tournament_selection.m

function f = tournament_selection(chromosome, pool_size, tour_size)

%% function tournament_selection(chromosome, pool_size, tour_size) 
% is the selection policy for selecting the individuals for the mating 
% pool. The selection is based on tournament selection. Argument 
% |chromosome| is the current generation population from which the 
% individuals are selected to form a mating pool of size |pool_size| after 
% performing tournament selection, with size of the tournament being 
% |tour_size|. By varying the tournament size the selection pressure can be
% adjusted. But for NSGA-II the tour_size is fixed to two, but the user may
% feel free to experiment with different tournament size. Also it has been
% observed that a tournament size of more than five has no significant
% meaning. 
%
%% Tournament selection process
% In a tournament selection process n individuals are selected at random,
% where n is equal to |tour_size|. From these individuals only one is selected
% and is added to the mating pool, where size of the mating pool is
% |pool_size|. Selection is performed based on two criteria. First and
% foremost is the rank or the front in which the solutions reside.
% Individuals with lower rank are selected. Secondly if the rank of two
% individuals are the same then, the crowding distance is compared.
% Individuals with greater crowding distance is selcted. 


%  Copyright (c) 2009, Aravind Seshadri
%  All rights reserved.
%
%  Redistribution and use in source and binary forms, with or without 
%  modification, are permitted provided that the following conditions are 
%  met:
%
%     * Redistributions of source code must retain the above copyright 
%       notice, this list of conditions and the following disclaimer.
%     * Redistributions in binary form must reproduce the above copyright 
%       notice, this list of conditions and the following disclaimer in 
%       the documentation and/or other materials provided with the distribution
%      
%  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
%  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
%  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
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% Get the size of chromosome. The number of chromosome is not important
% while the number of elements in chromosome are important.
[pop, variables] = size(chromosome);
% The peunltimate element contains the information about rank.
rank = variables - 1;
% The last element contains information about crowding distance.
distance = variables;

% Until the mating pool is filled, perform tournament selection
for i = 1 : pool_size
    % Select n individuals at random, where n = tour_size
    for j = 1 : tour_size
        % Select an individual at random
        candidate(j) = round(pop*rand(1));
        % Make sure that the array starts from one. 
        if candidate(j) == 0
            candidate(j) = 1;
        end
        if j > 1
            % Make sure that same candidate is not choosen.
            while ~isempty(find(candidate(1 : j - 1) == candidate(j)))
                candidate(j) = round(pop*rand(1));
                if candidate(j) == 0
                    candidate(j) = 1;
                end
            end
        end
    end
    % Collect information about the selected candidates.
    for j = 1 : tour_size
        c_obj_rank(j) = chromosome(candidate(j),rank);
        c_obj_distance(j) = chromosome(candidate(j),distance);
    end
    % Find the candidate with the least rank
    min_candidate = ...
        find(c_obj_rank == min(c_obj_rank));
    % If more than one candiate have the least rank then find the candidate
    % within that group having the maximum crowding distance.
    if length(min_candidate) ~= 1
        max_candidate = ...
        find(c_obj_distance(min_candidate) == max(c_obj_distance(min_candidate)));
        % If a few individuals have the least rank and have maximum crowding
        % distance, select only one individual (not at random). 
        if length(max_candidate) ~= 1
            max_candidate = max_candidate(1);
        end
        % Add the selected individual to the mating pool
        f(i,:) = chromosome(candidate(min_candidate(max_candidate)),:);
    else
        % Add the selected individual to the mating pool
        f(i,:) = chromosome(candidate(min_candidate(1)),:);
    end
end