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Jmetal和PlatEMO中计算IGD时的结果差异

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• 如果你不知道IGD是如何计算的，欢迎查看原先的博文IGD反转世代距离-多目标优化评价指标概念及实现

最近的实验过程中，发现即使是同样的种群，在PlatEMO和Jmetal上计算有差异，大概Jmetal比PlatEMO上少一个 数量级

Jmetal Code

public double invertedGenerationalDistance(double [][] front,
                                     double [][] trueParetoFront,
                                     int numberOfObjectives) {

    /**
     * Stores the maximum values of true pareto front.
     */
    double [] maximumValue ;

    /**
     * Stores the minimum values of the true pareto front.
     */
    double [] minimumValue ;

    /**
     * Stores the normalized front.
     */
    double [][] normalizedFront ;

    /**
     * Stores the normalized true Pareto front.
     */
    double [][] normalizedParetoFront ;

    // STEP 1. Obtain the maximum and minimum values of the Pareto front
    maximumValue = utils_.getMaximumValues(trueParetoFront, numberOfObjectives);
    minimumValue = utils_.getMinimumValues(trueParetoFront, numberOfObjectives);

    // STEP 2. Get the normalized front and true Pareto fronts
    normalizedFront       = utils_.getNormalizedFront(front,
    		                                          maximumValue,
    		                                          minimumValue);
    normalizedParetoFront = utils_.getNormalizedFront(trueParetoFront,
    		                                          maximumValue,
    		                                          minimumValue);

    // STEP 3. Sum the distances between each point of the true Pareto front and
    // the nearest point in the true Pareto front
    double sum = 0.0;
    for (double[] aNormalizedParetoFront : normalizedParetoFront)
      sum += Math.pow(utils_.distanceToClosedPoint(aNormalizedParetoFront,
              normalizedFront),
              pow_);


    // STEP 4. Obtain the sqrt of the sum
    sum = Math.pow(sum,1.0/pow_);

    // STEP 5. Divide the sum by the maximum number of points of the front
    double generationalDistance = sum / normalizedParetoFront.length;

    return generationalDistance;
  } // generationalDistance

PlatEMO Code

function score = IGD(Population,optimum)
% <min>
% Inverted generational distance

%------------------------------- Reference --------------------------------
% C. A. Coello Coello and N. C. Cortes, Solving multiobjective optimization
% problems using an artificial immune system, Genetic Programming and
% Evolvable Machines, 2005, 6(2): 163-190.
%------------------------------- Copyright --------------------------------
% Copyright (c) 2021 BIMK Group. You are free to use the PlatEMO for
% research purposes. All publications which use this platform or any code
% in the platform should acknowledge the use of "PlatEMO" and reference "Ye
% Tian, Ran Cheng, Xingyi Zhang, and Yaochu Jin, PlatEMO: A MATLAB platform
% for evolutionary multi-objective optimization [educational forum], IEEE
% Computational Intelligence Magazine, 2017, 12(4): 73-87".
%--------------------------------------------------------------------------

    PopObj = Population.best.objs;
    if size(PopObj,2) ~= size(optimum,2)
        score = nan;
    else
        score = mean(min(pdist2(optimum,PopObj),[],2));
    end
end

二者区别

1. Jmetal 在STEP1中对于True PF和Obtain PF都做了归一化操作 而 PlatEMO中对于PF和obtain PF没有进行归一化操作
2. Jmetal在STEP3和STEP4中，IGD的计算是模仿GD的计算，假设用a表示True上的点对Obtain上获得的点的最近距离，则两者的差异在于
3. 两者的参考文献不同 Jmetal - Reference: Van Veldhuizen, D.A., Lamont, G.B.: Multiobjective Evolutionary Algorithm Research: A History and Analysis. Technical Report TR-98-03, Dept. Elec. Comput. Eng., Air Force Inst. Technol. (1998) PlatEMO - C. A. Coello Coello and N. C. Cortes, Solving multiobjective optimization problems using an artificial immune system, Genetic Programming and Evolvable Machines, 2005, 6(2): 163-190.

改进Jmetal

• 如果你想要Jmetal和PlatEMO中算的一致，可以使用以下经过调整的代码

    public double invertedGenerationalDistance(double[][] front,
                                               double[][] trueParetoFront,
                                               int numberOfObjectives) {

        /**
         * Stores the maximum values of true pareto front.
         */
        double[] maximumValue;

        /**
         * Stores the minimum values of the true pareto front.
         */
        double[] minimumValue;

        /**
         * Stores the normalized front.
         */
        double[][] normalizedFront;

        /**
         * Stores the normalized true Pareto front.
         */
        double[][] normalizedParetoFront;

        normalizedFront = front;
        normalizedParetoFront = trueParetoFront;


//    // STEP 3. Sum the distances between each point of the true Pareto front and
//    // the nearest point in the true Pareto front
//    double sum = 0.0;
//    for (double[] aNormalizedParetoFront : normalizedParetoFront)
//      sum += Math.pow(utils_.distanceToClosedPoint(aNormalizedParetoFront,
//                      normalizedFront),
//              pow_);
//
//
//    // STEP 4. Obtain the sqrt of the sum
//    sum = Math.pow(sum,1.0/pow_);

        double sum = 0.0;
        for (double[] aNormalizedParetoFront : normalizedParetoFront)
            sum += utils_.distanceToClosedPoint(aNormalizedParetoFront,
                    normalizedFront);


        // STEP 5. Divide the sum by the maximum number of points of the front
        double generationalDistance = sum / normalizedParetoFront.length;

        return generationalDistance;
    } // generationalDistance