多目標優化擁擠距離計算

覺得有用的話,歡迎一起討論相互學習~

• 擁擠距離主要是維持種群中個體的多樣性。具體而言，一般來說是指種群按照支配關系進行非支配排序后,單個Rank層中個體的密集程度。常用於支配關系的多目標算法中，例如NSGA-II.

• 主要步驟如下：

  1. 取單個前沿中個體按照一個目標上的值從小到大排序
  2. 將最大目標值作為max,最小目標值保留作為min。並且這兩個極值點的擁擠距離都被設置為inf即無窮大。 因此注意，一個層中可能有多個具有inf的點，即如果層中有多個點在至少一個目標上相等，並且最大或最小，那么這些點的擁擠距離都是無窮大！！因為目標上呈現垂直的關系也是屬於非支配的關系！！如果出現這種情況，說明你算法的多樣性很爛！~或者在某些算法早期可能出現這種情況
  3. 在這個目標上計算每個個體最相鄰個體之間的距離，即i-1和i+1的目標值的差。並使用max和min對次值進行歸一化。
  4. 遍歷目標，將目標上已經歸一化的擁擠距離相加。
  5. 進入下一層front前沿
  6. 擁擠距離越大越好，最后按照擁擠距離重新排序各層，進而排序種群

matlab

function CrowdDis = CrowdingDistance(PopObj)
% Calculate the crowding distance of each solution in the same front

    [N,M]    = size(PopObj);

    CrowdDis = zeros(1,N);
    Fmax     = max(PopObj,[],1);
    Fmin     = min(PopObj,[],1);
    for i = 1 : M
        [~,rank] = sortrows(PopObj(:,i));
        CrowdDis(rank(1))   = inf;
        CrowdDis(rank(end)) = inf;
        for j = 2 : N-1
            CrowdDis(rank(j)) = CrowdDis(rank(j))+(PopObj(rank(j+1),i)-PopObj(rank(j-1),i))/(Fmax(i)-Fmin(i));
        end
    end
end

jmetal

public void crowdingDistanceAssignment(SolutionSet solutionSet, int nObjs) {
        int size = solutionSet.size();

        if (size == 0)
            return;

        if (size == 1) {
            solutionSet.get(0).setCrowdingDistance(Double.POSITIVE_INFINITY);
            return;
        } // if

        if (size == 2) {
            solutionSet.get(0).setCrowdingDistance(Double.POSITIVE_INFINITY);
            solutionSet.get(1).setCrowdingDistance(Double.POSITIVE_INFINITY);
            return;
        } // if

        // Use a new SolutionSet to evite alter original solutionSet
        SolutionSet front = new SolutionSet(size);
        for (int i = 0; i < size; i++) {
            front.add(solutionSet.get(i));
        }

        for (int i = 0; i < size; i++)
            front.get(i).setCrowdingDistance(0.0);

        double objetiveMaxn;
        double objetiveMinn;
        double distance;

        for (int i = 0; i < nObjs; i++) {
            // Sort the population by Obj n
            front.sort(new ObjectiveComparator(i));
            objetiveMinn = front.get(0).getObjective(i);
            objetiveMaxn = front.get(front.size() - 1).getObjective(i);

            // Set de crowding distance
            front.get(0).setCrowdingDistance(Double.POSITIVE_INFINITY);
            front.get(size - 1).setCrowdingDistance(Double.POSITIVE_INFINITY);

            for (int j = 1; j < size - 1; j++) {
                distance = front.get(j + 1).getObjective(i) - front.get(j - 1).getObjective(i);
                distance = distance / (objetiveMaxn - objetiveMinn);
                distance += front.get(j).getCrowdingDistance();
                front.get(j).setCrowdingDistance(distance);
            } // for
        } // for
    } // crowdingDistanceAssing