多目标遗传算法代码.docx

1、多目标遗传算法代码. % function nsga_2(pro) % Main Function % Main program to run the NSGA-II MOEA. % Read the corresponding documentation to learn more about multiobjective % optimization using evolutionary algorithms. % initialize_variables has two arguments; First being the population size % and the second

2、 the problem number. 1 corresponds to MOP1 and 2 % corresponds to MOP2. %inp_para_definition=input_parameters_definition; % Initialize the variables % Declare the variables and initialize their values % pop - population % gen - generations % pro - problem number %clear;clc;tic; pop = 100; % 每一代的种群数

3、gen = 100; % 总共的代数 pro = 2; % 问题选择1或者2，见switch 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 % objective space is just two dimensional. V = 6; case 2 M = 3; V = 12;

4、 case 3 % case 1和case 2 用来对整个算法进行常规验证，作为调试之用；case 3 为本工程所需； M = 2; %(output parameters 个数) V = 8; %(input parameters 个数) K = 10; end % Initialize the population chromosome = initialize_variables(pop,pro); % Sort the initialized population % Sort the population using non-domination-sort. This returns

5、 two columns % for each individual which are the rank and the crowding distance % corresponding to their position in the front they belong. 真是牛 X了。 chromosome = non_domination_sort_mod(chromosome,pro); % Start the evolution process . . % The following are performed in each generation % Select the pa

6、rents % Perfrom crossover and Mutation operator % Perform Selection 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 - si

7、ze 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; %下面进行二人锦标赛配对

8、，新的群体规模是原来群体的一半 parent_chromosome = tournament_selection(chromosome,pool,tour); % Perfrom crossover and Mutation operator % The original NSGA-II algorithm uses Simulated Binary Crossover (SBX) and % Polynomial crossover. Crossover probability pc = 0.9 and mutation % probability is pm = 1/n, where n

9、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

10、 = 20; % 针对对象是上一步产生的新的个体parent_chromosome %对parent_chromosome 每次操作以较大的概率进行交叉（产生两个新的候选人），或者较小的概率变异（一个新的候选人）操作，这样 %就会产生较多的新个体 offspring_chromosome = genetic_operator(parent_chromosome,pro,mu,mum); % Intermediate population % Intermediate population is the combined population of parents and % offspring

11、s of the current generation. The population size is almost 1 and % half times the initial population. main_pop,temp=size(chromosome); offspring_pop,temp=size(offspring_chromosome); intermediate_chromosome(1:main_pop,:)=chromosome; . . intermediate_chromosome(main_pop+1:main_pop+offspring_pop,1:M+V)=

12、offspring_chromosome; %intermediate_chromosome=inter_chromo(chromosome,offspring_chromosome,pro); % 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 % populatio

13、n. intermediate_chromosome = . non_domination_sort_mod(intermediate_chromosome,pro); % 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 populatio

14、n size is reached. The % last front is included in the population based on the individuals with % least crowding distance chromosome = replace_chromosome(intermediate_chromosome,pro,pop); if mod(i,10) fprintf(%dn,i); end end % Result % Save the result in ASCII text format. save solution.txt chromoso

15、me -ASCII % Visualize % The following is used to visualize the result for the given problem. switch pro case 1 plot(chromosome(:,V + 1),chromosome(:,V + 2),y+); title(MOP1 using NSGA-II); xlabel(f(x_1); ylabel(f(x_2); case 2 plot3(chromosome(:,V + 1),chromosome(:,V + 2),chromosome(:,V + 3),*); title

16、(MOP2 using NSGA-II); xlabel(f(x_1); ylabel(f(x_2); zlabel(f(x_3); end %disp(run time is:) %toc; % function 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

17、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. % Both the MOPs has 0 to 1 as

18、 its range for all the decision variables. min = 0; max = 1; switch problem case 1 M = 6; K = 8; % k=决策变量(M=6)+目标变量(K-M=2)=8 case 2 M = 12; K = 15; case 3 % case 1和case 2 用来对整个算法进行常规验证，作为调试之用；case 3 为本工程所需； M = 8; %(input parameters 个数) K = 10; end for i = 1 : N % Initialize the decision variables f

19、or 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 % function f = evaluate_objective(x,problem) % Function to evaluate the objective functions for the given input vector % x. x has the

20、 decision variables switch problem case 1 f = ; % Objective function one f(1) = 1 - exp(-4*x(1)*(sin(6*pi*x(1)6; sum = 0; . . for i = 2 : 6 sum = sum + x(i)/4; end % Intermediate function g_x = 1 + 9*(sum)(0.25); % Objective function one f(2) = g_x*(1 - (f(1)/(g_x)2); case 2 f = ; % Intermediate fun

21、ction g_x = 0; for i = 3 : 12 g_x = g_x + (x(i) - 0.5)2; end % Objective function one f(1) = (1 + g_x)*cos(0.5*pi*x(1)*cos(0.5*pi*x(2); % Objective function two f(2) = (1 + g_x)*cos(0.5*pi*x(1)*sin(0.5*pi*x(2); % Objective function three f(3) = (1 + g_x)*sin(0.5*pi*x(1); case 3 f = ; % Objective fun

22、ction one f(1) = 0; % Objective function one f(2) = 0; end % % Non-Donimation Sort %按照目标函数最小了好 % 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 assig

23、ning 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; case 3 % case 1和case 2 用来对整个算法进行常规验证，作为调试之用；case 3 为本工程所需； . . M = 2; %(output parameters 个数) V = 8; %(input parameters 个

24、数) K = 10; 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 支配i的解的个数 individual(i).n = 0; % Individuals which this individual dominate 被i支配的解 individual(

25、i).p = ; for j = 1 : N dom_less = 0; dom_equal = 0; dom_more = 0; for k = 1 : M if (x(i,V + k) return a increasing orer data sequence 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),:); % 对解（染色体）进行排序，按照front分层 end %到这里分层结束,下面就是计算距离了 current_index = 0; % Find the crowding distance for each individual in each front % ,计算不同层的拥挤距离是没有意义的 for front = 1 : (length(F) - 1) objective = ; distance = 0; y = ;