Optimal Transport in Multilayer Networks for Traffic Flow Optimization

Round 1

Reviewer 1 Report

In general, the article deals with important topics from the perspective of problems in transport networks, especially in urban areas. It is written in intelligible language - it is generally easy to read. In my opinion, authors should add only the conclusions section. There, I propose to include the conclusions of the discussion of the results in section 3. This will help to understand better where the novelty of the methods proposed in the article is hidden. 

Author Response

Thanks for the suggestion, we added a Conclusions section that summarize the main contribution given by our paper. In detail:

• we summarized the main scope of our algorithm, i.e. finding optimal transport flows on multilayer networks;

• we pointed out that the parameter ?? allows for a detailed description of how different transportation modes contribute to the total cost;

• we summarized the experiments we performed on synthetic and real data;

• lastly, we gave possible suggestions on how our work could be extended in the future.

Author Response File: Author Response.pdf

Reviewer 2 Report

The Authors deal with the problem of designing the multilayer networks and modeling traffic distribution and extracting optimal flows in such types of networks. It is the key issue for planning a multi-modal transport network, which requires very complex analyzes. In the proposed approach, searching for the shortest paths need the transformation of the network and the introduction of an additional layer. Furthermore, each layer is assigned a separate parameter that regulates how the fluxes distribute in the layer. In the analyzes, the topological measures based on graphs have been used. I find the issues taken up by the Authors as very important, interesting and current. In my opinion, the subject is appropriate for the journal „Algorithms”.

The manuscript is written in consistent and logical manner and the structure is correct. The formalisms introduced in the description of the network model are adequate to the level of detail of the mapping of the issue under study. The manuscript also contains a comprehensive set of references.

However, I have some minor comments:

- In my opinion, the title of the article seems too general. It should be more detailed.

- The Authors did not emphasize the goal of the article sufficiently in the introduction.

- In addition to the algorithm presented between the lines 206 and 207, a block diagram would also be useful.

- I suppose that it is about „the edge between the node u in layer α and node v in layer γ” (not β) in the line 91,

- As for the principle of placing figures in the text, the text should contain a reference to the figure first, and only then should the figure be placed in a graphic form. This rule is not respected in case of the Figure 1, which is placed between lines 92 and 93, and it is only referenced in line 131.

Author Response

The Authors deal with the problem of designing the multilayer networks and modeling traffic distribution and extracting optimal flows in such types of networks. It is the key issue for planning a multi-modal transport network, which requires very complex analyzes. In the proposed approach, searching for the shortest paths need the transformation of the network and the introduction of an additional layer. Furthermore, each layer is assigned a separate parameter that regulates how the fluxes distribute in the layer. In the analyzes, the topological measures based on graphs have been used. I find the issues taken up by the Authors as very important, interesting and current. In my opinion, the subject is appropriate for the journal „Algorithms”. The manuscript is written in consistent and logical manner and the structure is correct. The formalisms introduced in the description of the network model are adequate to the level of detail of the mapping of the issue under study. The manuscript also contains a comprehensive set of references. However, I have some minor comments:

In my opinion, the title of the article seems too general. It should be more detailed.

• Thanks for your suggestion. We changed the title to “Optimal transport in multilayer networks for traffic flow optimization”.

The Authors did not emphasize the goal of the article sufficiently in the introduction.

• Thanks for pointing this out, we added a short paragraph at the end of the Introduction section where we highlighted the main goal and contributions of our work.

In addition to the algorithm presented between lines 206 and 207, a block diagram would also be useful.

• We complemented the pseudocode of Algorithm 1 with a flow chart visualization, this is shown in Figure 3.

I suppose that it is about “the edge between the node u in a layer? and node v in layer ?” (not ?) in the line 91,

• Corrected, thanks!

As for the principle of placing figures in the text, the text should contain a reference to the figure first, and only then should the figure be placed in a graphic form. This rule is not respected in case of the Figure 1, which is placed between lines 92 and 93, and it is only referenced in line 131.

• Thanks for pointing this out, we made sure to respect the convention.

Author Response File: Author Response.pdf