1985531NSGA-II.zip_目标规划

%% Initialize population % % 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 initializes 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. function f = initialize_variables(N,problem) % Both the MOP's given in Homework # 5 has 0 to 1 as its range for all the % decision variables. min = 0; max = 1; switch problem case 1 M = 6; K = 8; case 2 M = 12; K = 15; end for 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,:),problem); end %% Non-Donimation Sort % This 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 front is calculated. function f = non_domination_sort_mod(x,problem) [N,M] = size(x); switch problem case 1 M = 2; V = 6; case 2 M = 3; V = 12; end front = 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; % 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 & 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]; end end % Find the subsequent fronts while ~isempty(F(front).f) Q = []; for i = 1 : length(F(front).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 individual(F(front).f(i)).p(j)]; end end end end front =front + 1; F(front).f = Q; end [temp,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),:); end current_index = 0; % Find the crowding distance for each individual in each front for 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 = []; for 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 = sorted_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 + 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); end y(:,M + V + 2) = distance; y = y(:,1 : M + V + 2); z(previous_index:current_index,:) = y; end f = z(); %% Tournament Selection. function f = selection_individuals(chromosome,pool_size,tour_size) % function selection_individuals(chromosome,pool_size,tour_size) % function selection_individuals(chromosome,pool_size,tour_size) is the % selection policy for selecting the individuals for the mating pool. The % selection is based on tournament selection. Argument 'chromosome' is the % current generation population from which the individuals are selected to % form a mating pool of size 'pool_size' after performing tournament % selection, with size of the tournament being 'tour_size'. By varying the % tournament size the selection pressure can be adjusted. [pop,variables] = size(chromosome); rank = variables - 1; distance= variables; for i = 1 : pool_size for j = 1 : tour_size candidate(j) = round(pop*rand(1)); if candidate(j) == 0 candidate(j) = 1; end if j > 1 while ~isempty(find(candidate(1 : j - 1) == candidate(j))) candidate(j) = round(pop*rand(1)); if candidate(j) == 0 candidate(j) = 1; end end end end for j = 1 : tour_size c_obj_rank(j) = chromosome(candidate(j),rank); c_obj_distance(j) = chromosome(candidate(j),distance); end min_candidate = ... find(c_obj_rank == min(c_obj_rank)); if length(min_candidate) ~= 1 max_candidate = ... find(c_obj_distance(min_candidate) == max(c_obj_distance(min_candidate))); if length(max_candidate) ~= 1 max_candidate = max_candidate(1); end f(i,:) = chromosome(candidate(min_candidate(max_candidate)),:); else f(i,:) = chromosome(candidate(min_candidate(1)),:); end end %% Genetic Operator. function f= genetic_operator(parent_chromosome,pro,mu,mum); [N,M] = size(parent_chromosome); switch pro case 1 M = 2; V = 6; case 2 M = 3; V = 12; end p = 1; was_crossover = 0; was_mutation = 0; l_limit = 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 parent_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) <= 0.5 bq(j) = (2*u(j))^(1/(mu+1)); else bq(j) = (1/(2*(1 - u(j))))^(1/(mu+1)); end child_1(j) = ... 0.5*(((1 + bq(j))*parent_1(j)) + (1 - bq(j))*parent_2(j)); child_2(j) = ... 0.5*(((1 - bq(j))*parent_1(j)) + (1 + bq(j))*parent_2(j)); if child_1(j) > u_limit child_1(j) = u_limit; elseif child_1(j) < l_limit child_1(j) = l_limit; end if child_2(j) > u_limit child_2(j) = u_limit; elseif 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 does not result in variables out of % the search space. For both the MOP's 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) < 0.5 delta(j) = (2*r(j))^(1/(mum+1)) - 1; else delta(j) = 1 - (2*(1 - r(j)))^(1/(mum+1)); end child_3(j) = child_3(j) + delta(j); if child_3(j) > u_limit child_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