NSGAII源程序.docx

1、NSGAII源程序function f = crowding_distance(x,problem)% This function calculates the crowding distanceN,M = size(x);switch problem case 1 M = 2; V = 6; case 2 M = 3; V = 12;end% Crowding distance for each frontfor i = 1 : length(F(front).f) y(i,:) = x(F(front).f(i),:);endfor i = 1 : M sorted(i).individu

2、al,sorted(i).index = sort(y(:,V + i); distance(sorted(i).index(1).individual = Inf; distance(sorted(i).index(length(sorted(i).index).individual = Inf;endnum,len = size(y);% Initialize all the distance of individuals as zero.for i = 1 : M for j = 2 : num - 1 distance(j).individual = 0; end objective(

3、i).range = . sorted(i).individual(length(sorted(i).individual) - . sorted(i).individual(1); % Maximum and minimum objectives value for the ith objectiveend% Caluclate the crowding distance for front one.for i = 1 : M for j = 2 : num - 1 distance(j).individual = distance(j).individual + . (sorted(i).

4、individual(j + 1) - sorted(i).individual(j - 1)/. objective(i).range; y(sorted(i).index(j),M + V + 2) = distance(j).individual; endend/PRE Published with MATLAB 7.0function f = genetic_operator(parent_chromosome,pro,mu,mum);% This function is utilized to produce offsprings from parent chromosomes.%

5、The genetic operators corssover and mutation which are carried out with% slight modifications from the original design. For more information read% the document enclosed.N,M = size(parent_chromosome);switch pro case 1 M = 2; V = 6; case 2 M = 3; V = 12;endp = 1;was_crossover = 0;was_mutation = 0;l_li

6、mit = 0;u_limit = 1;for i = 1 : N if rand(1) 0.9 child_1 = ; child_2 = ; parent_1 = round(N*rand(1); if parent_1 1 parent_1 = 1; end parent_2 = round(N*rand(1); if parent_2 1 parent_2 = 1; end while isequal(parent_chromosome(parent_1,:),parent_chromosome(parent_2,:) parent_2 = round(N*rand(1); if pa

7、rent_2 1 parent_2 = 1; end end parent_1 = parent_chromosome(parent_1,:); parent_2 = parent_chromosome(parent_2,:); for j = 1 : V % SBX (Simulated Binary Crossover) % Generate a random number u(j) = rand(1); if u(j) u_limit child_1(j) = u_limit; elseif child_1(j) u_limit child_2(j) = u_limit; elseif

8、child_2(j) l_limit child_2(j) = l_limit; end end child_1(:,V + 1: M + V) = evaluate_objective(child_1,pro); child_2(:,V + 1: M + V) = evaluate_objective(child_2,pro); was_crossover = 1; was_mutation = 0; else parent_3 = round(N*rand(1); if parent_3 1 parent_3 = 1; end % Make sure that the mutation d

9、oes not result in variables out of % the search space. For both the MOPs the range for decision space % is 0,1. In case different variables have different decision % space each variable can be assigned a range. child_3 = parent_chromosome(parent_3,:); for j = 1 : V r(j) = rand(1); if r(j) u_limit ch

10、ild_3(j) = u_limit; elseif child_3(j) l_limit child_3(j) = l_limit; end end child_3(:,V + 1: M + V) = evaluate_objective(child_3,pro); was_mutation = 1; was_crossover = 0; end if was_crossover child(p,:) = child_1; child(p+1,:) = child_2; was_cossover = 0; p = p + 2; elseif was_mutation child(p,:) =

11、 child_3(1,1 : M + V); was_mutation = 0; p = p + 1; endendf = child;Published with MATLAB 7.0function f = initialize_variables(N,problem)% function f = initialize_variables(N,problem)% N - Population size% problem - takes integer values 1 and 2 where,% 1 for MOP1% 2 for MOP2% This function initializ

12、es the population with N individuals and each% individual having M decision variables based on the selected problem.% M = 6 for problem MOP1 and M = 12 for problem MOP2. The objective space% for MOP1 is 2 dimensional while for MOP2 is 3 dimensional.% Both the MOPs has 0 to 1 as its range for all the

13、 decision variables.min = 0;max = 1;switch problem case 1 M = 6; K = 8; case 2 M = 12; K = 15;endfor i = 1 : N % Initialize the decision variables for j = 1 : M f(i,j) = rand(1); % i.e f(i,j) = min + (max - min)*rand(1); end % Evaluate the objective function f(i,M + 1: K) = evaluate_objective(f(i,:)

14、,problem);end/PRE Published with MATLAB 7.0 Non-Donimation SortThis function sort the current popultion based on non-domination. All the individuals in the first front are given a rank of 1, the second front individuals are assigned rank 2 and so on. After assigning the rank the crowding in each fro

15、nt is calculated. N,M = size(x);switch problem case 1 M = 2; V = 6; case 2 M = 3; V = 12;endfront = 1;% There is nothing to this assignment, used only to manipulate easily in% MATLAB.F(front).f = ;individual = ;for i = 1 : N % Number of individuals that dominate this individual individual(i).n = 0;

16、% Individuals which this individual dominate individual(i).p = ; for j = 1 : N dom_less = 0; dom_equal = 0; dom_more = 0; for k = 1 : M if (x(i,V + k) x(j,V + k) dom_less = dom_less + 1; elseif (x(i,V + k) = x(j,V + k) dom_equal = dom_equal + 1; else dom_more = dom_more + 1; end end if dom_less = 0

17、& dom_equal = M individual(i).n = individual(i).n + 1; elseif dom_more = 0 & dom_equal = M individual(i).p = individual(i).p j; end end if individual(i).n = 0 x(i,M + V + 1) = 1; F(front).f = F(front).f i; endend% Find the subsequent frontswhile isempty(F(front).f) Q = ; for i = 1 : length(F(front).

18、f) if isempty(individual(F(front).f(i).p) for j = 1 : length(individual(F(front).f(i).p) individual(individual(F(front).f(i).p(j).n = . individual(individual(F(front).f(i).p(j).n - 1; if individual(individual(F(front).f(i).p(j).n = 0 x(individual(F(front).f(i).p(j),M + V + 1) = . front + 1; Q = Q in

19、dividual(F(front).f(i).p(j); end end end end front = front + 1; F(front).f = Q;endtemp,index_of_fronts = sort(x(:,M + V + 1);for i = 1 : length(index_of_fronts) sorted_based_on_front(i,:) = x(index_of_fronts(i),:);endcurrent_index = 0;% Find the crowding distance for each individual in each frontfor

20、 front = 1 : (length(F) - 1) objective = ; distance = 0; y = ; previous_index = current_index + 1; for i = 1 : length(F(front).f) y(i,:) = sorted_based_on_front(current_index + i,:); end current_index = current_index + i; % Sort each individual based on the objective sorted_based_on_objective = ; fo

21、r i = 1 : M sorted_based_on_objective, index_of_objectives = . sort(y(:,V + i); sorted_based_on_objective = ; for j = 1 : length(index_of_objectives) sorted_based_on_objective(j,:) = y(index_of_objectives(j),:); end f_max = . sorted_based_on_objective(length(index_of_objectives), V + i); f_min = sor

22、ted_based_on_objective(1, V + i); y(index_of_objectives(length(index_of_objectives),M + V + 1 + i). = Inf; y(index_of_objectives(1),M + V + 1 + i) = Inf; for j = 2 : length(index_of_objectives) - 1 next_obj = sorted_based_on_objective(j + 1,V + i); previous_obj = sorted_based_on_objective(j - 1,V +

23、i); if (f_max - f_min = 0) y(index_of_objectives(j),M + V + 1 + i) = Inf; else y(index_of_objectives(j),M + V + 1 + i) = . (next_obj - previous_obj)/(f_max - f_min); end end end distance = ; distance(:,1) = zeros(length(F(front).f),1); for i = 1 : M distance(:,1) = distance(:,1) + y(:,M + V + 1 + i)

24、; end y(:,M + V + 2) = distance; y = y(:,1 : M + V + 2); z(previous_index:current_index,:) = y;endf = z();Published with MATLAB 7.0Main FunctionMain program to run the NSGA-II MOEA. Read the corresponding documentation to learn more about multiobjective optimization using evolutionary algorithms. in

25、itialize_variables has two arguments; First being the population size and the second the problem number. 1 corresponds to MOP1 and 2 corresponds to MOP2. ContentsInitialize the variables Sort the initialized population Start the evolution process Result Visualize Initialize the variablesDeclare the

26、variables and initialize their values pop - population gen - generations pro - problem numberpop = 200;gen = 1;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

27、 % objective space is just two dimensional. V = 6; case 2 M = 3; V = 12;end% Initialize the populationchromosome = initialize_variables(pop,pro);Sort the initialized populationSort the population using non-domination-sort. This returns two columns for each individual which are the rank and the crowd

28、ing 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 Selectionfor i = 1 : gen % Sel

29、ect 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 siz