Improved Differential Evolution Algorithm to Solve the Advertising Method Selection Problem
Round 1
Reviewer 1 Report
The authors propose the Improved Differential Evolution (IDE) for application to the Advertisement Method Selection Problem. The authors present the problem, the algorithm and perform an empirical study, where they compare the IDE with some competitors. Unfortunately, the problem and algorithm description is to shallow and the empirical comparison lacks several important information. Thus, I recommend a major revision of the article.
Detailed comments:
lines 80 to 90: Please use appropriate references. For example, for none of the presented algorithms the initial developers are mentioned (Holland for GA, Price and Storn for DE, or Eberhart, Kennedy and Shi for PSO).
lines 91 to 116: The review of DE is missing important information and references. I advise that the authors take a closer look at a recent survey on DE (e.g. Recent advances in differential evolution – An updated survey, Das et al.,2016). For example, what about other algorithms combining DE and (other) local search techniques? Or why not use a DE which can handle combinatorial problems?
Figure 2: What is the motivation of the constraint that only one Advertisement Method can be used?
line 148: Please clearly define all the variables. Also, change the equation numbering from )1( to (1) (same holds up to Eq. 5). Since DE is in its basic variant an algorithm for unconstrained optimization, how are the constraints handled?
line 165 to 166: The sentence starting with: "The solution that is rejected ...." makes no sense in its current form.
line 210: "Method 1 uses 180 min to create ... which is the full capacity of Advertisement Method 1." Previously, it was stated that Advertisement Method 1 has a time budget of 180 hours (see line 199). And where do these times come from? Are they taken from real-world examples?
Which values are used for F and CR in DE? And what population size is used?
Table 3: Typically, run time is hard to compare since several effects outside the algorithm might affect the run time. However, I do understand the choice here since the aim is a comparison with LINGO. Still, please report the number of function evaluations with the results. Also for brevity, please highlight the best performing results.
What are the termination criteria used for LINGO? And when did LINGO found the optimal solution?
line 357: 5 repetitions seem very small for a statistically sound experiment.
line 389: "will not plot the graph of best objective..." - But you did in Figure 9, right?
Author Response
Dear Reviewer
Thank you very much for your comments. It indeed can improve the qaulity of the paper lot. We have studied your comments and correct them as you in see in details as the attached file. We hope that the qaulity of the article will be good enought to publish.
Best regards
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper is interesting, I only have two concerns that need to be addressed:
1)In section 1, the statement
"A heuristic is a methodology that can resolve difficult problems within a reasonable amount of 78 computational time, yet while it does not guarantee an optimal solution, it can guarantee that the 79 given solutions created through a good heuristic will be of good quality." is very vague and a bit ambiguous. Please bear in mind that a heuristic approach is the one that does not make an assumption on the problem at hand and that heuristic do not necessarily guarantee good quality solutions. The text must be modified. Please take into consideration that also differential evolution suffers from premature convergence and stagnation (look at https://doi.org/10.1063/1.5089969) and thus not necessarily produce a solution of satisfactory quality in those cases. The same poor performances occur when a structural bias arises, as thoroughly investigated in https://doi.org/10.1016/j.ins.2019.05.019 and https://doi.org/10.1063/1.5089972
2)The paper is well structured but still, I would suggest performing a linguistic check to remove linguistic imprecision thus making the manuscript more suitable for publication
Author Response
Dear Reviewer
Thank you very much for your comments. It indeed can improve the qaulity of the paper lot. We have studied your comments and correct them as you in see in details as the attached file. We hope that the qaulity of the article will be good enought to publish.
Best regards
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors addressed my previous comments sufficiently. However, the article still contains some typos and some questions need to be addressed.
page 3, Introduction: In the field of Evolutionary Computation, one uses exploration instead of diversification and exploitation instead of intensification. Please use these terms since they are the accepted standard terms. Eq. (2). Please check this equation since it does not have the same terms as the example (lines 150 - 156). In Eq. (2) the time appears (T_jk) but not the probability of the occurrence of the scenario (R_jk) line 180: One would hardly want to escape the optimal solution, but rather a local optimal solution. Figures 3 to Figure 8: These are not figures but tables. Also, I was wondering what the numbers in the product vector and the advertisement vector do represent. As I understand your approach, the numbers are merely used for sorting but have no "real" meaning. Maybe you could elaborate on that. lines 225 to 229: Does this described procedure always end up with all products assigned to an advertising method or could there be a case where some products remain unassigned (for example the time capacity is exceeded for the last product/advertising method pair)? line 215: Here the times are still stated as hours. lines 257 to 259: This is already stated in Algorithm 1 and could be removed. The same applies to the three-cyclic move. Eq. (9): T will be between 100 and 99 since the fraction is between 0 and 1. Is this equation is really required or could T just be chosen as a constant? Algorithm 1: The second to last line should read: T=T+1 (capital letters) Eq. (12): If the aim is to maximize, should be the unequal sign be > instead of <=? Table 2: Currently the research is not reproducible since no information about the instances exists (i.e. what are the times, budgets, etc.). Please, if possible, provide these details of those instances (for example by a link to a web page) or at least give some properties regarding the missing values. Eq. (13): generated instead of "genearted" line 405: You state that the lower bound values provided by Lingo were used, but Table 5 lists the upper bounds. Maybe provide both in Table 5.
Author Response
Dear Reviewer
Thank you very much for your comments. It indeed can improve the qaulity of the paper lot. We have studied your comments and correct them as you in see in details as the attached file. We hope that the qaulity of the article will be good enought to publish.
Best regards
Author Response File: 
Author Response.docx
Round 3
Reviewer 1 Report
The addressed the comments satisfactorily. After a final language check, the paper can be published.
Author Response
Dear Editor
Thank you very much for your comments. It indeed can improve the quality of the paper lot. We use the service of MDPI English Editing and Global Languages Translation Center Ltd., Part for this revision. We have studied your comments and correct them as you see in details as attached file. We hope that the quality of the article will be good enough to publish.
Best regards,
Asst. Prof. Dr. Tassin Srivarapongse
Author Response File: Author Response.pdf
