NSGA2算法MATLAB实现（能够自定义优化函数） – OmegaXYZ |
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NSGA2算法MATLAB实现（能够自定义优化函数） – OmegaXYZ
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以前写了一个简单的NSGA2的算法能够用在ZDT1函数上：http://www.omegaxyz.com/2017/05/04/nsga2matlabzdt1/ 那个NSGA2的算法不具有普遍性，下面参考课国外的课题小组的代码重新修改了内部冗余内容，使之能够自定义优化函数。
NSGA2的过程为： 1、随机产生一个初始父代Po，在此基础上采用二元锦标赛选择、交叉和变异操作产生子代Qo， Po 和Qo群体规模均为N 2、将Pt和Qt并入到Rt中（初始时t=0），对Rt进行快速非支配解排序，构造其所有不同等级的非支配解集F1、F2…….. 3、按照需要计算Fi中所有个体的拥挤距离，并根据拥挤比较运算符构造Pt+1，直至Pt+1规模为N，图中的Fi为F3 具体解释请见：http://www.omegaxyz.com/2017/04/14/nsga-iiintro/ C++代码请见（测试函数ZDT1）：http://www.omegaxyz.com/2017/04/20/nsga2zdt1/ 下面是完整版的代码： ①nsga2-optimization.m MATLAB 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647 function nsga_2_optimization%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %此处可以更改 %更多机器学习内容请访问omegaxyz.com pop = 500; %种群数量gen = 500; %迭代次数M = 2; %目标数量V = 30; %维度min_range = zeros(1, V); %下界max_range = ones(1,V); %上界%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% chromosome = initialize_variables(pop, M, V, min_range, max_range);chromosome = non_domination_sort_mod(chromosome, M, V); for i = 1 : gen pool = round(pop/2); tour = 2; parent_chromosome = tournament_selection(chromosome, pool, tour); mu = 20; mum = 20; offspring_chromosome = genetic_operator(parent_chromosome,M, V, mu, mum, min_range, max_range); [main_pop,~] = size(chromosome); [offspring_pop,~] = size(offspring_chromosome); clear temp intermediate_chromosome(1:main_pop,:) = chromosome; intermediate_chromosome(main_pop + 1 : main_pop + offspring_pop,1 : M+V) = offspring_chromosome; intermediate_chromosome = non_domination_sort_mod(intermediate_chromosome, M, V); chromosome = replace_chromosome(intermediate_chromosome, M, V, pop); if ~mod(i,100) clc; fprintf('%d generations completed\n',i); endend if M == 2 plot(chromosome(:,V + 1),chromosome(:,V + 2),'*'); xlabel('f_1'); ylabel('f_2'); title('Pareto Optimal Front');elseif M == 3 plot3(chromosome(:,V + 1),chromosome(:,V + 2),chromosome(:,V + 3),'*'); xlabel('f_1'); ylabel('f_2'); zlabel('f_3'); title('Pareto Optimal Surface');end②initialize_variables.m MATLAB 12345678910 function f = initialize_variables(N, M, V, min_range, max_range)min = min_range;max = max_range;K = M + V;for i = 1 : N for j = 1 : V f(i,j) = min(j) + (max(j) - min(j))*rand(1); end f(i,V + 1: K) = evaluate_objective(f(i,:), M, V);end③non_domination_sort_mod.m MATLAB 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106 function f = non_domination_sort_mod(x, M, V)[N, ~] = size(x);clear mfront = 1;F(front).f = [];individual = []; for i = 1 : N individual(i).n = 0; 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) MATLAB 123456789101112131415161718192021222324252627282930313233343536 function f = tournament_selection(chromosome, pool_size, tour_size)[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)),:); endend⑤genetic_operator.m MATLAB 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115 function f = genetic_operator(parent_chromosome, M, V, mu, mum, l_limit, u_limit)[N,m] = size(parent_chromosome); clear mp = 1;was_crossover = 0;was_mutation = 0; for i = 1 : N % With 90 % probability perform crossover if rand(1)⑦自定义评价函数（我选用的ZDT1函数） MATLAB 1234567891011 function f = evaluate_objective(x, M, V)f = [];f(1) = x(1);g = 1;sum = 0;for i = 2:V sum = sum + x(i);endg = g + 9*sum / (V-1));f(2) = g * (1 - sqrt(x(1) / g));end500个种群运行500代的结果：
代码打包下载：http://download.csdn.net/download/xyisv/10217700 Github项目地址：https://github.com/xyjigsaw/NSGA2_MATLAB |
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