Revision.txt

REVIEW NO. 1

Comments to the authors:
    Analysis and Enhancement of the Simulated Binary Crossover*

    The paper presents a new extesion to Simulated Binary Crossover (SBX) 
    considering the stopping criterion to alter its internal operation.

    The subject is interesting and the obtained results show a satisfactory 
    perspective, but several language errors were found. Such as:

    * Whole paper:
        * Syllable division problem;
        * Change:
#            * "table X" by "Table X";
#            * "equation X" by "Equation X";
#            * "figure X" by "Figure X";
#            * "algorithm X" by "Algorithm X";    

    * The paper is not so easy to read - reorganize the Tables, Figures, Results 
    and so on. For example: The citation of Table III appears before the citation 
    of Table I.

    * Abstract - "Experimental validation shows a significant improvement in the 
    performance of all the MOEAs when applying". How much better?

    * Change:
#        * "Implementation and analyses of the SBX operator:" by "Implementation and 
    analyses of SBX operator:";
#        * "this section is discussed the principal characteristics of the SBX 
#    operator. Essentially, the behavior of the operator is" by "this section 
#    discusses the principal characteristics of SBX operator. Essentially, the 
#    behavior of operator is";
#        * "best results than the Case 1, Case 2 and Case 3," by "best results than 
#    Case 1, Case 2 and Case 3,".

    * Redo the phrase:
        * "due that it provides a rotationally";
        * "is suitable for due that few decisions".

    * "35 independent executions". Explain about used random seeds.

#    * "In order to analyze the performance of each Case (Case 5 is ignored)". Why?

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REVIEW NO. 2

Comments to the authors:
    * Some comments on practical applications and non-stationary objective functions
    are desirable.
    * There are quite number of awkward expressions (and also misspellings) in this
    manuscript, and it is not at the international conference quality.  So, this
    reviewer *strongly* recommends to the authors that this manuscript should be
    proofread by a native speaker of English.

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REVIEW NO. 3

Comments to the authors:
    This paper presents an analysis of the performance of the Simulated Binary Crossover (SBX) 
    recombination operator in response to annealing the effect of the SBX operator. Three 
    methods for annealing over generations are tested: 1) increasing the probability that a value is 
    copied unchanged from its parent, 2) decreasing the probability that values are exchanged 
    between parents, and 3) by increasing the distribution index parameter (which effectively 
    decreases the noise introduced during crossover). All methods effectively change the 
    operator from exploration to exploitation over generations by inducing smaller and fewer 
    changes to the individuals. Based on this analysis, a novel recombination operator is 
    suggested that combines decreasing the probability of exchanging values between parents 
    with increasing the distribution index parameter. Results show that the new recombination 
    operator outperforms regular SBX in three different multi-objective algorithms (NSGA-II, 
    MOEA/D, and SMS-EMOA) on the DTLZ, WFG, and UF benchmarks.

    The idea of annealing the mutation or recombination operators is not new [1], and dynamically 
    changing the effect of SBX has been examined in terms of self-adaptation [2], but I am not 
    familiar with any work annealing the SBX operator at a steady rate, or specifically focussing on 
    its effect in a multi-objective domain. As such, examining the effect of linearly annealing the 
    impact of the SBX recombination operator in a multi-objective domain is the main contribution 
    of this paper.

    Unfortunately, the paper is difficult to read an understand because it contains many grammar 
    errors and unclear writing (see "Grammar comments" below for examples from the first page 
    of the paper). As a result, I am unable to properly evaluate the contribution of the paper and I 
    can provide only a few comments with respect to the actual content of the paper (see "Other 
    comments" below).  I would suggest rewriting the paper with the help of a native English 
    speaker. Sadly, I have to recommend to reject this paper, not because of its scientific content 
    (which I can not evaluate), but because of its writing.  


    Other comments:

##    "The Pareto dominance is defined as the set of the best solutions that are not dominated by 
    any feasible solution."
#    - I have seen the set of "solutions that are not dominated by any feasible solution" referred to 
#    as the Pareto front, the Pareto frontier, or the Pareto set, but never as the Pareto dominance. 
#    Pareto dominance generally refers to the dominance relationship itself, not the set of solutions 
#    that may be defined by such a relationship.

 #   "A current version is the NSGA-III which is designed to deal with many-objective problems 
 #   [14]."
 #   - Reference 14 does not refer to NSGA-III. Based on the references provided, I can not verify 
 #   whether NSGA-III is indeed effective at dealing with many-objective problems.

    - With respect to the explanation of Pareto dominance and the Pareto front, the term Pareto 
    front is often used to define the set of non-dominated solutions within a set of solutions (and I 
    do not believe this is incorrect; if the set of solutions is considered the system, the set of non-
    dominated solutions form the Pareto front within that system). As such, following Deb. et al 
    [3], I would recommend referring to the Pareto front of the entire optimization problem as the 
    true Pareto front or true Pareto-optimal front instead. 

#    - Equation 4 seems to contain an error where n is written while it should have been nc.

#    "A very used variant of the MOEA/D is the MOEA/D-DE, which use the DE operators [15] and 
#    the polynomial mutation operator [16] in the reproduction phase, also it has two extra 
#    measures for maintaining the population diversity [17]. However, these two extra mechanisms 
#    are not enough to deal with long-term executions."
#    - There is no reference added to the final sentence. Is there any literature demonstrating that 
#    these two mechanisms are indeed insufficient when the algorithm is run for many 
#    generations?

    - Tables I, II, and II are mentioned in section III, but how to read them is not explained until 
    section IV.

    "Crossover is one of the most important operators in EAs."
    - Debatable. There exist many EAs that solely rely on mutation operators instead. 


    Grammar comments:

#    "our proposal are"
#    - Should be: "our proposal is".

#    "where is not suitable a deterministic approach."
#    - A better ordering would be: "where a deterministic approach is not suitable."

#    "indicate a decision variable"
#    - Should be: "indicates a decision variable"

#    "n correspond to"
#    - Should be: "n corresponds to"

#    "Particularly, a MOP which consists in minimization of"
#    - It should be "consists of" rather than "consists in", though I don't think "consists" is actually 
#    the right term to use in this context.

#    "Accordingly this"
#    - Should just be: "Accordingly"

#    "if does not exist any"
#    - Should be: "if there does not exist any"

#    "The Pareto set correspond"
#    - Should be: "The Pareto set corresponds"

#    "Therefore is required to obtain diverse and converged solutions among the Pareto front."
#    - "Therefore is" should be: "Therefore it is" and "required" should probably be replaced with 
#    "necessary".

#    "these representative methods are considered as ththat can bee state-of-the-art."
#    - "ththat can bee" should be removed.

#    "and has showed a better performance"
#    - Should be: "and has shown a better performance"

#    "To deal with this issues"
#    - Should be: "To deal with these issues"


    References:

    [1] Lin, Wen-Yang, Wen-Yung Lee, and Tzung-Pei Hong. "Adapting crossover and mutation 
    rates in genetic algorithms." J. Inf. Sci. Eng. 19.5 (2003): 889-903.

    [2] Deb, Kalyanmoy, and Hans-Georg Beyer. "Self-adaptation in real-parameter genetic 
    algorithms with simulated binary crossover." Proceedings of the 1st Annual Conference on 
    Genetic and Evolutionary Computation-Volume 1. Morgan Kaufmann Publishers Inc., 1999.

    [3] Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE 
    transactions on evolutionary computation 6.2 (2002): 182-197.