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