Enhancing Multi-Objective Optimization with Automatic Construction of Parallel Algorithm Portfolios

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The reviewer finds your paper presents very interesting results.

 

But why are the equation numbers (4) and (5) after (6) through (9)?

The reviewer thinks this is something that should be corrected.

 

In this paper, we explore the use of various evolutionary algorithms in parallel to automatically search for optimal solutions in multi-objective optimization problems. While such an approach can be highly effective, it often demands significant computational resources. However, a noteworthy aspect of this paper is the introduction of a new evaluation metric, which appears to function effectively. Although the proposed method is experimental in nature, it has shown very promising results, suggesting its strong potential for current applications. On the other hand, there are some theoretical weaknesses regarding why the proposed method works so well. Nevertheless, evolutionary algorithms often present challenges when it comes to theoretical explanation. If they yield good results, they can be deemed effective in practice. As for the figures and tables, there are no issues, and I have no specific comments on them.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The authors propose to apply the  an embarassingly parallel  approach (PAP) to Multi-objective Optimization Problems. Briefly, the algorithm  runs all member algorithms independently in parallel to get multiple solutions. Then, the best solution will be taken  as the final output. This idea was already presented in literature. Its main difference from conventional PAPs  lies in the way of determining the final output. The authors propose a variant which  compare the solution sets found by member algorithms  (in parallel, without any syncronyzation)  and output the best solution set by using  the  Restructure  procedure . 

My comments are about the Restructure procedure. Could the authors provide more details on how this procedure operate?  Further, as the authors claim that they employs  parallel solution strategy such that it can utilize parallel computing architectures with ease,  I am wondering to know if Restructure is performed in parallel or in serial ? I understand that it is performed in serial. In this case, why do not the author implement the procedure in parallel? In this way, the algorithm could be actually parallel. Otherwise,  it is  simply embarassingly parallel.  

In Eq (1) n is the decision vector size and m is the objective space dimension. 

In Table 1 the notation is differfent. Dim is the dimension of the decision vector and M is the objective vector dimension. I ask for a clarification. 

In table 1 M is the objective vector dimension and in line 173 M is a performance metric too. I am quite confused with the simbols used in the article. 

 

Beside Table 7, it should be interesting to see the speed up of the parallel algorithm compared to the serial time. 

 

 

 

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

Theorem 1 & 2 should be called Definitions, not Theorems!

Only GA and DE are mentioned as MOEA approaches.  There are others, e.g., MOPSO, SPEA, PAES, EMOCA.  Minimally, these should be cited.  Ideally, comparisons should include some of these.

Plural of "offspring" is also "offspring", not "offsprings"

 

Author Response

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Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

In my previous report I asked to authors to plot the speed up not the execution time. The reason is that it is quite obvious that the overall time will be reduced but looking at the speed up they can understand that their approach is very inefficient in terms of paralle computing. If they try to compute the speedup from the execution times they will found that it is very low compared to the ideal values which should be around 16. 
As a conseguence, they cannot conclude that the algorithm is efficient. 
In conclusion, as the article focus on a parallel algorithm they should use the perdormance metrics of parallel algotrithms: speedup and efficiency. After that they should note that it is very important to parallelize also the Restructure procedure. Otherwise, if they do not intend to parallelize such procedure, they should highlight ( by analyzing the speedup and the efficiency) that their approach is not so effective ( in terms of parallel computing). It is just a frist tentative and naive solution. 

Finally, the authors can decide to not pa

Author Response

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Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

The article inherits reviewer’s comments