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.

Contents

• Tournament selection process

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.

% 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

Published with MATLAB® 7.0