A Labelling Method for the Travelling Salesman Problem

Round 1

Reviewer 1 Report

The paper proposes a novel approach to TSP problems. The authors aim to reduce the complexity of TSP algorithms by introducing the labeling method. The organization of the paper needs some improvements, which are stated below:
1) In the introduction section, the types of TSP algorithms are mentioned. It should be better to show them references. Then, the readers could be found and understood for what they are.

2) The novelty of the paper is that the labeling method may be able to decrease the complexity of the TSP algorithms. However, it is not clear how the proposed model helps reduce complexity. It is suggested that it be given in the experimental results and conclusion sections.

3) The authors believe that K-1 time iterations are enough to solve the TSP problems. But the reason why  K-1 time iterations are enough is not clear. Please explain your reasons, or you should add sensitivity analysis to show why K-1 is decided.

4) There are no figure numbers in the manuscript. The authors should add figure numbers and explain the figures in the manuscript by giving citations with figure numbers.

5) References should be revised according to the journal writing guidelines.

6) There is no conclusion section. The summary of important findings and future research directions could be added as a new section at the end of the manuscript.

It could be better to review the entire manuscript carefully to minimize grammatical errors and typos.

Author Response

Revisions have done as given in the attachment,

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Dear authors of this research paper.  The Traveling salesman problem (TSP) is very relevant and in demand, including for transport problems and, for example, in different routing problems.  The travelling salesman problem is one of the most interesting subproblems of combinatorial optimization. The formulation of the problem is correct.  A very detailed scientometric analysis is presented which strengthens the research done in the paper. The presented solution allows to find the best route (taking into account all given criteria); effectiveness of Labelling has been confirmed by You.

Unfortunately, the article does not have a separate section - Conclusion. On page 15 you only say "we have developed a labelling method that can be used to compute the optimal TSP tour…..". But, it would be better to put it in a separate section.

Author Response

Revisions have been done.

Please see the attachment.

Author Response File: Author Response.docx