nsga_2.m ( File view )

  • By moeah 2014-04-18
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			function nsga_2(pop,gen)

%% 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.
%
%  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 
%  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
%  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
%  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
%  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
%  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
%  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
%  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
%  POSSIBILITY OF SUCH DAMAGE.

%% 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
    error('NSGA-II: Please enter the population size and number of generations as input arguments.');
end
% Both the input arguments need to of integer data type
if isnumeric(pop) == 0 || isnumeric(gen) == 0
    error('Both input arguments pop and gen should be integer datatype');
end
% Minimum population size has to be 20 individuals
if pop < 20
    error('Minimum population for running this function is 20');
end
if gen < 5
    error('Minimum number of generations is 5');
end
% 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);


%% 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);

%% 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;
    % 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. Th
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Name Size Date
01.96 kB
01.96 kB
tournament_selection.html10.01 kB2006-03-16|16:37
replace_chromosome.html7.98 kB2006-03-16|16:38
objective_description_function.html6.25 kB2006-03-16|16:31
nsga_2.html20.78 kB2006-03-16|16:29
non_domination_sort_mod.html18.88 kB2006-03-16|16:35
initialize_variables.html6.42 kB2006-03-16|16:30
genetic_operator.html14.78 kB2006-03-16|16:30
evaluate_objective.html7.08 kB2006-03-16|16:28
NSGA131.01 kB2006-03-19|20:24
evaluate_objective.m2.16 kB2006-03-16|16:28
genetic_operator.m6.93 kB2009-07-16|10:08
initialize_variables.m3.34 kB2009-07-16|10:09
non_domination_sort_mod.m8.30 kB2009-07-16|10:09
nsga_2.m9.30 kB2009-07-16|10:09
objective_description_function.m3.52 kB2009-07-16|10:09
replace_chromosome.m4.02 kB2009-07-16|10:09
tournament_selection.m4.91 kB2009-07-16|10:09
license.txt1.31 kB2009-07-19|16:16
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nsga_2.m (153.84 kB)

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