NSGA-II快速非支配排序算法理解

def fast_nondominated_sort( P ):
    F = [ ]
    for p in P:
        Sp = [ ]
         np = 0
         for q in P:
             if p > q:                #如果p支配q，把q添加到Sp列表中
                 Sp.append( q )
             else if p < q:        #如果p被q支配，则把np加1
                 np += 1
 
        if np == 0:
            p_rank = 1        #如果该个体的np为0，则该个体为Pareto第一级
      F1.append( p )
    F.append( F1 )
    i = 0
    while F[i]:
        Q = [ ]
        for p in F[i]:
            for q in Sp:        #对所有在Sp集合中的个体进行排序
                nq -= 1
                if nq == 0:     #如果该个体的支配个数为0，则该个体是非支配个体
                    q_rank = i+2    #该个体Pareto级别为当前最高级别加1。此时i初始值为0，所以要加2
                    Q.append( q )
        F.append( Q )
        i += 1

void population::nodominata_sort()
//求pareto解（快速非支配排序）
{
    int i,j,k;
    indivial H[2*popsize];
    int h_len=0;
    for(i=0;i<2*popsize;i++)
    {
        R[i].np=0;//支配个数np
        R[i].is_domied=0;//被支配的个数
        len[i]=0;//初始化
    }
    for(i=0;i<2*popsize;i++)
    {
        for(j=0;j<2*popsize;j++)
        {
            if(i!=j)//自己不能支配自身
            {
                if(is_dominated(R[i],R[j]))
                {
                    R[i].domi[R[i].is_domied++]=j;
                    //如果i支配j，把i添加到j的is_domied列表中
                }
                else if(is_dominated(R[j],R[i]))
                    R[i].np+=1;
                    //如果i被j支配，则把np加1
            }
        }
        if(R[i].np==0)//如果该个体的np为0，则该个体为Pareto第一级
        {
            len_f=1;
            F[0][len[0]++]=R[i];//将R[i]归并
        }
    }
    i=0;
    while(len[i]!=0)
    {
        h_len=0;
        for(j=0;j<len[i];j++)
        {
            for(k=0;k<F[i][j].is_domied;k++)
            //对所有在is_domied集合中的个体进行排序
            {
                R[F[i][j].domi[k]].np--;
                if( R[F[i][j].domi[k]].np==0)
                //如果该个体的支配个数为0，则该个体是非支配个体
                {
                    H[h_len++]=R[F[i][j].domi[k]];
                    R[F[i][j].domi[k]].rank=i+1;
                }
            }
        }
        i++;
        len[i]=h_len;
        if(h_len!=0)
        {
            len_f++;
            for(j=0;j<len[i];j++)
            {
                F[i][j]=H[j];
            }
        }
    }
}

%-------非支配排序        
 
        fnum=0;                                             %当前分配的前沿面编号
        cz=false(1,size(functionvalue,1));                  %记录个体是否已被分配编号
        frontvalue=zeros(size(cz));                         %每个个体的前沿面编号
        [functionvalue_sorted,newsite]=sortrows(functionvalue);    %对种群按第一维目标值大小进行排序
        while ~all(cz)                                      %开始迭代判断每个个体的前沿面,采用改进的deductive sort
            fnum=fnum+1;
            d=cz;
            for i=1:size(functionvalue,1)
                if ~d(i)
                    for j=i+1:size(functionvalue,1)
                        if ~d(j)
                            k=1;                            
                            for m=2:size(functionvalue,2)
                                if functionvalue_sorted(i,m)>functionvalue_sorted(j,m)
                                    k=0;
                                    break
                                end
                            end
                            if k
                                d(j)=true;
                            end
                        end
                    end
                    frontvalue(newsite(i))=fnum;
                    cz(i)=true;
                end
            end
        end