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NonDominatedSorting.m
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NonDominatedSorting.m
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%____________________________________________________________________________________
% Multi-objective exponential distribution optimizer (MOEDO) source codes version 1.0 (NDS+CD)
% Author and programmer: Pradeep Jangir
% Authors:- Kanak Kalita, Janjhyam Venkata Naga Ramesh, Lenka Cepova, Sundaram B. Pandya, Pradeep Jangir & Laith Abualigah
% e-Mail: pkjmtech@gmail.com
% Multi-objective exponential distribution optimizer (MOEDO): a novel math-inspired multi-objective algorithm for global optimization and real-world engineering design problems
% Kanak Kalita, Janjhyam Venkata Naga Ramesh, Lenka Cepova, Sundaram B. Pandya, Pradeep Jangir & Laith Abualigah
% Scientific Reports volume 14, Article number: 1816 (2024)
% DOI:https://doi.org/10.1038/s41598-024-52083-7%
%____________________________________________________________________________________
function [fronts, maxFront] = NonDominatedSorting(F)
% Initialize
[S, n, frontNumbers] = deal(cell(size(F, 1), 1));
[rank, distances] = deal(zeros(size(F, 1), 1));
front = 1;
maxFront = 0;
% Calculate domination
for i = 1:size(F, 1)
S{i} = [];
n{i} = 0;
for j = 1:size(F, 1)
if dominates(F(i, :), F(j, :))
S{i} = [S{i}, j];
elseif dominates(F(j, :), F(i, :))
n{i} = n{i} + 1;
end
end
if n{i} == 0
rank(i) = 1;
if isempty(frontNumbers{front})
frontNumbers{front} = i;
else
frontNumbers{front} = [frontNumbers{front}, i];
end
end
end
% Assign fronts
while ~isempty(frontNumbers{front})
Q = [];
for i = frontNumbers{front}
for j = S{i}
n{j} = n{j} - 1;
if n{j} == 0
rank(j) = front + 1;
Q = [Q, j];
end
end
end
front = front + 1;
frontNumbers{front} = Q;
end
maxFront = front - 1;
% Organize fronts
fronts = cell(maxFront, 1);
for i = 1:maxFront
fronts{i} = frontNumbers{i};
end
end