Application of an Improved A* Algorithm for the Path Analysis of Urban Multi-Type Transportation Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper investigates an extension to the well-known A* search algorithm for the case of urban transportation planning, specifically for the case of public transportation. The main strengths of the paper are following proposed extensions:

1. Using multivariate functions as the target of optimization (and distance heuristic) to include multiple criteria that travellers have. Beyond travel time and costs, a specific focus is given to the number of transfers and walking distance, both of which are important considerations for planning public transport journeys.

2. The explicitl consideration of of multimodal travel where driving is combined with public transportation by using P&R facilities.


However, despite the conceptual importance of the above points, I belive that the work presented in this paper is not adequate for publication. I think that the following are the main issues:

 -- There is very little engagement with literature on path finding. The authors cite several papers, but these only serve as general references for the A* algorithm and no serious discussion is presented on how the current work relates to what has already been done.
 
 -- While the focus on multivariate objective function is reasonable, many of the stated goals of the paper are already implemented in map applications (e.g. choosing a route that minimizes transfers vs walking). I do not know if any of these services use A* or other algorithms, and if yes, how are these criteria implemented, however, given the prominent availability of solutions that claim to provide conceptually similar solutions, I believe it would be necessary to provide a more in-depth investigation of related scientific work and more clearly identify the novelty of the current work.
 
 -- The experiments provided to evaluate the proposed solutions in the paper are very minimal and do not demostrate clearly the novelty and applicability of results (e.g. the solutions presented in Fig. 8 and 9 as Plan 1 and 2 are the ones offered first by Baidu maps). I think part of the problem comes from the fact that the authors only present a qualitative and descriptive presentation of solutions in a few limited examples. Given the focus of the paper on algorithm development, I believe that the paper should include serious quantitative and statistical evaluation of results (for a wide range of examples).
 
 -- Presentation of the algorithm is a bit vague. E.g. notation is not defined formally, the weights used in the multivariate functions are never introduced (and their values are not given), sometimes seemingly contradictory statements are made (e.g. "G(N) denotes the paid traveling cost from starting node O to any point N" in line 178, vs "G(N) is computing, the transfer number, the travel time, and the travel costs from starting node O to any point N are synchronously obtained" on line 181-182 make it unclear if G(N) includes only travel cost or a combination). Flowcharts (Fig. 4 and 6) do not have a clear logic, some nodes branch in multiple directions without making clear what decides the path taken (e.g. the "Same line" node has links "Yes" and "No" that lead to dead-ends, and an unmarked link that continues the algorithm).
 
 -- I'm not convinced that the algorithm will work as indended (although this depends if e.g. different platforms in the same station are considered one node or multiple nodes, which is a bit unclear). Specifically, if a node can be reached via multiple paths (which is common in transportation networks), only one path will be kept; is the two paths have the same amount of transfers, then I assume this is the one with shorter travel time. However, this means that continuing with the line that was not taken would be registered as a transfer. E.g. considering the example shown in Fig. 1, if the goal is to travel from node 2 to 5, it is obvious that R_1 could be chosen to minimize the number of transfers. However, if the travel time up to node 4 is shorter with line R_2, then this path will be registered when adding node 4 to the ExNodes set. Then, the travel from node 4 to 5 (with line R_1) will be registered as a transfer. Of course, this issue can be avoided if multiple paths are saved or if public transportation transfer stations are represented with a separate node for each node. However, it is not adequately explained whether this was attempted.

 

Comments on the Quality of English Language

Generally, English use is fine with minor issues (some sentences are hard to understand).

Author Response

Dear reviewer 1,

Thank you very much for your comments on this manuscript in your busy schedule. We appreciate your approval of our responses to your previous suggestions. We have carefully read your comments and revised each of them this time. The revisions are shown using line  following the track version in the response letter. 

Reviewers' comments:

This paper investigates an extension to the well-known A* search algorithm for the case of urban transportation planning, specifically for the case of public transportation. The main strengths of the paper are following proposed extensions:

1. Using multivariate functions as the target of optimization (and distance heuristic) to include multiple criteria that travellers have. Beyond travel time and costs, a specific focus is given to the number of transfers and walking distance, both of which are important considerations for planning public transport journeys.
2. The explicitl consideration of of multimodal travel where driving is combined with public transportation by using P&R facilities.

However, despite the conceptual importance of the above points, I belive that the work presented in this paper is not adequate for publication. I think that the following are the main issues:

Response: Thank you for your comments and feedbacks to improve the manuscript. In this revision, we carefully revised the manuscript following your comments in order to make it to be adequate for pubilication and provided a point-to-point response in this letter.

Manuscript – line numbers refer to the ‘track’ version

（1）There is very little engagement with literature on path finding. The authors cite several papers, but these only serve as general references for the A* algorithm and no serious discussion is presented on how the current work relates to what has already been done.

Response: Thanks for your suggestion. We have added the review of the literature on path finding and discussed how the current work relates to what has already been done. Please see Line 64-105.

（2）While the focus on multivariate objective function is reasonable, many of the stated goals of the paper are already implemented in map applications (e.g. choosing a route that minimizes transfers vs walking). I do not know if any of these services use A* or other algorithms, and if yes, how are these criteria implemented, however, given the prominent availability of solutions that claim to provide conceptually similar solutions, I believe it would be necessary to provide a more in-depth investigation of related scientific work and more clearly identify the novelty of the current work.

Response: Thank you for your advice. We have conducted a more in-depth investigation of related scientific work and identified the novelty of the current work in the manuscript at Line 106-133 and explain it as follows.

One of the main contributions of this paper is to propose an improved A* algorithm based on hybrid network to solve the problem that the traditional A* algorithm is only suitable for path analysis of a single transportation network, and to realize the optimal travel plan that provides travellers with a combination of public transportation and P&R transfers.

There are many different types of bus lines within the city, including special bus lines, airport express lines, tourist routes and general lines, with many overlapping stops on the lines. In addition, train and bus stations often overlap to facilitate transfers. Therefore, in this paper, pre-processing should be done before the algorithm is implemented:

1. The bus and rail data are pre-processed and adjacent stations are merged to form an array of stations with the same name to facilitate the subsequent implementation of the algorithm. The rules for merging stations are described in the previous version the of paper, please see Line 379-390.

2. For any input start point and end point location, first of all, find the station arrays adjacent to the starting point and ending point according to the specific coordinates and obtain two arrays of starting station and ending station respectively.

Based on the above two aspects, the implementation of the algorithm based on the hybrid network is to start from the array of the starting point to the array of the ending point gradually traversal search, until it gets a variety of optimal combinations of plans. That is to say, the original input of the starting point and the ending point, is not directly involved in the algorithm. When outputting the final travel plan, the walking paths from the original starting point and ending point to the station arrays should be outputting synchronized. This part of the path search, carried out in a single road network generally uses the way of walking or bike sharing, the implementation of which is more conventional and independent of the algorithms discussed in this paper. Therefore, it is not explained or expressed in this paper. In addition, the maximum distance between sites in the site array can be up to 500 meters according to the rules of site merging. If the travel plan, which is given after the path search between any starting point and ending point is completed, involves switching between stations within the arrays with the same name, this part of the walking path search is also completed in a single road network, which is independent of the algorithms discussed in this paper.

The implementation logic and standards should be similar for mapping applications related to walking transfer, without involving hybrid network issues. Otherwise, it will complicate simple issues.

The goals of this paper are achieved in stages. In the process of archieving the final goal, the realized goal in the map application will be included. But this is not the whole of this paper. The ultimate goal of this paper is to provide the traveller with the optimal travel solution for a combination of public transportation and P&R transfers.

（3）The experiments provided to evaluate the proposed solutions in the paper are very minimal and do not demostrate clearly the novelty and applicability of results (e.g. the solutions presented in Fig. 8 and 9 as Plan 1 and 2 are the ones offered first by Baidu maps). I think part of the problem comes from the fact that the authors only present a qualitative and descriptive presentation of solutions in a few limited examples. Given the focus of the paper on algorithm development, I believe that the paper should include serious quantitative and statistical evaluation of results (for a wide range of examples).

Response: Thanks for your advice. The cases shown in Figures 8 and 9 are not very convincing in view of the realization goals of this paper, so the cases in the text are replaced again, please see Line 418-426 and Line 543-604.

To better illustrate the novelty and applicability of the algorithm, this paper arbitrarily selects 10 coordinate points within the administrative division of Shanghai. These points include road intersections, schools, residential areas, business parks, transportation hubs, landmarks, etc., and make sure that the 10 points can cover the suburbs, central cities, downtown, Pudong and Puxi areas. Then these 10 points are the starting and ending points of each other, and the algorithm in this paper is run to search for the optimal travel plan. If there is a P&R transfer station in the search path, the travel plan gives priority to the P&R transfer combination plan, which is also in line with the current trend of low-carbon travel. The case study is shown in Appendix A.

（4）Presentation of the algorithm is a bit vague. E.g. notation is not defined formally, the weights used in the multivariate functions are never introduced (and their values are not given), sometimes seemingly contradictory statements are made (e.g. "G(N) denotes the paid traveling cost from starting node O to any point N" in line 178, vs "G(N) is computing, the transfer number, the travel time, and the travel costs from starting node O to any point N are synchronously obtained" on line 181-182 make it unclear if G(N) includes only travel cost or a combination). Flowcharts (Fig. 4 and 6) do not have a clear logic, some nodes branch in multiple directions without making clear what decides the path taken (e.g. the "Same line" node has links "Yes" and "No" that lead to dead-ends, and an unmarked link that continues the algorithm).

Response: Thanks for your comment. We followed your advice to improve our presentation of the algorithm.

Regarding the weighting problem, we have revised the original description: ‘The different needs of travellers in restricted and unrestricted networks are realized in the heuristic function by prioritising the control of each evaluation criterion’. Please see Line 189-191, 245-246, 265-268, 276-279, 349-350.

The discription "G(N) denotes the paid traveling cost from starting node O to any point N"  is inaccurate. And it is corrected to "G(N) denotes transfer number, the travel time, and the travel costs from starting node O to any point N", Please see Line 248-249.

The two flowcharts in Figures 4 and 6 have been modified. Please see Line 255 and 332.

(5) I'm not convinced that the algorithm will work as indended (although this depends if e.g. different platforms in the same station are considered one node or multiple nodes, which is a bit unclear). Specifically, if a node can be reached via multiple paths (which is common in transportation networks), only one path will be kept; is the two paths have the same amount of transfers, then I assume this is the one with shorter travel time. However, this means that continuing with the line that was not taken would be registered as a transfer. E.g. considering the example shown in Fig. 1, if the goal is to travel from node 2 to 5, it is obvious that R_1 could be chosen to minimize the number of transfers. However, if the travel time up to node 4 is shorter with line R_2, then this path will be registered when adding node 4 to the ExNodes set. Then, the travel from node 4 to 5 (with line R_1) will be registered as a transfer. Of course, this issue can be avoided if multiple paths are saved or if public transportation transfer stations are represented with a separate node for each node. However, it is not adequately explained whether this was attempted.

Response: Thanks for your comment. We explain the work of the algorithm in more detail here.

As mentioned in the answer to the second question, considering that there are many different types of bus lines in the city, including special bus lines, airport express lines, tourist lines and general lines, many overlapping stations exist on the lines. In this paper, before implementing the algorithm, we need to do the pre-processing work of station merging: pre-processing the bus and rail traffic data, and merging the adjacent stations to form an array of stations with the same name, to facilitate the subsequent implementation of the algorithm. The rules for station merging have long been described in the paper, see lines 359-370, the merged array of stations with the same name, the original station ID and the ID of the line to which it belongs is also synchronised to record and store.

Therefore, taking Figure 1 as an example, according to the priority of the multivariate heuristic function, which limits the number of network permutations to the highest priority, two paths are registered when traversing to node 4, R_1(2→3→4) and R_2(2→3→4), and the next node 4 is then extended according to the least number of permutations to obtain the optimal path R_1(2→3→4→5).

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is a well written paper. A major revision is needed for all bullets below:

1- The contributions of this work in the last paragraph in the introduction need to be better explained.

2- The main findings of this work should be discussed in the introduction in the last paragraph. 

3- The managerial implications of this study, i.e. “what’s the big deal?”, are not well-explained. How would operations managers be benefited from the findings of your study? What are the specific action plans based on the research findings? These should be addressed.

4- In equation 2, n and d indice sets are missing. They should  be added.

5- There are studies integrating restictired and unrestricted modes transport. Particularly, it is found out that on average bike-sharing (unrestricted) substitutes public transport (restrictred) as following paper suggest. This is also in context of park-and-ride. You can note that relationship and cite and discuss following work:

2023. Do the First-and Last-Mile Matter? Examining the Complementary and Substitution Effects of Bike-Sharing Platforms on Public Transit. SSRN, Article-in-press (January 16, 2023).

6- A sensitivity analysis, analysing the variability of input and their impact on output, can be conducted.

7- In this paper, one mode which is walking is missing. you can cite following work integrating walking and traversing integration on line 44, [5-9]

[9] 2022. Optimising vehicle and on-foot porter routing in urban logistics. Transportation research part D: transport and environment, 109, p.103371.

Author Response

Dear reviewer 2,

Thank you very much for your comments on this manuscript in your busy schedule. We appreciate your approval of our responses to your previous suggestions. We have carefully read your comments and revised each of them this time. The revisions are shown using line following the track version in the response letter. 

Reviewers' comments:

The paper is a well written paper. A major revision is needed for all bullets below:

Response: We are pleased to know that you are satisfied with our responses. Thank you for your comments and feedbacks to improve the manuscript. In this revision, we revised the manuscript following your comments and provided a point-to-point response in this letter.

Manuscript – line numbers refer to the ‘track’ version

(1) The contributions of this work in the last paragraph in the introduction need to be better explained.

Response: Thanks for your advice.The last paragraph in the introduction has been modified to be better explain the contributions of this work. Please see Line 116-127.

(2) The main findings of this work should be discussed in the introduction in the last paragraph.

Response: Thanks for your advice. The last paragraph of the introduction has been revised to discuss the main findings of this work. Please see Line 106-115.

(3) The managerial implications of this study, i.e. “what’s the big deal?”, are not well-explained. How would operations managers be benefited from the findings of your study? What are the specific action plans based on the research findings? These should be addressed.

Response: Thanks for your advice. We discussed the benefits from research findings and added the specific action plans based on the research findings. Please see Line128-133 .

(4) In equation 2, n and d indice sets are missing.

Response: Thanks for your advice. We followed your advice added n and d indice sets in equation 2. Please see Line 184-185.

(5) There are studies integrating restictired and unrestricted modes transport. Particularly, it is found out that on average bike-sharing (unrestricted) substitutes public transport (restrictred) as following paper suggest. This is also in context of park-and-ride. You can note that relationship and cite and discuss following work:

2023. Do the First-and Last-Mile Matter? Examining the Complementary and Substitution Effects of Bike-Sharing Platforms on Public Transit. SSRN, Article-in-press (January 16, 2023).

Response: Thanks for your advice. The work mentioned has been cited and discussed at Line 693-701.

(6) A sensitivity analysis, analysing the variability of input and their impact on output, can be conducted.

Response: Thanks for your suggestion. We will perform sensitivity analysis to analyse the variability of inputs and their impact on output in the future.

(7) In this paper, one mode which is walking is missing. you can cite following work integrating walking and traversing integration on line 44, [5-9]

[9] 2022. Optimising vehicle and on-foot porter routing in urban logistics. Transportation research part D: transport and environment, 109, p.103371.clarify ‘through forbidding grazing, rotational grazing’

Response: Thanks for your advice. We have cited the work integrating walking and traversing integration at Line 44.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This study addresses the problem of optimal path analysis in modern urban transportation networks which contain both restricted and unrestricted networks. It proposed an improved A^* algorithm to provide travelers with important routing options.

 

It seems that the paper has already gone through several rounds of revision, and with a few minor changes it will be ready for publication.

 

1.      Please provide both track changed and clean version in your future submission.

2.      The English grammar could be polished in some areas to improve clarity.

3.      The quality of the figure should be improved.

4.      The size of some tables could be readjusted for better readability.

 

 

Comments on the Quality of English Language

The English grammar could be polished in some areas to improve clarity.

Author Response

Dear reviewer,

Thank you very much for your comments on this manuscript in your busy schedule. We appreciate your approval of our responses to your previous suggestions. We have carefully read your comments and revised each of them this time. The revisions are shown using line numbers following the track version in the response letter.

 

Reviewers' comments:

This study addresses the problem of optimal path analysis in modern urban transportation networks which contain both restricted and unrestricted networks. It proposed an improved A* algorithm to provide travelers with important routing options.

It seems that the paper has already gone through several rounds of revision, and with a few minor changes it will be ready for publication.

Response: Thank you for your comments and feedbacks to improve the manuscript. In this revision, we carefully revised the manuscript following your comments in order to make it to be adequate for pubilication.

1. Please provide both track changed and clean version in your future submission.

Response: Thanks for your advice. Since MDPI only allowed us to submit one file to the reviewers, we put track version and clean version into one PDF file to prevent the line numbers from changing.

2. The English grammar could be polished in some areas to improve clarity.

Response: Thanks for your comments. We checked our manuscript and polished its English grammar and reworked its some sentences to make it more clear as illstrated on track version from section ‘Abstract‘to section ‘Disscussion and Conclusion’.

3. The quality of the figure should be improved.

Response: Thanks for your advice. We imporved the quality of figure which are not clarity, such as Figure 4(Line 260, 261), Figure 6(Line 338, 339), Figure 13(Line 612-617). And Table 5(Line 611) was revised in order to concide with the change of Figure 13.

4. The size of some tables could be readjusted for better readability.

Response: Thanks for your advice. We readjusted the size of Table 1(Line 414), 2(Line 420) , 3(Line 475), 4(Line 497), and 5(Line 611) for their better  readability. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I thank the authors for making revisions to the paper. However, I still cannot recommend the publication of this paper in MDPI Applied Sciences. The updated manuscript only partially addresses some of my original concerns. Specifically, the authors have added more review of related literature, but it is still unclear how the methods proposed here offer improvements to already available commercial services. While I understand that the algorithms used by such services might not be publicly available, I find that given the immediate practical implications of the work, more attempts should be made to compare it to existing solutions. Related to this, my main concern remains the very limited evaluation of the proposed solution and the lack of quantification of performance or comparison even to previous academic works. Given that the focus of this article is algorithm development, I belive that quantitative evaluation of performance would be essential.

I'm sorry I cannot be more positive this time.

Author Response

Dear reviewer,

Thank you very much for your sencond comments on this manuscript in your busy schedule. We appreciate your approval of our responses to your previous suggestions. We have carefully read your comments and revised each of them this time. The revisions are shown using line and page numbers following the track version in the response letter.

Manuscript – line numbers refer to the ‘track’ version.

Reviewer 1's comments:

I thank the authors for making revisions to the paper. However, I still cannot recommend the publication of this paper in MDPI Applied Sciences. The updated manuscript only partially addresses some of my original concerns. Specifically, the authors have added more review of related literature, but it is still unclear how the methods proposed here offer improvements to already available commercial services. While I understand that the algorithms used by such services might not be publicly available, I find that given the immediate practical implications of the work, more attempts should be made to compare it to existing solutions. Related to this, my main concern remains the very limited evaluation of the proposed solution and the lack of quantification of performance or comparison even to previous academic works. Given that the focus of this article is algorithm development, I belive that quantitative evaluation of performance would be essential.

I'm sorry I cannot be more positive this time.

Response: Thank you for your comments and feedbacks to improve the manuscript. In this revision, we carefully revised the manuscript following your comments in order to make it to be adequate for pubilication.

1. To expliain how the algorithms proposed here offer improvements to already available commercial services we incereased the section“4.1.4. Comparison of Path Service Algorithms with Other Electronic Maps” (see Line 572-591).

First, we compared with the existing commercial e-maps by using Bing Map and Amap for path search in two cases in section 3.3 (see Table 5, Figures 13 and 14 at Line 582-591). It showed that both of them could not achieve P&R travel plan design, and could not provide P&R travel plan combing self-driving and public transportation. And with the promotion of green low-carbon concept and the improvement of P&R car park hardware facilities, there is an increasing demand for commercial e-maps to provide P&R travel plan services. It can be seen that the algorithm has good commercial potential (see Line 635-638).

2. In order to quantitatively assess the efficiency of the algorithms, two tasks are performed as followed.

1) Algorithm execution times are given for each scenario in Appendix A (see the last column of Table A1.).

2) The efficiency design of the algorithms is elaborated (see Line 557-571).

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is progressing in the correct direction. One more revision is needed to address following:

1) Delete "at home and abroad" on line 58.

All multiple authors references should follow plural verb, eg. line 61, should be "implement" not "implements"

Line 250-253 is not well written. You should rewrite.

2) Travel path planning is not only solved in the context of road transport. You can add and cite following works on line 94:

"Note that in maritime and air transport (different restricted networks), there are also studies in path planning. [37-38] ".

[37] 2017. The multi-port berth allocation problem with speed optimization and emission considerations. Transportation Research Part D: Transport and Environment, 54, pp.142-159.

[38] 2010, June. Dijkstra's algorithm based robust optimization to airline network planning. In 2010 International Conference on Mechanic Automation and Control Engineering (pp. 2783-2786). IEEE. 

Comments on the Quality of English Language

-

Author Response

Dear reviewer,

Thank you very much for your sencond comments on this manuscript in your busy schedule. We appreciate your approval of our responses to your previous suggestions. We have carefully read your comments and revised each of them this time. The revisions are shown using line and page numbers following the track version in the response letter.

Manuscript – line numbers refer to the ‘track’ version.

Reviewer 2's comments:

The paper is progressing in the correct direction.

Response: Thank you for your comments and feedbacks to improve the manuscript. In this revision, we carefully revised the manuscript following your comments.

One more revision is needed to address following:

(1) Delete "at home and abroad" on line 58.

Response: Thanks for your advice. Modifications have been completed at Line 58.

All multiple authors references should follow plural verb, eg. line 61, should be "implement" not "implements".

Response: Thanks for your advice. Modifications have been completed at Line 61 and 64.

Line 250-253 is not well written. You should rewrite.

Response: Thanks for your advice. Modifications have been completed at Line 227-236.

(2) Travel path planning is not only solved in the context of road transport. You can add and cite following works on line 94:

"Note that in maritime and air transport (different restricted networks), there are also studies in path planning. [37-38] ".

[37] 2017. The multi-port berth allocation problem with speed optimization and emission considerations. Transportation Research Part D: Transport and Environment, 54, pp.142-159.

[38] 2010, June. Dijkstra's algorithm based robust optimization to airline network planning. In 2010 International Conference on Mechanic Automation and Control Engineering (pp. 2783-2786). IEEE.

Response: Thanks for your advice. Modifications have been completed. Two papers have been cited at Line 94-97, and added as references (see Line 739-742).

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is significantly improved. It can be published.

Author Response

Dear reviewer,

Thank you very much for your comments on this manuscript in your busy schedule. We appreciate your approval of our responses to your previous suggestions.

We are pleased to know that you are satisfied with our responses. Thanks again for your work on our manuscrip!

Author Response File: Author Response.pdf