📄 non_domination_sort_mod.html
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<title>Non-Donimation Sort</title>
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<h1>Non-Donimation Sort</h1>
<p>This function sort the current popultion based on non-domination. All the individuals in the first front are given a rank
of 1, the second front individuals are assigned rank 2 and so on. After assigning the rank the crowding in each front is calculated.
</p><pre class="codeinput">[N,M] = size(x);
<span class="keyword">switch</span> problem
<span class="keyword">case</span> 1
M = 2;
V = 6;
<span class="keyword">case</span> 2
M = 3;
V = 12;
<span class="keyword">end</span>
front = 1;
<span class="comment">% There is nothing to this assignment, used only to manipulate easily in</span>
<span class="comment">% MATLAB.</span>
F(front).f = [];
individual = [];
<span class="keyword">for</span> i = 1 : N
<span class="comment">% Number of individuals that dominate this individual</span>
individual(i).n = 0;
<span class="comment">% Individuals which this individual dominate</span>
individual(i).p = [];
<span class="keyword">for</span> j = 1 : N
dom_less = 0;
dom_equal = 0;
dom_more = 0;
<span class="keyword">for</span> k = 1 : M
<span class="keyword">if</span> (x(i,V + k) < x(j,V + k))
dom_less = dom_less + 1;
<span class="keyword">elseif</span> (x(i,V + k) == x(j,V + k))
dom_equal = dom_equal + 1;
<span class="keyword">else</span>
dom_more = dom_more + 1;
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">if</span> dom_less == 0 & dom_equal ~= M
individual(i).n = individual(i).n + 1;
<span class="keyword">elseif</span> dom_more == 0 & dom_equal ~= M
individual(i).p = [individual(i).p j];
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">if</span> individual(i).n == 0
x(i,M + V + 1) = 1;
F(front).f = [F(front).f i];
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="comment">% Find the subsequent fronts</span>
<span class="keyword">while</span> ~isempty(F(front).f)
Q = [];
<span class="keyword">for</span> i = 1 : length(F(front).f)
<span class="keyword">if</span> ~isempty(individual(F(front).f(i)).p)
<span class="keyword">for</span> j = 1 : length(individual(F(front).f(i)).p)
individual(individual(F(front).f(i)).p(j)).n = <span class="keyword">...</span>
individual(individual(F(front).f(i)).p(j)).n - 1;
<span class="keyword">if</span> individual(individual(F(front).f(i)).p(j)).n == 0
x(individual(F(front).f(i)).p(j),M + V + 1) = <span class="keyword">...</span>
front + 1;
Q = [Q individual(F(front).f(i)).p(j)];
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
front = front + 1;
F(front).f = Q;
<span class="keyword">end</span>
[temp,index_of_fronts] = sort(x(:,M + V + 1));
<span class="keyword">for</span> i = 1 : length(index_of_fronts)
sorted_based_on_front(i,:) = x(index_of_fronts(i),:);
<span class="keyword">end</span>
current_index = 0;
<span class="comment">% Find the crowding distance for each individual in each front</span>
<span class="keyword">for</span> front = 1 : (length(F) - 1)
objective = [];
distance = 0;
y = [];
previous_index = current_index + 1;
<span class="keyword">for</span> i = 1 : length(F(front).f)
y(i,:) = sorted_based_on_front(current_index + i,:);
<span class="keyword">end</span>
current_index = current_index + i;
<span class="comment">% Sort each individual based on the objective</span>
sorted_based_on_objective = [];
<span class="keyword">for</span> i = 1 : M
[sorted_based_on_objective, index_of_objectives] = <span class="keyword">...</span>
sort(y(:,V + i));
sorted_based_on_objective = [];
<span class="keyword">for</span> j = 1 : length(index_of_objectives)
sorted_based_on_objective(j,:) = y(index_of_objectives(j),:);
<span class="keyword">end</span>
f_max = <span class="keyword">...</span>
sorted_based_on_objective(length(index_of_objectives), V + i);
f_min = sorted_based_on_objective(1, V + i);
y(index_of_objectives(length(index_of_objectives)),M + V + 1 + i)<span class="keyword">...</span>
= Inf;
y(index_of_objectives(1),M + V + 1 + i) = Inf;
<span class="keyword">for</span> j = 2 : length(index_of_objectives) - 1
next_obj = sorted_based_on_objective(j + 1,V + i);
previous_obj = sorted_based_on_objective(j - 1,V + i);
<span class="keyword">if</span> (f_max - f_min == 0)
y(index_of_objectives(j),M + V + 1 + i) = Inf;
<span class="keyword">else</span>
y(index_of_objectives(j),M + V + 1 + i) = <span class="keyword">...</span>
(next_obj - previous_obj)/(f_max - f_min);
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
distance = [];
distance(:,1) = zeros(length(F(front).f),1);
<span class="keyword">for</span> i = 1 : M
distance(:,1) = distance(:,1) + y(:,M + V + 1 + i);
<span class="keyword">end</span>
y(:,M + V + 2) = distance;
y = y(:,1 : M + V + 2);
z(previous_index:current_index,:) = y;
<span class="keyword">end</span>
f = z();
</pre><p class="footer"><br>
Published with MATLAB® 7.0<br></p>
<!--
##### SOURCE BEGIN #####
%% Non-Donimation Sort
% This function sort the current popultion based on non-domination. All the
% individuals in the first front are given a rank of 1, the second front
% individuals are assigned rank 2 and so on. After assigning the rank the
% crowding in each front is calculated.
[N,M] = size(x);
switch problem
case 1
M = 2;
V = 6;
case 2
M = 3;
V = 12;
end
front = 1;
% There is nothing to this assignment, used only to manipulate easily in
% MATLAB.
F(front).f = [];
individual = [];
for i = 1 : N
% Number of individuals that dominate this individual
individual(i).n = 0;
% Individuals which this individual dominate
individual(i).p = [];
for j = 1 : N
dom_less = 0;
dom_equal = 0;
dom_more = 0;
for k = 1 : M
if (x(i,V + k) < x(j,V + k))
dom_less = dom_less + 1;
elseif (x(i,V + k) == x(j,V + k))
dom_equal = dom_equal + 1;
else
dom_more = dom_more + 1;
end
end
if dom_less == 0 & dom_equal ~= M
individual(i).n = individual(i).n + 1;
elseif dom_more == 0 & dom_equal ~= M
individual(i).p = [individual(i).p j];
end
end
if individual(i).n == 0
x(i,M + V + 1) = 1;
F(front).f = [F(front).f i];
end
end
% Find the subsequent fronts
while ~isempty(F(front).f)
Q = [];
for i = 1 : length(F(front).f)
if ~isempty(individual(F(front).f(i)).p)
for j = 1 : length(individual(F(front).f(i)).p)
individual(individual(F(front).f(i)).p(j)).n = ...
individual(individual(F(front).f(i)).p(j)).n - 1;
if individual(individual(F(front).f(i)).p(j)).n == 0
x(individual(F(front).f(i)).p(j),M + V + 1) = ...
front + 1;
Q = [Q individual(F(front).f(i)).p(j)];
end
end
end
end
front = front + 1;
F(front).f = Q;
end
[temp,index_of_fronts] = sort(x(:,M + V + 1));
for i = 1 : length(index_of_fronts)
sorted_based_on_front(i,:) = x(index_of_fronts(i),:);
end
current_index = 0;
% Find the crowding distance for each individual in each front
for front = 1 : (length(F) - 1)
objective = [];
distance = 0;
y = [];
previous_index = current_index + 1;
for i = 1 : length(F(front).f)
y(i,:) = sorted_based_on_front(current_index + i,:);
end
current_index = current_index + i;
% Sort each individual based on the objective
sorted_based_on_objective = [];
for i = 1 : M
[sorted_based_on_objective, index_of_objectives] = ...
sort(y(:,V + i));
sorted_based_on_objective = [];
for j = 1 : length(index_of_objectives)
sorted_based_on_objective(j,:) = y(index_of_objectives(j),:);
end
f_max = ...
sorted_based_on_objective(length(index_of_objectives), V + i);
f_min = sorted_based_on_objective(1, V + i);
y(index_of_objectives(length(index_of_objectives)),M + V + 1 + i)...
= Inf;
y(index_of_objectives(1),M + V + 1 + i) = Inf;
for j = 2 : length(index_of_objectives) - 1
next_obj = sorted_based_on_objective(j + 1,V + i);
previous_obj = sorted_based_on_objective(j - 1,V + i);
if (f_max - f_min == 0)
y(index_of_objectives(j),M + V + 1 + i) = Inf;
else
y(index_of_objectives(j),M + V + 1 + i) = ...
(next_obj - previous_obj)/(f_max - f_min);
end
end
end
distance = [];
distance(:,1) = zeros(length(F(front).f),1);
for i = 1 : M
distance(:,1) = distance(:,1) + y(:,M + V + 1 + i);
end
y(:,M + V + 2) = distance;
y = y(:,1 : M + V + 2);
z(previous_index:current_index,:) = y;
end
f = z();
##### SOURCE END #####
-->
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