非支配排序算法通用MATLAB代码

dapmood · 发表于 2020-10-15 15:22

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规模为N的种群中的每个个体都要针对M个目标函数和种群中的N-1个个体进行比较，复杂度为O(MN)，因此种群中的N个个体都比较结束的复杂度为O(MN2)，即每进行一次Pareto分级的时间复杂度为O(MN2)。

该算法需要保存两个量：

(1).支配个数np。该量是在可行解空间中可以支配个体p的所有个体的数量。

(2).被支配个体集合SP。该量是可行解空间中所有被个体p支配的个体组成的集合。

matlab代码：

（注意PopObj填入的多目标的函数值，如果有两个目标，100个个体，那么就是100*2的矩阵，nSort是前沿面的编号）

function [FrontNO,MaxFNO] = NDSort(PopObj,nSort)
%NDSort - Do non-dominated sorting on the population by ENS
%
% FrontNO = NDSort(A,s) does non-dominated sorting on A, where A is a
% matrix which stores the objective values of all the individuals in the
% population, and s is the number of individuals being sorted at least.
% FrontNO(i) means the number of front of the i-th individual.
%
% [FrontNO,K] = NDSort(...) also returns the maximum number of fronts,
% except for the value of inf.
%
% In particular, s = 1 stands for find only the first non-dominated
% front, s = size(A,1)/2 stands for sort only half of the population
% (which is often used in the algorithm), and s = inf stands for sort the
% whole population.
%
% Example:
% [FrontNO,MaxFNO] = NDSort(PopObj,1)
[N,M] = size(PopObj);
FrontNO = inf(1,N);
MaxFNO = 0;
[PopObj,rank] = sortrows(PopObj);
while sum(FrontNO<inf) < min(nSort,N)
MaxFNO = MaxFNO + 1;
for i = 1 : N
if FrontNO(i) == inf
Dominated = false;
for j = i-1 : -1 : 1
if FrontNO(j) == MaxFNO
m = 2;
while m <= M && PopObj(i,m) >= PopObj(j,m)
m = m + 1;
end
Dominated = m > M;
if Dominated || M == 2
break;
end
end
end
if ~Dominated
FrontNO(i) = MaxFNO;
end
end
end
end
FrontNO(rank) = FrontNO;
end
2 a2 ]3 I; j+ x/ @

youOK · 发表于 2020-10-15 16:16

非支配排序算法通用MATLAB代码

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非支配排序算法通用MATLAB代码

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