function nsga_2()
%% Main Function
% Main program to run the NSGA-II MOEA.
% Read the corresponding documentation to learn more about multiobjective
% optimization using evolutionary algorithms.
% initialize_variables has two arguments; First being the population size
% and the second the problem number. '1' corresponds to MOP1 and '2'
% corresponds to MOP2.
%% Initialize the variables
% Declare the variables and initialize their values
% pop - population
% gen - generations
% pro - problem number
pop = 200;
gen = 1000;
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_variables(pop,pro);
%% Sort the initialized population
% Sort the population using non-domination-sort. This returns two columns
% for each individual which are the rank and the crowding distance
% corresponding to their position in the front they belong.
chromosome = non_domination_sort_mod(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. The
% original NSGA-II uses a binary tournament selection based on the
% crowded-comparision operator. The arguments are
% 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_chromosome = tournament_selection(chromosome,pool,tour);
% Perfrom crossover and Mutation operator
% The original NSGA-II algorithm uses Simulated Binary Crossover (SBX) and
% Polynomial crossover. Crossover probability pc = 0.9 and mutation
% probability is pm = 1/n, where n is the number of decision variables.
% Both real-coded GA and binary-coded GA are implemented in the original
% algorithm, while in this program only the real-coded GA is considered.
% The distribution indeices for crossover and mutation operators as mu = 20
% and mum = 20 respectively.
mu = 20;
mum = 20;
offspring_chromosome = genetic_operator(parent_chromosome,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_chromosome);
intermediate_chromosome(1:main_pop,:) = chromosome;
intermediate_chromosome(main_pop + 1 : main_pop + offspring_pop,1 : M+V) = ...
offspring_chromosome;
% 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_chromosome = ...
non_domination_sort_mod(intermediate_chromosome,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_chromosome(intermediate_chromosome,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
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