An Improved Compact Genetic Algorithm for Scheduling Problems in a Flexible Flow Shop with a Multi-Queue Buffer

Round  1

Reviewer 1 Report

In my opinion, this paper presents useful and interesting results and it can be accepted for publication as long as the authors read it several times and correct typos/grammatical errors.

Author Response

Response to Reviewer 1 Comments

Point 1: In my opinion, this paper presents useful and interesting results and it can be accepted for publication as long as the authors read it several times and correct typos/grammatical errors.


Response 1: Thanks for your careful, insightful and constructive comments and suggestions. We have read the article several times carefully and corrected many typos/grammatical errors.

Author Response File: Author Response.docx

Reviewer 2 Report

In general, the paper is not clearly written. A substantial improvement on grammar and on writing is required. 

Some detailed comments are listed below. 

Line 207: 

The variables porp's should be prop's.

Line 210, line 212: "times" is followed by "is". It seems to be incorrect. 

Line 200, line 213: The symbol "g" is not defined. 

The authors used past tense throughout the paper. It should be the present tense in most of the context. 

Lines 286-288:

What is the difference between "1 to n rows" and "1 to n lines"? They are grammatically wrong. It can be "the 1st to nth rows" or "the rows 1 to n". They should be the same, but the sentence is senmatically wrong. 

Lines 307 and 309:  What is the difference of model sigma^L and the parameter sigma of the Gaussian pdf? In the following paragraph, sigma^L is stated as Gaussian model. Then what is its difference from the Gaussian probabilistic model F^L (Lines 306-307)?

Line 312: The expression of the upper line of the equation is wrong. The index s should be replaced by a new index rather than s.

Lines 313-314: 

The sentence is not clearly written. There are also several grammatical errors. 

Line 315:

"the s line" and "the L generation" are wrong in grammar. 

Lines 325-327: 

The symbol g is not defined. Both equations (24) and (25) define sigma_s^L, but are different. This is not a acceptable way. 

Line 348: The sentence is not clearly written. 

Lines 355-387: The ICGA procedure is poorly written. The grammar is poor, and the procedure is not clearly written. It should be concise execution steps that is easily understanable to programmers. 

Figure 2 is not suitably presented. In the figure, the makespan is compared for only one parameters, while the other parameters are not specified. This is hard to understand and the figure is misleading. If the authors cannot suitable put the figure, remove it totally. 

On line 546, table 4: "Setup times parameters" looks wrong in grammar. 

In section 5.3.3 , why not compare the schemes 1-8 on the same figures?

Author Response

Response to Reviewer 2 Comments

Point 1: Line 207: The variables porp's should be prop's.


Response 1: It has been corrected. The detailed modifications are as follows.

                                                                           (15)

Point 2: Line 210, line 212: "times" is followed by "is". It seems to be incorrect.

Response 2: It has been corrected. The detailed modifications are as follows.

When, it means that when property  of job  and property  of job  are the same, no setup time is required to process the latter job on the machine. When , it represents that when property  of job  and property  of job  are different, the setup time is required to process the latter job on the machine.

Point 3: Line 200, line 213: The symbol "g" is not defined.

Response 3: We have modified the formulas for line 200 and line 213. The detailed modifications are as follows.

, , ,           (14)

, , ,              (16)

Point 4: The authors used past tense throughout the paper. It should be the present tense in most of the context.

Response 4: We have carefully checked the tense issues of the article and modified some of them.

Point 5: Lines 286-288: What is the difference between "1 to n rows" and "1 to n lines"? They are grammatically wrong. It can be "the 1st to nth rows" or "the rows 1 to n". They should be the same, but the sentence is senmatically wrong.

Response 5: The "1 to n lines" should be "1st to nth columns". The detailed modifications are as follows.

       In the probabilistic model, the 1st to nth rows correspond to jobs  to , and the 1st to nth columns correspond to individuals 1 to n.

Point 6: Lines 307 and 309:  What is the difference of model sigma^L and the parameter sigma of the Gaussian pdf? In the following paragraph, sigma^L is stated as Gaussian model. Then what is its difference from the Gaussian probabilistic model F^L (Lines 306-307)?

Response 6:  is the standard deviation () of the  column in the probabilistic model .  is the set of . That is,  is the set of standard deviations of all the columns in the probabilistic model . After careful study by the author, strictly speaking, is not a model but a set. And I haven't used  elsewhere in this article, only  is used, so we removed the  here. The detailed modifications are as follows.

The ICGA consists of two models: the original probabilistic model  and the new probabilistic model . The element  in the probabilistic model referred to the probability of job  appearing at position  in online processing queue.

Point 7: Line 312: The expression of the upper line of the equation is wrong. The index s should be replaced by a new index rather than s.

Response 7: We have rewritten and modified the content of this section. The detailed modifications are as follows.

The specific operations are: first, determine the range  for each probability value  on the X axis, where , . Then, determine the position of expectation value  on the X axis. Finally, the corresponding probability value  of probability value  in the new probabilistic model  is obtained by using Equation (28).

                      (28)

Point 8: Lines 313-314: The sentence is not clearly written. There are also several grammatical errors.

Response 8:  We have rewritten and modified the sentence. The detailed modifications are as follows.

       Equation (23) is the probability density function of the Gaussian distribution, where  is the expectation value of the  column in the probabilistic model , and the calculation formula is shown in Equation (24).

Point 9: Line 315:"the s line" and "the L generation" are wrong in grammar.

Response 9: We have rewritten and modified the sentence. The detailed modifications are as follows.

        is the standard deviation of the  column in the probabilistic model , and the calculation formula is shown in Equation (25).

Point 10:  Lines 325-327: The symbol g is not defined. Both equations (24) and (25) define sigma_s^L, but are different. This is not a acceptable way..

Response 10: It has been corrected. The detailed modifications are as follows.

                                  (25)

                              (26)

                                (27)

Point 11: Line 348: The sentence is not clearly written.

Response 11: We have rewritten and modified the sentence. The detailed modifications are as follows.

Equation (29) shows that when the value of  is i , the probability value  in the  column of the model which combines with learning coefficient  further increases the probability of job  being chosen on the position  in the online processing queue. In addition, other probability values of this column subtract .

Point 12: Lines 355-387: The ICGA procedure is poorly written. The grammar is poor, and the procedure is not clearly written. It should be concise execution steps that is easily understanable to programmers.

Response 12: We have rewritten and modified the content of this section. The detailed modifications are as follows.

Step 1: Initialize probabilistic model. According to the principle of maximum entropy, the initial probabilistic model  is , while the evolutional generation L is initialized as 0, namely .

Step 2: Generate new individuals based on probabilistic model. Through the roulette, the individual’s genic sampling values are selected in turn (jobs to be processed successively on each position of the online queue) according to the probability values of each column in the probabilistic model . Once a job is selected, it no longer participates in the subsequent selection, while the unselected jobs go on until all jobs are arranged. After that, a new individual is generated so that new individuals  are generated temporarily.

Step 3: Determine whether probability value maps to new probabilistic model. Calculate the standard deviation  of the probability value of/on the  column in the original probabilistic model , and determine whether  is larger than the threshold value  which starts the mapping operation. If , the probability value of the  column in the  is taken as the  column probability value in the new probabilistic model . If , step 4 will be operated.

Step 4: Map the probability value  in the original probabilistic model  to the new probabilistic model . Calculate the expectation value  of the probability value of the  column in the original probabilistic model . Determine the corresponding the probability density function of the Gaussian distribution, and calculate the probability value  in the new probabilistic model  corresponding to each probability value  in the  column.

Step 5: Repeat step 3 until all the columns in the original probabilistic model  are all mapped into the new probabilistic model .

Step 6: Regenerate new individuals. Using the roulette again, regenerate  new individuals  based on the probability values in the  and replace original individuals .

Step 7: new individuals  are decoded and the fitness function value is found for each new individual.

Step 8: According to the fitness function value, the superior individual  is selected to update the probabilistic model . The update operation is performed in accordance with Equation (29), making model  evolve under the guidance of . The update operation is described in Section 3.2, and evolutional generation is processed with .

Step 9: Whether the updated original probabilistic model  converges, that is, whether all probability values of model  are 1 or 0 is/are determined. If the convergence is met, the historically optimal individual is output and the evolution process ends. Otherwise, return to Step 2 to continue operation.

Point 13: Figure 2 is not suitably presented. In the figure, the makespan is compared for only one parameters, while the other parameters are not specified. This is hard to understand and the figure is misleading. If the authors cannot suitable put the figure, remove it totally.

Response 13: Figure 2 contains three small graphs showing the influence of three parameters change on the performance of the algorithm. We redesigned Figure 2 and repositioned it.

Point 14: On line 546, table 4: "Setup times parameters" looks wrong in grammar.

Response 14: It has been corrected. The detailed modifications are as follows.

       Setup times when the model of buses processed successively on a parallel machine of stagechanges

Point 15: In section 5.3.3 , why not compare the schemes 1-8 on the same figures?

Response 15: This paper designed 8 sets of simulation schemes as shown in Table 7. From the experimental data in Table 8, under the principle of adopting the same global optimization algorithm, compared with schemes 1~4, each metric of schemes 5–8 has been improved to some extent. This has shown that the local scheduling rules which are designed in this paper are reasonable and effective. Figure 4 and Figure 5 are for further testing and comparing to the optimization performance of the four algorithms in the iterative process and the ability to jump out of the local extremum. If all the 8 sets of curves are drawn on the same picture, it is not conducive to comparison and analysis, and it is not suitable for readers to read. Therefore, only schemes 5-8 are compared in Figure 4 and Figure 5.

       Table 7. 8 group simulation program information

Table 8. Evaluation index comparison of scheduling results of eight schemes

Author Response File: Author Response.docx

Round  2

Reviewer 2 Report

In the introduction section, many places should use the past tense when introducing the literature review. 

The revised version is hard to read. Also the response to this reviewer is not satisfying. For example, for the reviewer point 3: "Line 200, line 213: The symbol "g" is not defined.", the response is not readable, and "g" is still not defined in the revised version . 

Also, the response to point 12 is not desirable.The procedure should be in a flowchart that is amenable to a programmer. However, for each step it is a paragraph. 

In summary, this manuscript is not well clearly written. 

Author Response

Thank you for your comments concerning our manuscript entitled “ICGA Algorithm for Scheduling Problems in Flexible Flow Shop with Multi-Queue Buffer” (ID: Processes-488586). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Point 1: In the introduction section, many places should use the past tense when introducing the literature review.

Response 1: We have made correction according to the Reviewer’s comments in the revisions.

Point 2: For the reviewer point 3: "Line 200, line 213: The symbol "g" is not defined." the response is not readable, and "g" is still not defined in the revised version .

Response 2: There seems to be no symbol “g” in line 200 and line 213. It should be the display errors. And we have contacted the editor about this problem. And I will resubmit the version by PDF.

Line 200 and line 213 are as follows in my Word:

Point 3: The response to point 12 is not desirable. The procedure should be in a flowchart that is amenable to a programmer. However, for each step it is a paragraph.

Response 3: We have re-written this part according to the Reviewer’s suggestion and add a flowchart of the ICGA algorithm. 

Author Response File: Author Response.pdf

Round  3

Reviewer 2 Report

The comments for the earlier version have been addressed. 

Author Response

Dear Reviewer:

         Thank you for your comments concerning our manuscript entitled “ICGA Algorithm for Scheduling Problems in Flexible Flow Shop with Multi-Queue Buffer” (ID: Processes-488586). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. 

Best Regards