U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm

Round  1

Reviewer 1 Report

The paper “U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm” describes metaheuristic methods for solving the U-shaped Assembly Line Balancing Problem. The content of the paper is adequate for the purposes of the journal.

Title: The title of the paper is informative. It includes important terms and the message of the article.

Abstract: The abstract describes the context and provide a general picture of the methodological approach.

Keywords: Keywords are well chosen.

Introduction: Introduction defines the focus and the research questions. It does not explain the structure of the text. Please add a paragraph including the structure of the text.

Literature review: The literature review support to understand the correlation of presented research results with literature. A summary table comparing the contributions could support the explanation. I advise to include some articles focusing on other application of metaheuristic algorithms in the field of in-plant logistics and supply chain (see 10.4028/www.scientific.net/SSP.261.503 or 10.1155/2018/5180156).

Mathematical model. The mathematical model is extensively discussed. Some minor comment:

Line 263: write “if station…” instead of “station”

Equation 3: please check: j=1..M. Is it true?

Algorithm. The algorithm is extensively described. The key functionality has been explained and the computer application for implementation is revealed. The details of software engineering part are interesting for anyone aiming to replicate the implementation (pseu-code). Minor remarks:

 I would change the sequence of the three genetic operators in Figure 3: selection, recombination and mutation.

Why have you chosen the binomial crossover? Please, add a one sentence explanation, if suitable.

Line 351: What “Improved Diff.” means?

Results. Results are clear and adequate.

Conclusions. Conclusions are clear. Implications, limitations and future research directions are discussed. In addition, what kind of lesson emerges from the paper for managers, if any?

Author Response

(Reviewer 1)

2.) Literature review, revised by adding in page 3.

4.) Algorithm, 4.1)  From the literature and related research studies Step DE algorithm composes of four main steps: 1. initialization, 2. mutation 3. recombination and 4. selection process.

4.3) What “Improved Diff.”, revised by adding in page 13.

   Conclusions, revised by adding in page 20.

Reviewer 2 Report

Authors have studied the application of DE algorithm to U-Shaped assembly line balancing problems. The idea is interested but the practical significance is missing in the manuscript. There is a need to improve the manuscript seriously to get in a more profitable way to the readers. The following points should be included into the manuscript

1) In Abstract, line 1-4, authors should split into two sentences.  Also, the last two lines in the abstract should be redefined in a more collaborative ways.

2) In page 2, line 65, authors should cite the following references to support the text “Many researchers have developed methods exact and metaheuristic…. A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478, 499-523, 2019. (b) A hybrid PSO – GA algorithm for constrained optimization problems, Applied Mathematics and Computation, Elsevier, 274, 292 – 305, 2016 (b) Solving structural Engineering Design Optimization Problems using an artificial bee colony algorithm, Journal of Industrial and Management Optimization,10(3), 777 – 794, 2014 (c) A hybrid GA-GSA algorithm for optimizing the performance of an industrial system by utilizing uncertain data, Handbook of Research on Artificial Intelligence Techniques and Algorithms, (pp. 620 - 654), 2015,  doi: 10.4018/978-1-4666-7258-1.ch020

3) In the last paragraph of the introduction section, authors should state the objective of the work clearly.

4) The author should indicate why DE algorithms have been used in the present manuscript instead of other meta-heuristic algorithms. Further, authors should explain what are the advantages of it with respect to other algorithms.

5) The introduction should be enhanced. For it, authors should add all the following references into the introduction section for better readability and minimizing the gap between the presented study and existing study related to metaheuristic techniques. (a) Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system, Journal of Manufacturing Systems, 33(2), 353 – 367, 2014 (b) Reliability, availability and maintainability analysis of industrial systems using PSO and fuzzy approach, MAPAN – Journal of Metrology Society of India, 29(2), 115 – 129, 2014 (c) An efficient biogeography based optimization algorithm for solving reliability optimization problems, Swarm and Evolutionary Computation, Elsevier, 24, 1 – 10 2015 (d) An approach for solving constrained reliability-redundancy allocation problems using Cuckoo search algorithm, Beni-Suef University, Journal of Basic and Applied Science, 4, 14 – 25, 2015, Elsevier.

6) In Sections authors does not provide values for all parameters mentioned in the approach. Moreover, nothing is mentioned about how different parameter values are chosen.

7) In the result section, authors have presented their computed results in the form of Table only, but fail to explain the significance of the approach. Authors need to address it by explaining the computed results into the result and discussion.

8) The conclusions are quite poor. I suggest including some managerial insights, the limitations of the proposal, and some suggestions for the future research agenda.

9) The language of the paper needs to be polished, as there are several error and mistakes in the manuscript.

10)  Reference section need to be updated with the suggested articles. Also it is seen that articles cited in the manuscript is very old. Authors should update the references from year 2016-2018 articles.

Author Response

(Reviewer 2)

2.) Introduction, revised  by  adding the following references to support the text Many researchers have developed methods exact and metaheuristic in page 2, line 64,74.

4.)5.) Introduction, revised  by  adding  the  following references in to the introduction section for better readability and minimizing the gap between the presented study and existing study related to metaheuristic techniques. in page 2, line 74.

These suitable variables were set from the experiment from following references to the support paper. in page 8, line 305.

8.) The conclusions, revised by adding last paragraph in page 20.

10.) Reference, revised by adding update the references in page 21.

Round  2

Reviewer 2 Report

Section 4, description of DE algorithm is not impressive. There is a need to present a complete description for the reader about the DE algorithm in this field.  See Ref. [30] for the complete write-up.

Create a separate section from 4.1 onwards.

In section 4.1.2., authors have presented improved DE by applying Eqs. (9)- (12), but they failed to explain how they defined and what are the improvement of it from the standard DE.

Since the DE or such algorithm start with the random number generation within the domain, so what are the procedures chosen to eliminate its discrepancy during each run.

In the last lines of the conclusion section, authors should add the references which support the future research work.

As the presented work is on DE, but it is very strange to see that the base papers of DE are missing in the manuscript.

There is a certain error in the Reference section. For instance, in Ref. [5], year is 2019 instead of 2018. Check all other references and its formatting. 

Author Response

(Reviewer 2)

1.) Section 4, present a complete description  the DE algorithm and  create a separate section from 4.1  

revised by adding in page 7, line 289.

2.) Section 4.1.2, authors have presented improved DE by applying Eqs. (9)- (12), but they failed to explain how they defined and what are the improvement of it from the standard  DE. Since the DE or such algorithm start with the random number generation within the domain, so what are the procedures chosen to eliminate its discrepancy during each run. 

revised by adding in page 11, line 381-399.

3.) In the last lines of the conclusion section, authors should add the references which support the future research work. 

revised by adding in page 20, line 541.

4.) Reference section, For instance, in Ref. [5], year is 2019 instead of 2018. Check all other references and its formatting. 

revised by adding in page 20-22.