Pavement Maintenance Decision Making Based on Optimization Models

Round 1

Reviewer 1 Report

- row 34 <>: delete the latter ‘durable’;

- row 61 <>: put the missing space;

- rows 113-114 << Two models were solved …>>: in light of the previous statement <<… two optimization models were developed …>> consider to correct into “The two models were solved …”;

- row 119-120 <>: what do you mean by “partial roads”? maybe you have to better reformulate the whole statement;

- row 244 <<… and schemes were shown in map.>>: indicate which schemes and which map you are referring to; or delete this part of sentence;

- row 321 <<… FID …>>: an acronym never defined before;

- row 334 <<… 3 solutions was highlighted …>>: correct “was” into “were” or into “have been”;

- row 335 <>: if you are referring to the two model of this paper, consider to correct into “The two optimal models have been applied to …”.

Author Response

Dear reviewer1:

     Thank you for your careful review and valuable advice. We have accepted your advices and modified our manuscript. The point-by-point response is attached with the file.

     Thank you very much!

Author Response File: Author Response.pdf

Reviewer 2 Report

It is an interesting real-world problem being considered. The structure of your paper should be improved by providing a more critical and detailed introduction with regards to existing work and solution methods. This should then be followed by an outline of the models you are formulating and the solution methods being used. This is especially so for the first model, which is being solved using a sequential least squares quadratic program solver, even though it is an integer linear program. Some specific comments and grammar corrections are included below.

36-36: should be "adverse environmental"

37-39: perhaps "Insufficient budgets for maintaining the pavement in an appropriate condition are the primary obstacle in pavement maintenenance programs [1]."

44: "complex" could be misleading, would "difficult", "non-trivial", or "complicated" instead be better?

61: space between "Saaty" and "[7]".

79-80: how do they do anything when road information is insufficient?

89: space before "[1]".

93-94: why is this split into two paragraphs?

104: do flexible pavements need to be treated differently?

108-110: it is not apparent from the preceding list of publications that much work has been done on GAs. A little more discussion of at least some of the references mentioned and how they extended/improved GAs would support this statement. You have not provided any description on why/how GAs are effective on these problems in the section referred to.

111: "problem has been introduced and formulated as a multi-objective..."

119-120: what is meant by "partial roads"? This opening sentence should be improved.

127: remove comma: "daily patrol data that can be".

141-142: "m roads (m<=N) are prioritised for maintenance" instead of "are prior to be maintained".

143-144: "(3) the road quality is maximized".

144: It is not clear what you mean by "based on human experience will result", and how can there be 2^N schemes unless your budget is sufficient to pay for the maintenance of an arbitrary number of roads up to and including a total of N roads? Are you just saying that by formulating the problem such that each decision variable is a boolean representing whether a road is included in the maintenance schedule/priority list?

146: N doesn't have to be excessively large for this to be infeasible to do manually.

146: "This is an".

150-152: Is this a heuristic approach? Is the solution provided globally optimal, locally optimal or approximately so?

158: "engineering management" and then "research literature, but their use".

Figure 1: Third box down on left should read "Applying models...". Third box down on left in the dashed box should read "Using least squares...".

173: Doesn't this objective function implicitly weight towards roads with small areas and cheap maintenance costs so that you can get the most number of roads improved?

174: In (2), "Area_{i0}" should just be "Area_i". Also, why use the dot for multiplication here but nowhere else?

202: "throught the AHP".

213: What happens when there is no feasible solution, that is, when the cost of maintaining the roads with PCI_i < D is greater than 10M CNY?

219: Same as for line 173.

220: You use an asterisk for multiplication here in equation (7) but used a dot in equation (2). At least be consistent with the multiplication symbols if you are going to use them.

229: "equation (8), D is...maintenance threshold; when the PCI".

230-231: "threshold value, it is compulsory to maintain that road."

231: Same query as for line 213 but for this model.

234-235: Still not clear that these are going to be globally optimal values.

235: "from the model and the maintenance scheme returned from the solvers were plotted on a map."

237: "In total, 149".

240: "using Equation (3)."

246: Please provide some basic statistics of the dataset, e.g. average PCI, minimum and maximum PCI, percentage of budget for roads with PCI less than 70.

260-263: It is not clear what Z and Z' are. Z(i) is the optimal value from the first model, which is what you are solving for. Z'(x^i) is the fitted value of the pavement condition, presumably being fit by the least squares method? It isn't clear why you are using an SQP solver for an integer linear program (specifically, a binary linear program). Furthermore, the reference [21] appears to be formulating and solving an integer linear program (as mentioned on lines 105-107), and not a least squares problem. Are you solving the first problem as an integer linear program and then using a least squares method to fit something to that? If so, why are you using the least squares method at all (as you already have the solution to the first problem)? What are you fitting to the optimal solution?

266-267: Didn't you already do that when you computed Z(i) before solving the least squares problem?

268-281: How are the dual objective values weighted, i.e. how do you compute a fitness score including both Z1 and Z2?

287-291: Reference.

301: 8 million CNY budget

Table 3: Replace "budgets" with "budget".

310: "budget is shown".

313: "maintenance according".

314: What is FID?

324: "3,000th generation."

350: "(13) for both models".

Section 5.1: This doesn't really add anything except to reinforce the question as to why a least squares method was used to solve the first problem.

378-380: Doesn't really look like it takes an abrupt turn. Didn't you just say that you believe you have computed the Pareto frontier in lines 372-373 using a heuristic algorithm? What here now suggests that it is often difficult?

Section 5: Why are formulating new models in the discussion section? Put these in an earlier section on problem formulation, present the results of all four models in the results section, and discuss them all in the discussion.

388: Asterisk again.

389: Is there any justifcation for choosing these numerical values? How sensitive is the model to these choices?

401: Asterisks again.

399-411: Did you solve this second multi-objective model?

421: Three optimization models?

Author Response

Thank you for your careful review and valuable advice. We have accepted almost all your advices and modified our manuscript. The point-by-point response is attached with the file.Thank you very much!

Author Response File: Author Response.pdf

Reviewer 3 Report

Dear authors, I ask you to answer a number of questions and comments:
1. For such a significant problem, the list of references is too small and it is necessary to delete all publications older than 10 years, since their relevance is questionable.
2. Conclusions and discussion do not reveal all the work done and research.
3. The abstract is not informative.

Author Response

Thank you for your valuable advice. We have accepted all your advices and modified our manuscript. The point-by-point response is flowing:

Point 1: For such a significant problem, the list of references is too small and it is necessary to delete all publications older than 10 years, since their relevance is questionable.

Response 1: We added some new cited publications and updated the references.
Point2:  Conclusions and discussion do not reveal all the work done and research.

Response 2: We accepted your advices and updated conclusion and discussion.

Point 3: The abstract is not informative.

Response 3: We accepted your comments and modified the abstract.

Thank you very much!