nsga_2.m

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% Main program to run the NSGA-II MOEA.

function nsga_2()

% Initialize the variables
% Declare the variables and initialize their values
% pop - population
% gen - generations
% pro - problem number
pop = 100;
gen = 5;
pro = 1;

switch pro
    case 1
        % M is the number of objectives.
        M = 2;
        % V is the number of decision variables. In this case it is
        % difficult to visualize the decision variables space while the
        % objective space is just two dimensional.
        V = 6;
    case 2
        M = 3;
        V = 12;
end

% Initialize the population
chromosome = initialize(pop,pro);

% Sort the initialized population
chromosome = non_domination(chromosome,pro);

% Start the evolution process
% The following are performed in each generation.Select the parents.Perfrom crossover and Mutation operator.Perform Selection

for i = 1 : gen
    % Select the parents.Parents are selected for reproduction to generate offspring.  
    % pool - size of the mating pool. It is common to have this to be half the population size.
    % tour - Tournament size. Original NSGA-II uses a binary tournament selection, but to see the effect of tournament size 
    %        this is kept arbitary, to be choosen by the user.
    pool = round(pop/2);
    tour = 2;
    parent = tournament(chromosome,pool,tour);

    % Perfrom crossover and Mutation operator
    mu = 20;
    mum = 20;
    offspring = genetic(parent,pro,mu,mum);

    % Intermediate population
    % Intermediate population is the combined population of parents and offsprings of the current generation. The population 
    % size is almost 1 and half times the initial population.
    [main_pop,temp] = size(chromosome);
    [offspring_pop,temp] = size(offspring);
    intermediate(1:main_pop,:) = chromosome;
    intermediate(main_pop + 1 : main_pop + offspring_pop,1 : M+V) = offspring;

    % Non-domination-sort of intermediate population
    % The intermediate population is sorted again based on non-domination sort before the replacement operator is performed on 
    % the intermediate population.
    intermediate = non_domination(intermediate,pro);
    % Perform Selection
    % Once the intermediate population is sorted only the best solution is selected based on it rank and crowding distance. 
    % Each front is filled in ascending order until the addition of population size is reached. The last front is included in 
    %the population based on the individuals with least crowding distance
    chromosome = replace(intermediate,pro,pop)
    if ~mod(i,10)
        fprintf('%d\n',i);
    end
end

%% Result
% Save the result in ASCII text format.
save solution.txt chromosome -ASCII

%% Visualize
% The following is used to visualize the result for the given problem.
switch pro
    case 1
        plot(chromosome(:,V + 1),chromosome(:,V + 2),'*');
        title('MOP1 using NSGA-II');
        xlabel('f(x_1)');
        ylabel('f(x_2)');
    case 2
        plot3(chromosome(:,V + 1),chromosome(:,V + 2),chromosome(:,V + 3),'*');
        title('MOP2 using NSGA-II');
        xlabel('f(x_1)');
        ylabel('f(x_2)');
        zlabel('f(x_3)');
end