A Variable Neighbourhood Search-Based Algorithm for the Transit Route Network Design Problem

Round 1

Reviewer 1 Report

The authors propose an algorithm based on Variable Neighborhood Search (VNS) to solve the transit root network design problem (TRNDP) in this work. The authors test the algorithm's performance on benchmark networks and compare it to state-of-the-art algorithms. The problem addressed in this work is relevant to the scientific community and society in general. The proposed solution is efficient with very high accuracy.

I have a little comment regarding the presentation of the results. Equations 4-10 are just listed without any additional explanation, which makes this part of the text hard to read. The combination of equations 4-10 with the text in the paragraph from lines 199-206 would make this part of the manuscript easier to read and understand.

Author Response

Reviewer #1 comments

General comment:

The authors propose an algorithm based on Variable Neighborhood Search (VNS) to solve the transit route network design problem (TRNDP) in this work. The authors test the algorithm's performance on benchmark networks and compare it to state-of-the-art algorithms. The problem addressed in this work is relevant to the scientific community and society in general. The proposed solution is efficient with very high accuracy.

 

Response:

We would like to thank the reviewer for the positive assessment of our work.

 

 

Comment #1:

I have a little comment regarding the presentation of the results. Equations 4-10 are just listed without any additional explanation, which makes this part of the text hard to read. The combination of equations 4-10 with the text in the paragraph from lines 199-206 would make this part of the manuscript easier to read and understand.

 

Response:

We thank the reviewer for pointing this out. We have corrected the presentation and added the explanation under each equation.

Reviewer 2 Report

Dear Authors,

Thank you very much for sending an interesting article about the transit algorithm. At first glance, the article looks quite messy. Please check the notation of equations from 4 to 10, eg in 8 "S" is only half visible and the whole is not justified.

Figure 1 requires a more extensive description in the text with a marking of what the specific colors mean or maybe they do not have any meaning. Along with a detailed description of the processes from a to f.

Figure 2 is not really even a drawing. A better solution would be to represent this in a flowchart.

The caption for Table 3 is in the wrong place.

The most important lack is the omission of the last chapter called the conclusion, which gives future readers closure to the authors' research.

Regards

Author Response

Reviewer #2 comments

 

General comment:

Dear Authors,

 

Thank you very much for sending an interesting article about the transit algorithm.

Response:

We would like to thank the reviewer for the overall positive assessment of our work and the helpful comments. We believe we have addressed the reviewers’ concerns in the revised version.

 

 

Comment #1:

At first glance, the article looks quite messy. Please check the notation of equations from 4 to 10, eg in 8 "S" is only half visible and the whole is not justified.

 

Response:

We thank the reviewer for bringing this oversight to our attention. We have corrected the format and enlarged the symbols.

 

Comment #2:

Figure 1 requires a more extensive description in the text with a marking of what the specific colors mean or maybe they do not have any meaning. Along with a detailed description of the processes from a to f.

Response:

We thank the reviewer for the suggestion. We have now added a clarification with respect to Figure 1 to indicate that the left-hand side shows the route before each process and the right hand side shows the resulting route. To more clearly demonstrate processes involving a single route, the stop colors are different to allow for tracking the exact changes in the resulting route set. For the partial insertion process which involves two routes, the same colours are used for nodes belonging to the same route to allow for distinguishing between the two routes. This clarification has been added above Figure 1. Further, to clarify the processes from a to f, we have also added a reference to each part of Figure 1 in the text where these are described, along with an exact description matching the nodes in the figure.

 

 

Comment #3:

Figure 2 is not really even a drawing. A better solution would be to represent this in a flowchart.

Response:

We thank the reviewer for the suggestion. We have now replaced the pseudocode with a flowchart.

 

 

Comment #4:

The caption for Table 3 is in the wrong place.

Response:

We thank the reviewer for pointing this out. We have now corrected this.

 

 

Comment #5:

The most important lack is the omission of the last chapter called the conclusion, which gives future readers closure to the authors' research.

Response:

We apologize for any confusion. We hope the title of the last section “Discussion” was not misleading. We have now amended the title of the final section to “Conclusions” and elaborated on our research findings.

Round 2

Reviewer 2 Report

Dear Authors
Thank you. Now, I have nothing to add. 
regards