears. In the explanation of formula notation, parameters should be italicized (for example, in the explanations of Formulas 2 and 3). Please check this throughout the entire paper.

Response： Thank you very much for your comments. We apologize for our inappropriate expression. We have corrected this error in our revision.As shown below:

However, there are three core shortcomings in the established studies: first, insufficient modeling of OD(origin-destination) passenger flow stochasticity, especially the lack of effective portrayal of the dynamic impact of demand fluctuations on resource utilization.

 

Comment : It is recommended to add a flowchart in section 2.3 to illustrate the algorithm steps and factors considered in the optimization process. This would help readers better understand the author's optimization approach.

Response： Thank you very much for your interactions, combined with the opinions of other reviewers, we have comprehensively considered the algorithms involved in the article has been supplemented and improved, while adding the first off flow charts to help readers better understand our optimization methods.（298-351）

 

Comment : In section 3.2, regarding the source of model parameter values, if there are reference bases, relevant literature should be cited.

Response： Thank you very much for your suggestion, we understand that transparency of the parameter settings is crucial for the credibility of the model. The literature has been applied regarding the sources of the model parameter values.

 

Comment : The authors are advised to add comparisons with optimization results from other methods in the discussion section. The current model treats OD demand as static data, but travel demand in low-density areas exhibits spatiotemporal heterogeneity.

Response： Thank you very much for your comments. Based on your comments, we have added the limitation that travel demand in low-density areas exhibits spatial and temporal heterogeneity in the discussion section. (639-657)

 

Comment : The case study does not validate the model's adaptability in dynamic demand scenarios. It is recommended to: add discussion of this limitation in the discussion section; or supplement with dynamic demand sensitivity testing to enhance model extensibility.

Response： Thank you very much for your suggestion, we have added a discussion of the model's adaptability to dynamic demand scenarios in the discussion section.

 

Special thanks to you for your good comments.

 

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper. We appreciate for your warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Yours sincerely,

 

Liyun Wang

 

Reviewer 2 Report

Comments and Suggestions for Authors

Your manuscript, "A microcirculation optimization model for public transportation networks in low-density areas considering equity--A case of Lanzhou," addresses an important and often underserved area of research with a commendable focus on equity. The proposed two-layer planning model is a valuable conceptual framework. However, to enhance the paper's clarity, impact, and scientific rigor, several key areas require significant revision and clarification.

1. Methodology and Model Clarity (Major Revisions Required)

1. Optimization Algorithm Ambiguity: This is a critical point of confusion.
• Section 2.3 explicitly states a "genetic algorithm" is used and outlines its steps [1, p. 7].
• However, Section 3.2 ("Model parameterization") introduces parameters such as "individual and social learning factors" (0.1 and 0.075, respectively) and a "dynamic inertia factor interval" (0.8 to 1.0) [1, p. 8]. These characteristics are specific to Particle Swarm Optimization (PSO), not canonical Genetic Algorithms.
• Suggestion: Please unequivocally clarify which algorithm was used. If it were a standard GA, the PSO-specific parameters in Section 3.2 would be incorrect and need to be removed or replaced with appropriate GA parameters. Suppose a PSO or a hybrid algorithm (e.g., GA-PSO) was employed. In that case, the description in Section 2.3 and the subsequent parameterization in 3.2 must be thoroughly revised to accurately reflect this, including the rationale for the hybrid approach and how the different algorithmic components interact.
2. Algorithm Termination Criterion: The termination criterion in Step 5 of Section 2.3, described as "legacy kangaroo" [1, p. 7], is not a standard term and appears to be a placeholder or mistranslation.
• Suggestion: Please replace this with a clearly defined, standard termination criterion (e.g., a maximum number of iterations, convergence tolerance, or no improvement in fitness for a specified number of generations).
3. "Per capita social cost sharing (AC)" Indicator: The definition and formulation of the AC indicator (Equation 3) [1, p. 5] require further explanation for clarity and reproducibility.
• The terms BNm ("number of vehicles passing through the station") and BSm ("constraint on the number of lines passing through the station") and their role in the summation with qw need to be precisely defined. How BSm acts as a constraint within this cost-sharing formulation is not immediately apparent.
• Suggestion: Provide a more detailed mathematical and conceptual explanation of each component of Equation 3 and how they contribute to the overall AC value. Ensure the units and interactions are clear.
4. Model Parameters:
• The "multi-objective regulation parameters 0.15, 4" mentioned in Section 3.2 for the upper-level model are not explained [1, p. 8].
• Suggestion: Clearly state what these parameters represent, how their values were determined (e.g., calibration, literature, sensitivity analysis), and their specific role in the multi-objective optimization.
• The "fuel consumption conversion coefficient of f0.1" [1, p. 8] lacks units.
• Suggestion: Please specify the units for this coefficient (e.g., L/km, kg CO2/L).

1. Results and Discussion (Revisions Required)

1. Presentation of Route Optimization Results (Section 3.3.2): This section provides important data on initial and optimized route schemes, including costs, mileage, transfers, and comparisons of travel time and costs for car and bus users before and after optimization (Tables 2-6, Figures 5-8) [1, pp. 10-15].
• Suggestion:
• Ensure the discussion of these results is straightforward and comprehensive. Explain precisely how the presented optimization (e.g., in Table 3, "Optimized route plan") leads to the improvements shown in Tables 4 ("Optimization results for car users") and 5 ("Optimization results for bus users").
• For example, in Table 5 for bus users post-optimization, some comfort metrics improved (i.e., decreased values), while others worsened (i.e., increased values). These trade-offs and the overall impact on passenger experience need to be discussed.
• Analyze the significant reduction in total passenger travel costs (Table 6) [1, p. 15] within the context of equity and efficiency goals.
2. OD Data Amplification ("Spatial Enhancement Method"): You state that original passenger flow data was too low and thus amplified using a "spatial enhancement method based on travel behavior characteristics" [1, pp. 9-10]. While pragmatic for model testing, this significant alteration requires more robust justification and discussion.
• Suggestion:
• Provide a more detailed explanation of the specific "spatial enhancement method" used. What were the "travel behavior characteristics" and "spatial weight correction factor" [1, p. 17] employed, and how was the magnitude of amplification determined?
• Critically discuss the potential impact of this data modification on the realism and applicability of the derived "optimized" network to the actual low-density conditions the study aims to address. How might the results differ with unamplified, sparse data?
• Acknowledge this as a significant limitation and explicitly state that the reported benefits (e.g., Gini coefficient improvement) are based on this enhanced dataset.
3. Algorithm Performance Claims: The discussion mentions that the algorithm converged in "64 iterations" with a population of N=20 [1, p. 17], which is unusually fast for many network optimization problems using standard GAs.
• Suggestion: Given the ambiguity about the algorithm itself, this claim needs to be carefully contextualized. If a more advanced or hybrid algorithm were used, this might explain the rapid convergence; however, it needs to be clearly stated. If a standard GA was used, provide more details on the problem complexity and any specific GA features that might have led to such quick convergence, or re-evaluate this claim.
4. "Impulse Service" Concept: The term "impulse service" is introduced in the discussion [1, p. 17] as a strategy for low-density networks ("guarantees the coverage of basic service at the expense of operational efficiency").
• Suggestion: If this is a key concept or outcome of your optimization strategy, it should be defined and ideally integrated much earlier in the paper, perhaps in the methodology section or as part of the optimization objectives and constraints.

III. Arguments, Coherence, and Support for Conclusions

1. Linking Conclusions to Results: The conclusions state that the model "effectively shortens the travel cost difference between different groups" and "guides the traveling groups to choose more public transportation journeys" [1, p. 18].
• Suggestion: Ensure these claims are strongly and directly supported by the quantitative results presented in the paper (including Section 3.3.2). For instance, the 0.79% improvement in the Gini coefficient for the combined strategy is noted [1, p. 16], but broader behavioral shift claims need clear empirical backing from your case study's outputs.

1. Language and Presentation (Minor Revisions Suggested)

1. Terminology: Review for unconventional phrasing (e.g., "legacy kangaroo" [1, p. 7]).
2. Clarity and Precision: Some sentences or descriptions could be more direct and unambiguous. For instance, the definition of the "relative deprivation coefficient of travel cost" [1, pp. 4, 18] and its calculation could be sharpened.
3. Flow and Structure: Ensure a logical flow between sections, especially when introducing new concepts or parameters.

By addressing these points, particularly the critical issues in methodology (algorithm, parameters) and results presentation (justification of data amplification), you can significantly strengthen your manuscript, enhance its reproducibility, and make a more impactful contribution to the field of public transportation planning in low-density areas. The focus on equity is highly valuable, and clarifying these aspects will allow that contribution to be more clearly understood and appreciated.

Comments on the Quality of English Language

The manuscript would benefit from a thorough review by a native English speaker or a professional editing service.

At times, the sentence structure is overly complex, and the phrasing can be awkward, making it challenging for the reader to follow the arguments smoothly.

Some terms used are unconventional or appear to be direct translations that do not convey the intended meaning effectively in standard academic English.

A notable example is "legacy kangaroo" [1, p. 7] as an algorithm termination criterion. This needs to be replaced with standard terminology.

Author Response

Dear Reviewer,

Thank you for your comments concerning our manuscript entitled “A microcirculation optimization model for public transportation networks in low-density areas considering equity--A case of Lanzhou” (sustainability-3687306). These comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections which we hope meet with approval. Revised portions are marked in red on the paper. The primary corrections in the paper and the responses to the reviewer’s comments are as follows:

 

 

Response to Reviewer 2 Comments:

Reviewer 2.

Your manuscript, "A microcirculation optimization model for public transportation networks in low-density areas considering equity--A case of Lanzhou," addresses an important and often underserved area of research with a commendable focus on equity. The proposed two-layer planning model is a valuable conceptual framework. However, to enhance the paper's clarity, impact, and scientific rigor, several key areas require significant revision and clarification.

Ⅰ.Methodology and Model Clarity (Major Revisions Required)

Comment : Optimization Algorithm Ambiguity: This is a critical point of confusion.

Section 2.3 explicitly states a "genetic algorithm" is used and outlines its steps [1, p. 7].However, Section 3.2 ("Model parameterization") introduces parameters such as "individual and social learning factors" (0.1 and 0.075, respectively) and a "dynamic inertia factor interval" (0.8 to 1.0) [1, p. 8]. These characteristics are specific to Particle Swarm Optimization (PSO), not canonical Genetic Algorithms.

Suggestion: Please unequivocally clarify which algorithm was used. If it were a standard GA, the PSO-specific parameters in Section 3.2 would be incorrect and need to be removed or replaced with appropriate GA parameters. Suppose a PSO or a hybrid algorithm (e.g., GA-PSO) was employed. In that case, the description in Section 2.3 and the subsequent parameterization in 3.2 must be ·     0thoroughly revised to accurately reflect this, including the rationale for the hybrid approach and how the different algorithmic components interact.

Response： We have corrected our inappropriate expressions in the revision. In the revision we have added the description of the model, the upper model and the main use of genetic particle swarm algorithm the lower model using the stochastic user equilibrium (SUE) method based on the Logit model, and we have modified and improved the content of section 2.3. As follows:

Steps of Genetic Particle Swarm Algorithm for Solving Bi-Level Planning Models

Step1: Initialize population. Randomly generate the initial population, including the position and velocity of particles. The position of the particles corresponds to the decision variables in the two-layer planning model, such as the number of station construction, the number of bus routes, the frequency of bus routes and so on.

Step2: Calculate individual extreme value and global extreme value. For each particle, compare in real time the fitness evaluation value of its current iteration cycle with the quality record of its individual historical optimal solution, and dynamically update the quality record and spatial coordinates of its historical optimal solution when an improvement in the quality of the solution is detected.

Step3: Update particle velocity and position. Calculate the velocity and position of each particle in the next generation according to the velocity and position update formula of the particle swarm optimization algorithm.

Step4: Genetic manipulation. Firstly, a single-point genetic recombination strategy is implemented to realize the dimensional cross-fertilization of the parental solution, and then a probability-driven gene mutation mechanism is used to locally perturb the chromosome sequence.

Step5: Iteration termination condition judgment. The algorithm termination mechanism combined with the judgment contains both computational resource constraints such as the maximum number of iterations threshold setting, and solution quality assessment criteria such as the fitness value of the population optimal solution fluctuates below the set tolerance threshold in consecutive iteration cycles.

 

Logit-based algorithm for solving SUE models

Step1: Constructing road networks and determining effective path sets: first construct multi-modal transportation networks and determine effective path sets between O-D pairs by effective path search algorithms (e.g., combining Dijkstra's algorithm and depth-first search algorithm)..

Step2: Initialization: set the flow rate of each path

Step3: Logit Traffic Assignment and Impedance Calculation: a Logit Traffic Assignment is performed to calculate the selection probability of each traffic mode on different paths according to the path selection model (which represents the level of travelers' information), so as to obtain the assigned traffic volume of each road segment, and make n=1. The comprehensive travel cost of each effective path in the current network state is deduced through the traffic-impedance coupling mechanism.

Step4: Path flow update and additional traffic calculation: based on the O-D travel demand matrix, the Logit stochastic choice model is used to simulate the distribution decision of passengers in multi-modal paths, and then derive the traffic distribution characteristics of each path.

Step5: Roadway Traffic Update: Update the roadway traffic volume.

Step6: Convergence judgment: judge with whether to meet the convergence conditions. When monitoring the current solution and the preset convergence threshold of the match reaches the stability criteria, the system will terminate the calculation process and output the steady state traffic distribution scheme of multi-modal transportation network; if the standard is not met, then activate the iterative updating mechanism, then make n=n+1 through the cycle of executing the Logit model based on the calculation of the traffic distribution and the path impedance updating process, and gradually approaching the equilibrium state of the system.

（289-351）

 

Comment : Algorithm Termination Criterion: The termination criterion in Step 5 of Section 2.3, described as "legacy kangaroo" [1, p. 7], is not a standard term and appears to be a placeholder or mistranslation.

Suggestion: Please replace this with a clearly defined, standard termination criterion (e.g., a maximum number of iterations, convergence tolerance, or no improvement in fitness for a specified number of generations).

Response： We apologize for our miswriting and we have revised and corrected this error in the article in conjunction with the first question.

 

Comment : "Per capita social cost sharing (AC)" Indicator: The definition and formulation of the AC indicator (Equation 3) [1, p. 5] require further explanation for clarity and reproducibility.The terms BNm ("number of vehicles passing through the station") and BSm ("constraint on the number of lines passing through the station") and their role in the summation with qw need to be precisely defined. How BSm acts as a constraint within this cost-sharing formulation is not immediately apparent.

Suggestion: Provide a more detailed mathematical and conceptual explanation of each component of Equation 3 and how they contribute to the overall AC value. Ensure the units and interactions are clear.

Response： We apologize for our inappropriate expression. In the revision, we have rewritten this section to make it easier to read, as follows:

 denotes the constraint on the number of lines passing through the station,  denotes the mode of transportation chosen by the passenger,  denotes the OD point pair,  indicates total OD demand.(250-253)

 

Comment : Model Parameters:The "multi-objective regulation parameters 0.15, 4" mentioned in Section 3.2 for the upper-level model are not explained [1, p. 8].

Suggestion: Clearly state what these parameters represent, how their values were determined (e.g., calibration, literature, sensitivity analysis), and their specific role in the multi-objective optimization. The "fuel consumption conversion coefficient of f0.1" [1, p. 8] lacks units.

Suggestion: Please specify the units for this coefficient (e.g., L/km, kg CO2/L).

Response： Thank you very much for your suggestion and we apologize for our inappropriate expression. In response to your suggestion we have explained the multi-target parameters (0.15 and 4) and added the units for the fuel consumption conversion factor.(383-401)

 

Ⅱ.Results and Discussion (Revisions Required)

Comment : Presentation of Route Optimization Results (Section 3.3.2): This section provides important data on initial and optimized route schemes, including costs, mileage, transfers, and comparisons of travel time and costs for car and bus users before and after optimization (Tables 2-6, Figures 5-8) [1, pp. 10-15].

Suggestion:Ensure the discussion of these results is straightforward and comprehensive. Explain precisely how the presented optimization (e.g., in Table 3, "Optimized route plan") leads to the improvements shown in Tables 4 ("Optimization results for car users") and 5 ("Optimization results for bus users").For example, in Table 5 for bus users post-optimization, some comfort metrics improved (i.e., decreased values), while others worsened (i.e., increased values). These trade-offs and the overall impact on passenger experience need to be discussed.Analyze the significant reduction in total passenger travel costs (Table 6) [1, p. 15] within the context of equity and efficiency goals.

Response： We apologize for our inappropriate presentation. Based on your comments, the explanation of the results has been sorted out as follows:

The restructuring of the bus company's route network with the aim of optimizing operating costs has led to a significant simplification of the network structure: the average number of stops on a route has been reduced from 6.2 to 5.1. For example, Path 3 managed to reduce its operating mileage by 15% by streamlining four stops.However, the service frequency adjustment shows a polarizing trend: the departure interval of high-frequency routes (e.g., Paths 1 and 3) has been compressed to 20-30 minutes; while the departure interval of long-distance routes connecting to the countryside (Paths 6, 7, and 8) remains at a longer level of 180-360 minutes. As a result, the overall average service frequency has only been improved by 5.8%.The fare mechanism has also been adjusted in tandem. The average line fare was adjusted upward from $4.17 to $4.6, creating a stepped pricing structure centered on trunk routes: high-frequency routes basically maintained their original prices, and fares on rural routes did not show any significant increase.（464-477）

 

After reconfiguring the bus network according to the objective of optimizing passenger travel costs (see Table 5), the average number of stops on a route changed from 6.2 to 7.1. As a result, the service coverage of administrative villages increased by 12.8%; on the other hand, the total number of miles operated increased by 19.3%. Adjustments to departure intervals varied: high-frequency routes like Paths 1 and 9 basically maintained a 20-30 minute headway, the same as before the optimization; while long-distance key routes connecting rural areas, such as Paths 6, 8, and 10, still had 180-360 minute headways. Overall, the average frequency of departures (frequency density) is only 4.3% higher than before optimization. There were also changes in fares. The average fare on the optimized routes dropped from $4.17 to $3.91. It is worth noting that the fares of rural routes did not increase significantly in this path adjustment.（495-560）

 

The data in Table 6 show that the average cost of the combined optimized routes is 4.3RMB, which is slightly higher than the original network's 4.17RMB but significantly lower than the $4.6 of the bus company cost-only scenario. This suggests that the model strikes a balance in terms of fare regulation. For headway intervals: Headway intervals for high-frequency routes are maintained at 20-30 minutes, the same as the original network, while headway intervals for long-distance rural routes are shortened to 180-360 minutes, a 12% reduction from the scenario that only considers corporate cost optimization. This adjustment combines corporate cost and passenger cost considerations and effectively reduces the average waiting time of passengers. The topology analysis shows that the average number of nodes on the optimized routes is 6.5, which is 4.8% higher than the original network, but significantly lower than the 7.1 in the scenario considering only passenger costs. This reflects the synergistic optimization effect of the model on operational efficiency and service coverage. This is demonstrated by the following: Improved route efficiency: 11.2% reduction in operating miles through node streamlining on key routes. Mainline fares are kept stable, while the travel costs of low-income groups are compensated by adding new financially subsidized routes to balance the cost dynamics.Compared to the single optimization scheme, the comprehensive optimization has resulted in significant improvements in multiple benefits: Passenger benefits: The average single trip time was reduced by 9.7 minutes thanks to the optimization of high-frequency route connections.

Enterprise benefits: Reduced single-line operating costs through path compression and vehicle scheduling algorithm optimization. Social benefits: The service coverage rate of administrative villages rebounded to 93.5%, and the service blind spots were reduced to two. The study shows that the two-layer planning model effectively alleviates the structural contradiction of single-objective optimization.（539-563）

 

Comment : OD Data Amplification ("Spatial Enhancement Method"): You state that original passenger flow data was too low and thus amplified using a "spatial enhancement method based on travel behavior characteristics" [1, pp. 9-10]. While pragmatic for model testing, this significant alteration requires more robust justification and discussion.

Suggestion:Provide a more detailed explanation of the specific "spatial enhancement method" used. What were the "travel behavior characteristics" and "spatial weight correction factor" [1, p. 17] employed, and how was the magnitude of amplification determined?Critically discuss the potential impact of this data modification on the realism and applicability of the derived "optimized" network to the actual low-density conditions the study aims to address. How might the results differ with unamplified, sparse data?Acknowledge this as a significant limitation and explicitly state that the reported benefits (e.g., Gini coefficient improvement) are based on this enhanced dataset.

Response： Thank you for your careful and constructive review of this paper! Your comments on the OD data amplification (“spatial augmentation method”) are very pertinent and essential to the scientific rigor and refinement of our study. The core of the “spatial enhancement method based on travel behavior characteristics” is to combine the population distribution (as the source of travel demand) with the average number of passenger trips to simulate the potential pressure of passenger flow during peak hours. This is an indirect estimation based on spatial correlation, as opposed to direct scaling of the traditional OD matrix. The magnitude of the scaling is not arbitrary, but is determined by a combination of three key parameters: population: objective data, derived from authoritative demographic rasters. μ (Behavioral Characteristics - Average Daily Trip Rate): based on the results of a localized survey. We fully agree with the expert opinion that this data enhancement is a major methodological compromise and a central limitation of this study. It does reduce the direct applicability of the resulting network in absolute terms to the actual current ultra-low traffic environment. The “optimized” network generated based on the augmented data predicts higher absolute numbers of passengers, line frequencies, and vehicle demand than can actually be supported by current sparse demand. The limitations of this data enhancement are added in the discussion section. (633-648)

 

Comment : Algorithm Performance Claims: The discussion mentions that the algorithm converged in "64 iterations" with a population of N=20 [1, p. 17], which is unusually fast for many network optimization problems using standard GAs.

Suggestion: Given the ambiguity about the algorithm itself, this claim needs to be carefully contextualized. If a more advanced or hybrid algorithm were used, this might explain the rapid convergence; however, it needs to be clearly stated. If a standard GA was used, provide more details on the problem complexity and any specific GA features that might have led to such quick convergence, or re-evaluate this claim.

Response： We apologize for our inappropriate expressions, and we have modified them in our article, where we mainly use genetic particle swarm algorithms for model computation and simulation, and thus converge more rapidly. (289-342)

 

Comment : "Impulse Service" Concept: The term "impulse service" is introduced in the discussion [1, p. 17] as a strategy for low-density networks ("guarantees the coverage of basic service at the expense of operational efficiency").

Suggestion: If this is a key concept or outcome of your optimization strategy, it should be defined and ideally integrated much earlier in the paper, perhaps in the methodology section or as part of the optimization objectives and constraints.

Response： Thank you for your careful review of our manuscript and for your valuable suggestions. Your suggestions on the timing and integration of the “pulse service” concept are very pertinent and constructive. We fully agree with you that this concept, as a key framework for understanding the low-density operational characteristics of rural transit networks, and as an important context and goal for our subsequent optimization strategy, should have been clearly defined and integrated in the early part of the paper. In our initial writing, we focused on presenting the results of our empirical analysis, and in discussing the results, we introduced the term “pulse service” to describe the observed phenomenon of extreme long intervals and its implications. However, you rightly point out that the centrality of this concept requires that it be established in the methodology or goal-setting section. When we describe the challenges facing rural transit, we will explicitly refer to the “low-frequency service model” and its potential consequences, setting the stage for the “pulse service” concept and citing the literature. This is shown below:

The development of public transportation in low-density rural areas has long been constrained by the structural characteristics of dispersed population and uneven spatial and temporal distribution of travel demand, and is generally faced with the dual challenges of insufficient service coverage and operational inefficiency, which is deeply mired in the structural contradiction of imbalance between supply and demand^[1]. This low accessibility not only significantly increases the travel costs of residents, but also reinforces their reliance on private motorized travel, leading to increased carbon emissions and loss of social welfare. A particular operational dilemma in such systems is the “pulse service” model: service providers are often forced to use extremely long headway intervals in order to maintain basic route coverage with extremely limited resources. While this model guarantees minimum accessibility in the spatial dimension, it faces long waiting times at the expense of convenience. In order to solve this systemic problem, policies such as the Action Plan for the Construction of Digital Villages (2022-2025) explicitly propose the construction of an “integrated transport and postal” logistics service network, with the aim of improving the efficiency of resource utilization. However, the effective implementation of such integration policies is based on the structural optimization of the underlying transportation network, which is still facing the dual challenges of optimizing the road network layout and equitably allocating resources under the environment of sparse demand. In this context, how to build a scientific transportation resource allocation model to effectively alleviate or even reconstruct the prevalent “pulse service”^[2] mode under the established resource constraints, so as to bridge the “service faults” caused by it, and enhance the convenience and fairness of the service, becomes A key issue that needs to be resolved urgently in order to promote the equalization of public services in urban and rural areas.（34-57）

 

 

III. Arguments, Coherence, and Support for Conclusions

Comment : Linking Conclusions to Results: The conclusions state that the model "effectively shortens the travel cost difference between different groups" and "guides the traveling groups to choose more public transportation journeys" [1, p. 18].

Suggestion: Ensure these claims are strongly and directly supported by the quantitative results presented in the paper (including Section 3.3.2). For instance, the 0.79% improvement in the Gini coefficient for the combined strategy is noted [1, p. 16], but broader behavioral shift claims need clear empirical backing from your case study's outputs.

Response： Thank you very much for your comments. In the amendment we have organized the conclusion section as follows:

Example analysis shows that the public transportation network model considering the constraints of traffic equity on the one hand, the difference in travel costs between different groups shows a trend of narrowing, and the road resources are distributed more equitably; along with the increase in the public transportation sharing rate, the strategy guides the travelling groups to choose more public transportation, and on the other hand, it reduces the opportunity of the high-income groups to choose the private car.（681-687）

 

Language and Presentation (Minor Revisions Suggested)

Comment : Terminology: Review for unconventional phrasing (e.g., "legacy kangaroo" [1, p. 7]).

Response： We apologize for our inappropriate expression. Based on your comments, we have amended the wording.

 

Comment : Clarity and Precision: Some sentences or descriptions could be more direct and unambiguous. For instance, the definition of the "relative deprivation coefficient of travel cost" [1, pp. 4, 18] and its calculation could be sharpened.

Response： Thank you very much for pointing out the lack of clarity and precision in the definition and description of the calculation of “Relative Deprivation Factor for Travel Costs”. We have revised the definition in the paper based on your valuable comments.

 

Comment : Flow and Structure: Ensure a logical flow between sections, especially when introducing new concepts or parameters.

Response： Thank you very much for your comments. In our revisions, we've sorted out and ensured a logical flow between the sections.

By addressing these points, particularly the critical issues in methodology (algorithm, parameters) and results presentation (justification of data amplification), you can significantly strengthen your manuscript, enhance its reproducibility, and make a more impactful contribution to the field of public transportation planning in low-density areas. The focus on equity is highly valuable, and clarifying these aspects will allow that contribution to be more clearly understood and appreciated.

Comments on the Quality of English Language

Comment : The manuscript would benefit from a thorough review by a native English speaker or a professional editing service.

At times, the sentence structure is overly complex, and the phrasing can be awkward, making it challenging for the reader to follow the arguments smoothly.

Some terms used are unconventional or appear to be direct translations that do not convey the intended meaning effectively in standard academic English.

A notable example is "legacy kangaroo" [1, p. 7] as an algorithm termination criterion. This needs to be replaced with standard terminology.

Response： We apologize for our miswriting and we have corrected this error in our revision.

 

 

Special thanks to you for your good comments.

 

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper. We appreciate for your warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Yours sincerely,

 

Liyun Wang

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author has addressed all my questions, and I have no further comments.

Author Response

Thank you for your recognition of our manuscript“A microcirculation optimization model for public transportation networks in low-density areas considering equity--A case of Lanzhou” (sustainability-3687306). Confirm that the current version does not require further modification.

 

If there are any subsequent requirements, we will fully cooperate.

 

Once again, thank you very much for your comments and suggestions.

Yours sincerely,

 

Liyun Wang

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Consider condensing the literature review to focus more tightly on the most relevant prior work and to avoid redundancy.

Clarify the limitations of the data enhancement approach, especially regarding the applicability of results to current low-flow scenarios.

Where possible, provide more details (e.g., pseudocode or code availability) to support reproducibility of the algorithmic approach.

Enhance the discussion on policy implications, especially regarding how the model could be adapted for other rural or peri-urban contexts.

 

Comments on the Quality of English Language

A professional English language review is recommended to improve clarity and style.

Author Response

Thank you for your comments concerning our manuscript entitled “A microcirculation optimization model for public transportation networks in low-density areas considering equity--A case of Lanzhou” (sustainability-3687306). These comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections which we hope meet with approval. Revised portions are marked in red on the paper. The primary corrections in the paper and the responses to the reviewer’s comments are as follows:

 

Response to Reviewer 2 Comments:

Comment : Consider condensing the literature review to focus more tightly on the most relevant prior work and to avoid redundancy.

Response：Thank you very much for your suggestion. In our revision we have reorganized and condensed the literature review from the original 1779 characters to 1134 characters. (34-135)

 

Comment : Clarify the limitations of the data enhancement approach, especially regarding the applicability of results to current low-flow scenarios.

Response：Thank you very much for your suggestion. The limitations of the “data augmentation” approach have been modified and added to the discussion section of the article. They are shown below:

Second, the “Spatial Enhancement Method Based on Travel Behavioral Characteristics” adopted in this study solves the problem of model failure due to small original data flow by amplifying the original sparse OD data. However, it does not consider the dynamic change of travel and the competition of external traffic, and the generated data only represents an average state and cannot go to predict the unexpected events。（584-589）

 

Comment : Where possible, provide more details (e.g., pseudocode or code availability) to support reproducibility of the algorithmic approach.

Response：Thank you very much for the editor's attention and recognition of our research work. We fully understand the requirements of SCI journals for data sharing, but due to our lab's policies or confidentiality agreements, we are unable to provide the code. We have fully described the experimental design, analysis and results, as well as the process of data analysis and processing. If editors and reviewers have questions about specific data, we will endeavor to provide more detailed explanations and clarifications.

 

Comment : Enhance the discussion on policy implications, especially regarding how the model could be adapted for other rural or peri-urban contexts.

Response：Thank you very much for your suggestion. We have provided supplementary explanations on "Policy Discussions on How to Adapt the Model to Other rural or suburban Environments" in the discussion section of the article. As shown below:

Example analysis shows that the public transportation network model considering the constraints of traffic equity on the one hand, the difference in travel costs between different groups shows a trend of narrowing, and the road resources are distributed more equitably; along with the increase in the public transportation sharing rate, the strategy guides the travelling groups to choose more public transportation, and on the other hand, it reduces the opportunity of the high-income groups to choose the private car.（618-624）

 

Comments on the quality of the English language

Comment :It is recommended to conduct professional English language review to enhance clarity and style.

Response：Thank you very much for your suggestions, we have done our best to improve the manuscript by revising and touching up the incorrect grammar in the manuscript, these changes will not affect the content or framework of the paper. They are not listed here in our bin, but are marked in red in the revised manuscript.

Special thanks to you for your good comments.

 

We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper. We appreciate for your warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Yours sincerely,

 

Liyun Wang

 

Author Response File: Author Response.pdf