non-dominated sorting算法的matlab实现

实现了一个non-dominated sorting的算法，效率是最差的那种，但是感觉思路很清晰。先描述下思路吧：

1：对于全部的种群N，每一条染色体上的元素是这么个意思[决策变量 目标函数值 rank distance]，在这个地方我主要是设置rank，distance是另外步骤用的。

2：首先一个空的集合has_assigend_index 也就是已经找到rank的就挪到这里面来。

3：依次从第一个染色体开始，看看有没有已经被assigned，如果没有那就查看是否有别的dominate它，如果没有那么它就是non-dominate的了，设置当前的rank以及放入到has_assigned_index中去。一直到被全部放入到has_assigned_index。那么就完成了全部的rank的设置，并且同时还按照front的level的到对应的结果集，这个是用于distance的时候用的。

代码如下：
function [ chromosomes, fronts ] = nondominated_sorting( chromosomes, number_of_decision_variables, number_of_objectives )
% each chromosome contains four segments,[decision_variables,
% corresponding_objective_value, rank_of_front, crowding_distance].
% when this function is finished, rank of each chromosome will be assigned
% the third segment.
% Besides, a struct named “fronts” would be also got, it’s form is like
% this: fronts{i}=[chromosome1, ….], i is the rank of chromosome1…

V = number_of_decision_variables;
Q = number_of_objectives;
[M, N] = size(chromosomes);
F = 0;
fronts = [];
% once the chromosome i is assgned to the fronts, its’ index will be remove to
% has_assigned_index.
has_assigned_index = [];
F = 0;
while length(has_assigned_index) ~= M
length(has_assigned_index)
F = F + 1
fronts{F} = [];
for i = 1:M
dominate_i = [];
if isempty(find(has_assigned_index == i))
for j = 1:M
if (i ~= j) && (isempty(find(has_assigned_index == j)))
fprintf(‘compare %d, %d\n’, i, j);
less_count = 0;
equal_count = 0;
more_count = 0;
for k=V+1:V+Q
if chromosomes(i, k) < chromosomes(j, k)
less_count = less_count + 1;
elseif chromosomes(i, k) > chromosomes(j, k)
more_count = more_count + 1;
else
equal_count = equal_count + 1;
end
end
if (more_count > 0) && (less_count == 0)
% j dominates i
dominate_i = [dominate_i j];
end
end
end
if length(dominate_i) == 0
has_assigned_index = [has_assigned_index i];
chromosomes(i, end-1) = F;
fronts{F} = [fronts{F} i];
end
end
end

end