www.gusucode.com > 几种多目标优化算法集合，包括MOEAD，MOPSO，NNIA，NSGA2等 > NSGA-II/nsga_2.m
function nsga_2() % modified by zzb
%% function nsga_2(pop,gen)
% is a multi-objective optimization function where the input arguments are
% pop - Population size
% gen - Total number of generations
%
% This functions is based on evolutionary algorithm for finding the optimal
% solution for multiple objective i.e. pareto front for the objectives.
% Initially enter only the population size and the stoping criteria or
% the total number of generations after which the algorithm will
% automatically stopped.
%
% You will be asked to enter the number of objective functions, the number
% of decision variables and the range space for the decision variables.
% Also you will have to define your own objective funciton by editing the
% evaluate_objective() function. A sample objective function is described
% in evaluate_objective.m. Kindly make sure that the objective function
% which you define match the number of objectives that you have entered as
% well as the number of decision variables that you have entered. The
% decision variable space is continuous for this function, but the
% objective space may or may not be continuous.
%
% Original algorithm NSGA-II was developed by researchers in Kanpur Genetic
% Algorithm Labarotary and kindly visit their website for more information
% http://www.iitk.ac.in/kangal/
% Copyright (c) 2009, Aravind Seshadri
% All rights reserved.
%
pop = input('Input the population size: '); % modified by zzb
while(pop < 20) % modified by zzb
disp('Minimum population for running this function is 20'); % modified by zzb
pop = input('Input the population size: '); % modified by zzb
end % modified by zzb
gen = input('Input the total number of generations: '); % modified by zzb
while(gen < 5) % modified by zzb
disp('Minimum number of generations is 5'); % modified by zzb
gen = input('Input the total number of generations: '); % modified by zzb
end % modified by zzb
%% Simple error checking
% Number of Arguments
% Check for the number of arguments. The two input arguments are necessary
% to run this function.
% if nargin < 2 % modified by zzb
% error('NSGA-II: Please enter the population size and number of generations as input arguments.'); % modified by zzb
% end % modified by zzb
% Both the input arguments need to of integer data type
% if isnumeric(pop) == 0 || isnumeric(gen) == 0 % modified by zzb
% error('Both input arguments pop and gen should be integer datatype'); % modified by zzb
% end % modified by zzb
% Minimum population size has to be 20 individuals
% if pop < 20 % modified by zzb
% error('Minimum population for running this function is 20'); % modified by zzb
% end % modified by zzb
% if gen < 5 % modified by zzb
% error('Minimum number of generations is 5'); % modified by zzb
% end % modified by zzb
% Make sure pop and gen are integers
pop = round(pop);
gen = round(gen);
%% Objective Function
% The objective function description contains information about the
% objective function. M is the dimension of the objective space, V is the
% dimension of decision variable space, min_range and max_range are the
% range for the variables in the decision variable space. User has to
% define the objective functions using the decision variables. Make sure to
% edit the function 'evaluate_objective' to suit your needs.
[M, V, min_range, max_range] = objective_description_function();
%% Initialize the population
% Population is initialized with random values which are within the
% specified range. Each chromosome consists of the decision variables. Also
% the value of the objective functions, rank and crowding distance
% information is also added to the chromosome vector but only the elements
% of the vector which has the decision variables are operated upon to
% perform the genetic operations like corssover and mutation.
chromosome = initialize_variables(pop, M, V, min_range, max_range); % chromosome :pop X (M+V)
%% 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. At this stage
% the rank and the crowding distance for each chromosome is added to the
% chromosome vector for easy of computation.
chromosome = non_domination_sort_mod(chromosome, M, V); % chromosome input : M+V; chromosome output: M+V+2
%% Start the evolution process
% The following are performed in each generation
% * Select the parents which are fit for reproduction
% * Perfrom crossover and Mutation operator on the selected parents
% * Perform Selection from the parents and the offsprings
% * Replace the unfit individuals with the fit individuals to maintain a
% constant population size.
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; % tout <= 5 noticed by zzb
% Selection process
% A binary tournament selection is employed in NSGA-II. In a binary
% tournament selection process two individuals are selected at random
% and their fitness is compared. The individual with better fitness is
% selcted as a parent. Tournament selection is carried out until the
% pool size is filled. Basically a pool size is the number of parents
% to be selected. The input arguments to the function
% tournament_selection are chromosome, pool, tour. The function uses
% only the information from last two elements in the chromosome vector.
% The last element has the crowding distance information while the
% penultimate element has the rank information. Selection is based on
% rank and if individuals with same rank are encountered, crowding
% distance is compared. A lower rank and higher crowding distance is
% the selection criteria.
parent_chromosome = tournament_selection(chromosome, pool, tour); % chromosome: M+V+2; parent_chromosome: M+V+2
% Perfrom crossover and Mutation operator
% The original NSGA-II algorithm uses Simulated Binary Crossover (SBX) and
% Polynomial mutation. 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, ...
M, V, mu, mum, min_range, max_range); % parent_chromosome: M+V+2; offspring_chromosome: M+V
% Intermediate population
% Intermediate population is the combined population of parents and
% offsprings of the current generation. The population size is two
% times the initial population.
% [main_pop,temp] = size(chromosome); % modified by zzb
% [offspring_pop,temp] = size(offspring_chromosome); % modified by zzb
main_pop = size(chromosome,1); % modified by zzb
offspring_pop = size(offspring_chromosome,1); % modified by zzb
% temp is a dummy variable.
% clear temp
% intermediate_chromosome is a concatenation of current population and
% the offspring population.
% intermediate_chromosome(1:main_pop,:) = chromosome; % modified by zzb
intermediate_chromosome(1:main_pop,1 : M + V) = chromosome(:,1 : M + V); % modified by zzb
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, M, V); % intermediate_chromosome input : M+V; intermediate_chromosome output: M+V+2
% 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, M, V, pop); % intermediate_chromosome: M+V+2; chromosome: M+V+2
if ~mod(i,100) % modified by zzb
clc;
fprintf('%d generations completed\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 if objective space
% dimension is visualizable.
if M == 2
plot(chromosome(:,V + 1),chromosome(:,V + 2),'*');
title('MOP1 using NSGA-II');
xlabel('f(x_1)');
ylabel('f(x_2)');
elseif M ==3
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