Jmetal和PlatEMO中计算IGD时的结果差异

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

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

    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