NSGA-2.rar_NSGA-2_NSGA-2 MATLAB_NSGA_2 Matlab_NSGA—2

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/ %% 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. 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); % 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); % 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); [offspring_pop,temp] = size(offspring_chromosome); % 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; 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); % 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); if ~mod(i,100) 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),chr