Round 1

Reviewer 1 Report

A hybrid crow search algorithm for solving permutation flow shop scheduling problems

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RESEARCH:

Mention some non-conventional models to solve NP-Problems such as:

- Luis Fernando de Mingo López, Nuria Gómez Blas, Alberto Arteta: Optimal Performance: Underlying Octahedron Graph of Evolutionary Processors. Computing and Informatics 34(4): 858-876 (2015)

and bio-inspired models:

- Luis Fernando de Mingo López, Nuria Gómez Blas, Alberto Arteta Albert: Multidimensional knapsack problem optimization using a binary particle swarm model with genetic operations. Soft Comput. 22(8): 2567-2582 (2018)

TABLE 5.- please use bold font to mark the best algotithm

Some figure with the performace of the algorithm will be great.

Line 220-221.

Duplicate references title

Line 302.

?????

Author Response

Reviewer Comment P 1.1 — Mention some non-conventional models to solve NP-Problems such as: Luis Fernando de Mingo Lpez, Nuria Gmez Blas, Alberto Arteta: Optimal Performance: Underlying Octahedron Graph of Evolutionary Processors. Computing and Informatics 34(4): 858-876 (2015) and bio-inspired models: Luis Fernando de Mingo Lpez, Nuria Gmez Blas, Alberto Arteta Albert: Multidimensional knap- sack problem optimization using a binary particle swarm model with genetic operations. Soft Computing. 22(8): 2567-2582 (2018)

Response: Thank you very much for pointing out this shortcoming. Following your suggestion, we have added some state-of-the-art technologies and important problems in our study to emphasize the motivation of this article.

 

Reviewer Comment P 1.2 — TABLE 5.- please use bold font to mark the best algotithm Some figure with the performace of the algorithm will be great.

Response: Thank you very much for pointing out this shortcoming. Following your suggestion, we first added the “bold” format type of the comparison result. We then more clearly present previous experimental results. Some results will be depicted visually as a figure.

 

Reviewer Comment P 1.3 — Line 220-221. Duplicate references title

Response: Thank you very much for pointing out this shortcoming. This is a typographical error from the Latex file. We have corrected it accordingly.

 

Reviewer Comment P 1.4 — Line 302. ?????

Response: Thank you very much for pointing out this shortcoming. We have deleted this redundant sentence.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

This paper presents a good explanation to the permutation flow shop scheduling problem. It proposed the HCSA algorithm to solve this problem. It uses an SPV rule to convert a continuous sequence to a job sequence. The NEH algorithm was also used for population initialization, and SA-VNS was used as the local search to improve the quality of makepsan values. Performance evaluation demonstrated the feasibility of applying HCSA algorithm to solve the permutation flow shop scheduling problem. Also, good results are generated when compared with other algorithms.

My comments are as follows:-

·       Typo Errors, for example in Line 17 , and act the important

Line 59 The NEH [3] algorithm algorithm.

·       a Flowchart of the HCSA Algorithm will improve the paper, The chart starts with: step 1, create a solution using NEH algorithm, step 2, create a population by random values, step 3, determine the permutation through SPV Rules, step 4, set the parameters for SA and CSA,…etc.

 After specific number iteration if the criteria is reached then YES generate the optimal solution.

Future Suggestion

·       How about using the PSO based VNS? in which the positions and velocities of N particles in the d -dimensional space represent the potential randomly initialized solutions AND the parameters will be number of particles, inertia ω, c1 and c2 denote the cognitive parameter and social parameter constant.

·       Improve the performance of HCSA and test its efficiency on large-scale scheduling problems.

·       Try to combine graph structures and neighbourhood structures for speeding up the local search.

·       Develop other local search strategies to enhance the performance of the proposed Methodology.

·       It is desirable to apply this method to other varieties of combination optimization problems in the real world.

 

Comments for author File: Comments.docx

Author Response

Reviewer Comment P 2.1 — Typo Errors, for example in Line 17 , and act the important, Line 59 The NEH [3] algorithm algorithm.

Response: Thank you very much for pointing out this shortcoming. We have double-checked all typographical errors and corrected them.

 

Reviewer Comment P 2.2 — a Flowchart of the HCSA Algorithm will improve the paper, The chart starts with: step 1, create a solution using NEH algorithm, step 2, create a population by random values, step 3, determine the permutation through SPV Rules, step 4, set the parameters for SA and CSA,etc. After specific number iteration if the criteria is reached then YES generate the optimal solution.

Response: Thank you very much for pointing out this shortcoming. We have changed the pseudocode of Figure 5 in a flowchart format.

 

Reviewer Comment P 2.3 — How about using the PSO based VNS? in which the positions and velocities of N particles in the d-dimensional space represent the potential randomly initialized solutions AND the pa- rameters will be number of particles, inertia , c1 and c2 denote the cognitive parameter and social parameter constant.

Response: Thank you very much for pointing out this shortcoming. The following article has shown that the PSOMA (SA-based VNS) algorithm is better than the PSOVNS (VNS-based) algorithm. Our paper illustrates that the CSA algorithm-based SA-VNS algorithm is better than PSOMA and PSOVNS. In addition, the CSA only contains the two parameters even less than the PSO algorithm.

 

Liu, B.; Wang, L.; Jin, Y. An effective PSO-based memetic algorithm for flow shop scheduling. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 2007, 37, 1827.

 

Reviewer Comment P 2.4 — Improve the performance of HCSA and test its efficiency on large-scale scheduling problems.

Response: Thank you very much for pointing out this shortcoming. Following your suggestion, we will determine a larger benchmark and try to solve it in the future.

 

Reviewer Comment P 2.5 — Try to combine graph structures and neighbourhood structures for speeding up the local search.

Response: Thank you very much for pointing out this shortcoming. Considering your suggestion, in the future, we will try to implement a local search using these two structures instead of the original array-list structure.

 

Reviewer Comment P 2.6 — Develop other local search strategies to enhance the performance of the proposed Methodology.

Response: Thank you very much for pointing out this shortcoming. Following your suggestion, we are trying to adapt the Le´vy searching strategy to improve the local search.

 

Reviewer Comment P 2.7 — It is desirable to apply this method to other varieties of combination opti- mization problems in the real world.

Response: Thank you very much for pointing out this shortcoming. We have actually tried to transfer this algorithm to a suitable real-world problem (e.g., basketball tournament scheduling, automotive manufacturing, nurse scheduling, vehicle routing scheduling problem, etc.).

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper presents a hybrid method for global optimization. It combines multiple methods together to achieve better results.

The facts behind the chosen methods are not clear and the hybrid approach is more of choosing multiple methods to work in series with hoping for better results. For example, It is mentioned in the introduction that CSA is superior and quicker than PSO and some references are provided to support that fact. The authors still choose to compare their hybrid method with PSO to support their contribution.

Also, hybrid techniques are usually chosen to counteract the limitations and weaknesses of the original technique. Authors did not clearly specify the weaknesses of the original CSA to come up with this hybrid technique. Therefore, more studies are needed on the original algorithm to identify the weaknesses and come up with a new technique to overcome the limitations. Then results can be presented to support that fact.

 

Author Response

Reviewer 3

 

Reviewer Comment P 3.1 — The facts behind the chosen methods are not clear and the hybrid approach is more of choosing multiple methods to work in series with hoping for better results. For example, It is mentioned in the introduction that CSA is superior and quicker than PSO and some references are provided to support that fact. The authors still choose to compare their hybrid method with PSO to support their contribution.

Response: Thank you very much for pointing out this shortcoming. The PSO is the most popular nature-inspired swarm-based intelligence algorithm, but it is prone to premature convergence, especially when approaching local optima that are difficult to escape. Therefore, a sufficiently high particle diversity must be maintained to avoid premature convergence. The crow search algorithm (CSA) is a recently proposed swarm-based intelligence algorithm based on the intelligent behavior of crows, which only contains the two parameters determined based on the awareness probability and flight length parameters. In addition, the equation of the CSA is more  than the PSO because of the CSA without the velocity vector.

However, although we propose the NEH-based algorithm as the initial algorithm and the SA-based VNS algorithm as the local search, the two PSO-based algorithms (i.e., PSOVNS and PSOMA) also adapt the NEH- and VNS-based algorithms in their contribution. In fact, the main motivation of this study is to know what kind of NEH-based algorithm is suitable for the original CSA algorithm and determine if the SA-based VNS local search can improve the performance.

The simulation result showed the suitable NEH-based algorithm (NEHLJP) as the initial algorithm, and that the SA-based algorithm can improve the limitation of the results.

The future work will involve implementing a new NEH algorithm based on the NEHLJP strategy and a new local search strategy based on the Le´vy searching strategy instead of the VNA-based algorithm.

 

Reviewer Comment P 3.2 — Also, hybrid techniques are usually chosen to counteract the limitations and weaknesses of the original technique. Authors did not clearly specify the weaknesses of the original CSA to come up with this hybrid technique. Therefore, more studies are needed on the original algorithm to identify the weaknesses and come up with a new technique to overcome the limitations. Then results can be presented to support that fact.

Response: Thank you very much for pointing out this shortcoming. The performance of a CSA is controlled by two parameters, flight length f L and awareness probability AP, and it is often being trapped in local optima as well as the PSO algorithm. In addition, the challenge of the CSA is to find a suitable process for transferring the continuous optimization problems to the combination optimization problem. Thus, according to this reason and the following paper, we have designed the similarity environment to adapt the CSA with the NEH-based algorithm and the SA-based VNS local search strategy.

 

We have also surveyed some state-of-the-art papers to improve our original one. We will adapt these studies to improve the original CSA algorithm in the future.

Abdelaziz, A.Y.; Fathy, A. A novel approach based on crow search algorithm for optimal selection of conductor size in radial distribution networks. Engineering Science and Technology, an International Journal 2017, 20, 391402.

Jain, M.; Rani, A.; Singh, V. An improved Crow Search Algorithm for high-dimensional problems. Journal of Intelligent & Fuzzy Systems 2017, 33, 35973614

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Authors fairly addressed my questions and concerns. I Don't see any issue publishing the paper in current form.