Mathematical Models and Nonlinear Optimization in Continuous Maximum Coverage Location Problem
Round 1
Reviewer 1 Report
1. A continuous version of the maximal covering location problem is relatively new, the contribution of this manuscript should be more clear compared to other publications such as:
https://www.sciencedirect.com/science/article/pii/S0305054821000988
2. The formation time charts need a higher resolution.
3. Extensive proofreading is necessary, e.g.,
(Abstract) an location -> a location, Pyton -> Python
(Conclusion) The authors plan to direct their further research to the study of precisely the optimization problems of packing and covering in areas with variable metric parameters. -> needs to be rewritten
4. It is recommended that Table 1 is moved to Appendix if possible.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this article, the maximum coverage location
problem (MCLP), in a continuous formulation, is considered.
The background is reviewed in Section 2.
The mathematical model is described in section 3.1.
The complex object is given by (2), and the optimized
function is formulated as (5)-(8). In turn, the
nonlinear unconstrained optimization problem becomes (9).
The computer approach and optimization software is
outlined in section 3.2.
Finally, sone numerical results are presented in
Section 4.
The mathematical problem is of scientific importance,
with extensive applications, and the scientific approach
seems convincing.
The reviewer believes this work deserves a publication
at "Computation" after the following improvements are made.
(1) The reviewer wonders whether a theoretical analysis
could be derived for the numerical method to the optimized
problem (9).
The authors should make a remark on this issue in
the revision.
(2) In the existing literature, there have been quite a
few theoretical analysis for the iterative numerical
solvers for certain nonlinear optimization problems,
such as the preconditioned steepest descent (PSD) method.
These existing works include:
Preconditioned steepest descent methods for some
nonlinear elliptic equations involving p-Laplacian terms
A uniquely solvable, energy stable numerical scheme
for the functionalized Cahn-Hilliard equation and its
convergence analysis
A second-order energy stable Backward Differentiation
Formula method for the epitaxial thin film equation
with slope selection
An energy stable Fourier pseudo-spectral numerical
scheme for the square phase field crystal equation
Structure-preserving, energy stable numerical
schemes for a liquid thin film coarsening model
An iteration solver for the Poisson-Nernst-Planck
system and its convergence analysis
These related reference works should be cited
in the revision.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
-check the figures 1-3
-add a flowchart to describe your approach
-in the problem description section add some basic theorem to better explain the problem
-add some more illustrations about the equations, how eq. 11 is obtained?
-in the result section, there are no comparisons, to better show the advantages of your algorithms, some comparisons with new related, methods are required
-add some remarks about the potential improvement by the use of a new optimization scheme such as:Deep learned recurrent type-3 fuzzy system: Application for renewable energy modeling/prediction
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Line 202: "In [29, 30], ... (line 202)" should use Ref [29, 30] or AuthorName depending on the citation rules of this journal
Lines 218-215 (Eq.(4)) : the g^0 (?) symbols are garbled
Lines 298-313 (Eq.(14)) : same as above
Line 335: same as above, please look for more such occurrences yourself
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
The paper can be accepted in my opinion,
Author Response
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Author Response File: Author Response.pdf
