基于分解的多目标进化优化MOEA/D之切比雪夫方法的理解见上一篇博文。
这是晓风wangchao （博客地址：https://blog.csdn.net/qq_40434430）写的代码，是我在网上下载的MOEA/D代码中，我认为写的最好的一版。代码下载链接：https://download.csdn.net/download/jianan_ouyang/12347822
MOEAD.m
1 %---------------------------------------------------------------------- 2 %程序功能：实现MOEAD算法，测试函数为ZDT1,ZDT2,ZDT3,ZDT4,ZDT6,DTLZ1,DTLZ2 3 %说明：遗传算子为模拟二进制交叉和多项式变异 4 %作者：(晓风) 5 %email: 18821709267@163.com 6 %最初建立时间：2018.09.30 7 %最近修改时间：2018.10.08 8 %参考论文： 9 %MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition 10 %Qingfu Zhang, Senior Member, IEEE, and Hui Li 11 %IEEE TRANSACTIONS O 12 %---------------------------------------------------------- 13 clear all 14 clc 15 tic; 16 %------------------------参数输入-------------------------- 17 format long 18 global x_max x_min x_num f_num lamda z 19 rand('state',sum(100*clock)); 20 N=300;%种群大小 21 T=20;%邻居规模大小 22 fun='DTLZ2';% 23 funfun;%测试函数 24 lamda=genrate_lamda(N,f_num);%均匀分布的N个权重向量 25 max_gen=250;%进化代数 26 pc=1;%交叉概率 27 pm=1/x_num;%变异概率 28 yita1=2;%模拟二进制交叉参数2 29 yita2=5;%多项式变异参数5 30 %------------------------初始条件-------------------------- 31 %%计算任意两个权重向量间的欧式距离，查找每个权向量最近的T个权重向量的索引 32 B=look_neighbor(lamda,T); 33 %%在可行空间均匀随机产生初始种群 34 X=initialize(N,f_num,x_num,x_min,x_max,fun); 35 %%初始化z 36 for i=1:f_num 37 z(i) = min(X(:,x_num+i)); 38 end 39 %%初始化是否为非支配个体 40 X=deterdomination(X,N,f_num,x_num); 41 %%设置EP为初始种群里的非支配个体 42 EP=[]; 43 for i=1:N 44 if(X(i,x_num+f_num+1)==1) 45 EP=[X(i,:);EP]; 46 end 47 end 48 %------------------------迭代更新-------------------------- 49 for gen=1:max_gen 50 for i=1:N 51 %%基因重组，从B(i)中随机选取两个序列k，l 52 index1 = randperm(T); 53 parent1 = B(i,index1(1)); 54 parent2 = B(i,index1(2)); 55 off=cross_mutation(X(parent1,:),X(parent2,:),f_num,x_num,x_min,x_max,pc,pm,yita1,yita2,fun ); 56 %off=cross_mutation2(X(parent1,:),X(parent2,:),f_num,x_num,x_min,x_max,pc,pm,yita1,yita2,fun ); 57 %%更新z 58 for j=1:f_num 59 %%if(Zi<fi(y')),zi=fi(y') 60 z(j)=min(z(j),off(:,x_num+j)); 61 end 62 %%更新领域解 63 X=updateNeighbor(lamda,z,X,B(i,:),off,x_num,f_num); 64 %%更新EP 65 [number,~]=size(EP); 66 temp=0; 67 kk=[]; 68 for k=1:number 69 less=0;%y'的目标函数值小于个体的目标函数值数目 70 equal=0;%y'的目标函数值等于个体的目标函数值数目 71 greater=0;%y'的目标函数值大于个体的目标函数值数目 72 for mm=1:f_num 73 if(off(:,x_num+mm)>EP(k,x_num+mm)) 74 greater=greater+1; 75 elseif(off(:,x_num+mm)==EP(k,x_num+mm)) 76 equal=equal+1; 77 else 78 less=less+1; 79 end 80 end 81 %%%从EP中移除被y'支配的向量 82 if(greater==0 && equal~=f_num)%y'支配EP中的第K个个体 83 kk=[k kk]; 84 end 85 %%%如果EP中没有支配y'的个体，将y'加入EP 86 if(less==0 && equal~=f_num)%EP中的第K个个体支配y' 87 temp=1; 88 end 89 end 90 if(isempty(kk)==0) 91 EP(kk,:)=[]; 92 end 93 if(temp==0) 94 EP=[EP;off]; 95 end 96 end 97 if mod(gen,10) == 0 98 fprintf('%d gen has completed! ',gen); 99 end 100 % if f_num==2 101 % plot(EP(:,x_num+1),EP(:,x_num+2),'r*'); 102 % elseif f_num==3 103 % plot3( EP(:,x_num+1), EP(:,x_num+2),EP(:,x_num+3),'r*' ); 104 % set(gca,'xdir','reverse'); set(gca,'ydir','reverse'); 105 % end 106 % title(num2str(gen)); 107 % drawnow 108 end 109 filepath=pwd; 110 cd('G:xjllearnPromatlabLearn临时数据EP_DTLZ2'); 111 save solution5.txt EP -ASCII 112 cd(filepath); 113 toc; 114 %------------------------画图对比-------------------------- 115 if f_num==2 116 hold on 117 plot(EP(:,x_num+1),EP(:,x_num+2),'r*'); 118 elseif f_num==3 119 hold on 120 plot3( EP(:,x_num+1), EP(:,x_num+2),EP(:,x_num+3),'r*' ); 121 set(gca,'xdir','reverse'); set(gca,'ydir','reverse'); 122 end 123 % figure; 124 % if f_num==2 125 % hold on 126 % plot(X(:,x_num+1),X(:,x_num+2),'r*'); 127 % elseif f_num==3 128 % hold on 129 % plot3( X(:,x_num+1), X(:,x_num+2),X(:,x_num+3),'r*' ); 130 % set(gca,'xdir','reverse'); set(gca,'ydir','reverse'); 131 % end 132 %--------------------Coverage(C-metric)--------------------- 133 A=PP;B=EP(:,(x_num+1):(x_num+f_num));%%%%%%%%%%%%%%%%%%%% 134 [temp_A,~]=size(A); 135 [temp_B,~]=size(B); 136 number=0; 137 for i=1:temp_B 138 nn=0; 139 for j=1:temp_A 140 less=0;%当前个体的目标函数值小于多少个体的数目 141 equal=0;%当前个体的目标函数值等于多少个体的数目 142 for k=1:f_num 143 if(B(i,k)<A(j,k)) 144 less=less+1; 145 elseif(B(i,k)==A(j,k)) 146 equal=equal+1; 147 end 148 end 149 if(less==0 && equal~=f_num)%B(i)被A(j)支配 150 nn=nn+1;%被支配个体数目n+1 151 end 152 end 153 if(nn~=0) 154 number=number+1; 155 end 156 end 157 C_AB=number/temp_B; 158 disp('C_AB:'); 159 disp(C_AB); 160 %-----Distance from Representatives in the PF(D-metric)----- 161 A=EP(:,(x_num+1):(x_num+f_num));P=PP;%%%%%%%%%%%%%%%%%%% 162 [temp_A,~]=size(A); 163 [temp_P,~]=size(P); 164 min_d=0; 165 for v=1:temp_P 166 d_va=(A-repmat(P(v,:),temp_A,1)).^2; 167 min_d=min_d+min(sqrt(sum(d_va,2))); 168 end 169 D_AP=(min_d/temp_P); 170 disp('D_AP:'); 171 disp(D_AP); 172 filepath=pwd; 173 cd('G:xjllearnPromatlabLearn临时数据EP_DTLZ2'); 174 save C_AB5.txt C_AB -ASCII 175 save D_AP5.txt D_AP -ASCII 176 cd(filepath);
funfun.m
1 %--------------------ZDT1-------------------- 2 if strcmp(fun,'ZDT1') 3 f_num=2;%目标函数个数 4 x_num=30;%决策变量个数 5 x_min=zeros(1,x_num);%决策变量的最小值 6 x_max=ones(1,x_num);%决策变量的最大值 7 load('ZDT1.txt');%导入正确的前端解 8 plot(ZDT1(:,1),ZDT1(:,2),'g*'); 9 PP=ZDT1; 10 end 11 %--------------------ZDT2-------------------- 12 if strcmp(fun,'ZDT2') 13 f_num=2;%目标函数个数 14 x_num=30;%决策变量个数 15 x_min=zeros(1,x_num);%决策变量的最小值 16 x_max=ones(1,x_num);%决策变量的最大值 17 load('ZDT2.txt');%导入正确的前端解 18 plot(ZDT2(:,1),ZDT2(:,2),'g*'); 19 PP=ZDT2; 20 end 21 %--------------------ZDT3-------------------- 22 if strcmp(fun,'ZDT3') 23 f_num=2;%目标函数个数 24 x_num=30;%决策变量个数 25 x_min=zeros(1,x_num);%决策变量的最小值 26 x_max=ones(1,x_num);%决策变量的最大值 27 load('ZDT3.txt');%导入正确的前端解 28 plot(ZDT3(:,1),ZDT3(:,2),'g*'); 29 PP=ZDT3; 30 end 31 %--------------------ZDT4-------------------- 32 if strcmp(fun,'ZDT4') 33 f_num=2;%目标函数个数 34 x_num=10;%决策变量个数 35 x_min=[0,-5,-5,-5,-5,-5,-5,-5,-5,-5];%决策变量的最小值 36 x_max=[1,5,5,5,5,5,5,5,5,5];%决策变量的最大值 37 load('ZDT4.txt');%导入正确的前端解 38 plot(ZDT4(:,1),ZDT4(:,2),'g*'); 39 PP=ZDT4; 40 end 41 %--------------------ZDT6-------------------- 42 if strcmp(fun,'ZDT6') 43 f_num=2;%目标函数个数 44 x_num=10;%决策变量个数 45 x_min=zeros(1,x_num);%决策变量的最小值 46 x_max=ones(1,x_num);%决策变量的最大值 47 load('ZDT6.txt');%导入正确的前端解 48 plot(ZDT6(:,1),ZDT6(:,2),'g*'); 49 PP=ZDT6; 50 end 51 %-------------------DTLZ1-------------------- 52 if strcmp(fun,'DTLZ1') 53 f_num=3;%目标函数个数 54 x_num=10;%决策变量个数 55 x_min=zeros(1,x_num);%决策变量的最小值 56 x_max=ones(1,x_num);%决策变量的最大值 57 load('DTLZ1.txt');%导入正确的前端解 58 plot3(DTLZ1(:,1),DTLZ1(:,2),DTLZ1(:,3),'g*'); 59 PP=DTLZ1; 60 end 61 %-------------------DTLZ2-------------------- 62 if strcmp(fun,'DTLZ2') 63 f_num=3;%目标函数个数 64 x_num=10;%决策变量个数 65 x_min=zeros(1,x_num);%决策变量的最小值 66 x_max=ones(1,x_num);%决策变量的最大值 67 load('DTLZ2.txt');%导入正确的前端解 68 plot3(DTLZ2(:,1),DTLZ2(:,2),DTLZ2(:,3),'g*'); 69 PP=DTLZ2; 70 end
ws_approach.m
1 function f = ws_approach( lamda,f,i ) 2 %ws_approach 3 f=lamda(i,:)*f'; 4 5 6 end
updateNeighbor.m
1 function X = updateNeighbor( lamda,z,X,Bi,off,x_num,f_num ) 2 %更新领域解 3 for i=1:length(Bi) 4 gte_xi=tchebycheff_approach(lamda,z,X(Bi(i),(x_num+1):(x_num+f_num)),Bi(i)); 5 gte_off=tchebycheff_approach(lamda,z,off(:,(x_num+1):(x_num+f_num)),Bi(i)); 6 % gte_xi=ws_approach(lamda,X(Bi(i),(x_num+1):(x_num+f_num)),Bi(i)); 7 % gte_off=ws_approach(lamda,off(:,(x_num+1):(x_num+f_num)),Bi(i)); 8 if gte_off <= gte_xi 9 X(Bi(i),:)=off; 10 end 11 end
tchebycheff_approach.m
1 function fs = tchebycheff_approach( lamda,z,f,i) 2 %tchebycheff_approach 3 for j=1:length(lamda(i,:)) 4 if(lamda(i,j)==0) 5 lamda(i,j)=0.00001; 6 end 7 end 8 fs=max(lamda(i,:).*abs(f-z)); 9 end
object_fun.m
1 function f = object_fun( x,f_num,x_num,fun ) 2 % 测试函数的设置 3 %--------------------ZDT1-------------------- 4 if strcmp(fun,'ZDT1') 5 f=[]; 6 f(1)=x(1); 7 sum=0; 8 for i=2:x_num 9 sum = sum+x(i); 10 end 11 g=1+9*(sum/(x_num-1)); 12 f(2)=g*(1-(f(1)/g)^0.5); 13 end 14 %--------------------ZDT2-------------------- 15 if strcmp(fun,'ZDT2') 16 f=[]; 17 f(1)=x(1); 18 sum=0; 19 for i=2:x_num 20 sum = sum+x(i); 21 end 22 g=1+9*(sum/(x_num-1)); 23 f(2)=g*(1-(f(1)/g)^2); 24 end 25 %--------------------ZDT3-------------------- 26 if strcmp(fun,'ZDT3') 27 f=[]; 28 f(1)=x(1); 29 sum=0; 30 for i=2:x_num 31 sum = sum+x(i); 32 end 33 g=1+9*(sum/(x_num-1)); 34 f(2)=g*(1-(f(1)/g)^0.5-(f(1)/g)*sin(10*pi*f(1))); 35 end 36 %--------------------ZDT4-------------------- 37 if strcmp(fun,'ZDT4') 38 f=[]; 39 f(1)=x(1); 40 sum=0; 41 for i=2:x_num 42 sum = sum+(x(i)^2-10*cos(4*pi*x(i))); 43 end 44 g=1+9*10+sum; 45 f(2)=g*(1-(f(1)/g)^0.5); 46 end 47 %--------------------ZDT6-------------------- 48 if strcmp(fun,'ZDT6') 49 f=[]; 50 f(1)=1-(exp(-4*x(1)))*((sin(6*pi*x(1)))^6); 51 sum=0; 52 for i=2:x_num 53 sum = sum+x(i); 54 end 55 g=1+9*((sum/(x_num-1))^0.25); 56 f(2)=g*(1-(f(1)/g)^2); 57 end 58 %-------------------------------------------- 59 %--------------------DTLZ1------------------- 60 if strcmp(fun,'DTLZ1') 61 f=[]; 62 sum=0; 63 for i=3:x_num 64 sum = sum+((x(i)-0.5)^2-cos(20*pi*(x(i)-0.5))); 65 end 66 g=100*(x_num-2)+100*sum; 67 f(1)=(1+g)*x(1)*x(2); 68 f(2)=(1+g)*x(1)*(1-x(2)); 69 f(3)=(1+g)*(1-x(1)); 70 end 71 %-------------------------------------------- 72 %--------------------DTLZ2------------------- 73 if strcmp(fun,'DTLZ2') 74 f=[]; 75 sum=0; 76 for i=3:x_num 77 sum = sum+(x(i))^2; 78 end 79 g=sum; 80 f(1)=(1+g)*cos(x(1)*pi*0.5)*cos(x(2)*pi*0.5); 81 f(2)=(1+g)*cos(x(1)*pi*0.5)*sin(x(2)*pi*0.5); 82 f(3)=(1+g)*sin(x(1)*pi*0.5); 83 end 84 %-------------------------------------------- 85 end
look_neighbor.m
1 function B = look_neighbor( lamda,T ) 2 %计算任意两个权重向量间的欧式距离 3 N =size(lamda,1); 4 B=zeros(N,T); 5 distance=zeros(N,N); 6 for i=1:N 7 for j=1:N 8 l=lamda(i,:)-lamda(j,:); 9 distance(i,j)=sqrt(l*l'); 10 end 11 end 12 %查找每个权向量最近的T个权重向量的索引 13 for i=1:N 14 [~,index]=sort(distance(i,:)); 15 B(i,:)=index(1:T); 16 end
initialize.m
1 function chromo = initialize( pop,f_num,x_num,x_min,x_max,fun ) 2 % 种群初始化 3 chromo = repmat(x_min,pop,1)+rand(pop,x_num).*repmat(x_max-x_min,pop,1); 4 for i=1:pop 5 chromo(i,(x_num+1:(x_num+f_num))) = object_fun(chromo(i,:),f_num,x_num,fun); 6 chromo(i,(x_num+f_num+1)) = 0; 7 end 8 % for i=1:pop 9 % for j=1:x_num 10 % chromo(i,j)=x_min(j)+(x_max(j)-x_min(j))*rand(1); 11 % end 12 % chromo(i,(x_num+1:(x_num+f_num))) = object_fun(chromo(i,:),f_num,x_num,fun); 13 % end
genrate_lamda.m
1 function lamda = genrate_lamda( N,f_num ) 2 %产生初始化向量lamda 3 lamda2=zeros(N+1,f_num);%初始化 4 if f_num==2 5 array=(0:N)/N;%均匀分布的值 6 for i=1:N+1 7 lamda2(i,1)=array(i); 8 lamda2(i,2)=1-array(i); 9 end 10 len = size(lamda2,1); 11 index = randperm(len); 12 index = sort(index(1:N)); 13 lamda = lamda2(index,:); 14 elseif f_num==3 15 k = 1; 16 array = (0:25)/25;%产生均匀分布的值 17 for i=1:26 18 for j = 1:26 19 if i+j<28 20 lamda3(k,1) = array(i); 21 lamda3(k,2) = array(j); 22 lamda3(k,3) = array(28-i-j); 23 k=k+1; 24 end 25 end 26 end 27 len = size(lamda3,1); 28 index = randperm(len); 29 index = sort(index(1:N)); 30 lamda = lamda3(index,:); 31 end 32 end
deterdomination.m
1 function X = deterdomination( X,N,f_num,x_num ) 2 %初始化是否为非支配个体 3 for i=1:N 4 X(i,(x_num+f_num+1))=0; 5 end 6 7 for i=1:N 8 nn=0; 9 for j=1:N 10 less=0;%当前个体的目标函数值小于多少个体的数目 11 equal=0;%当前个体的目标函数值等于多少个体的数目 12 for k=1:f_num 13 if(X(i,x_num+k)<X(j,x_num+k)) 14 less=less+1; 15 elseif(X(i,x_num+k)==X(j,x_num+k)) 16 equal=equal+1; 17 end 18 end 19 if(less==0 && equal~=f_num) 20 nn=nn+1;%被支配个体数目n+1 21 end 22 end 23 if(nn==0) 24 X(i,(x_num+f_num+1))=1; 25 end 26 end 27 end
cross_mutation2.m
1 function chromo_offspring = cross_mutation2( chromo_parent_1,chromo_parent_2,f_num,x_num,x_min,x_max,pc,pm,yita1,yita2,fun ) 2 %模拟二进制交叉与多项式变异 3 %%%模拟二进制交叉 4 if(rand(1)<pc) 5 %初始化子代种群 6 off_1=zeros(1,x_num+f_num); 7 %进行模拟二进制交叉 8 gama=zeros(1,x_num); 9 for j=1:x_num 10 u1=rand; 11 if u1<=0.5 12 gama(j)=(2*u1)^(1/(yita1+1)); 13 else 14 gama(j)=(1/(2*(1-u1)))^(1/(yita1+1)); 15 end 16 off_1(j)=0.5*((1-gama(j))*chromo_parent_1(j)+(1+gama(j))*chromo_parent_2(j)); 17 %使子代在定义域内 18 if(off_1(j)>x_max(j)) 19 off_1(j)=x_max(j); 20 elseif(off_1(j)<x_min(j)) 21 off_1(j)=x_min(j); 22 end 23 end 24 %计算子代个体的目标函数值 25 off_1(1,(x_num+1):(x_num+f_num))=object_fun(off_1,f_num,x_num,fun); 26 end 27 %%%多项式变异 28 if(rand(1)<pm) 29 r=randperm(x_num); 30 ind=r(1); %选中变异的位置 31 r=rand; 32 if r<0.5 33 delta=(2*r)^(1/(1+yita2))-1; 34 else 35 delta=1-(2*(1-r))^(1/(yita2+1)); 36 end 37 off_1(ind)=off_1(ind)+delta*(x_max(ind)-x_min(ind)); 38 for j=1:x_num 39 %使子代在定义域内 40 if(off_1(j)>x_max(j)) 41 off_1(j)=x_max(j); 42 elseif(off_1(j)<x_min(j)) 43 off_1(j)=x_min(j); 44 end 45 end 46 %计算子代个体的目标函数值 47 off_1(1,(x_num+1):(x_num+f_num))=object_fun(off_1,f_num,x_num,fun); 48 end 49 chromo_offspring=off_1; 50 end
cross_mutation.m
1 function chromo_offspring = cross_mutation( chromo_parent_1,chromo_parent_2,f_num,x_num,x_min,x_max,pc,pm,yita1,yita2,fun ) 2 %模拟二进制交叉与多项式变异 3 %%%模拟二进制交叉 4 if(rand(1)<pc) 5 %初始化子代种群 6 off_1=zeros(1,x_num+f_num+1); 7 %进行模拟二进制交叉 8 u1=zeros(1,x_num); 9 gama=zeros(1,x_num); 10 for j=1:x_num 11 u1(j)=rand(1); 12 if u1(j)<=0.5 13 gama(j)=(2*u1(j))^(1/(yita1+1)); 14 else 15 gama(j)=(1/(2*(1-u1(j))))^(1/(yita1+1)); 16 end 17 off_1(j)=0.5*((1-gama(j))*chromo_parent_1(j)+(1+gama(j))*chromo_parent_2(j)); 18 %使子代在定义域内 19 if(off_1(j)>x_max(j)) 20 off_1(j)=x_max(j); 21 elseif(off_1(j)<x_min(j)) 22 off_1(j)=x_min(j); 23 end 24 end 25 %计算子代个体的目标函数值 26 off_1(1,(x_num+1):(x_num+f_num))=object_fun(off_1,f_num,x_num,fun); 27 end 28 %%%多项式变异 29 if(rand(1)<pm) 30 u2=zeros(1,x_num); 31 delta=zeros(1,x_num); 32 for j=1:x_num 33 u2(j)=rand(1); 34 if(u2(j)<0.5) 35 delta(j)=(2*u2(j))^(1/(yita2+1))-1; 36 else 37 delta(j)=1-(2*(1-u2(j)))^(1/(yita2+1)); 38 end 39 off_1(j)=off_1(j)+delta(j); 40 %使子代在定义域内 41 if(off_1(j)>x_max(j)) 42 off_1(j)=x_max(j); 43 elseif(off_1(j)<x_min(j)) 44 off_1(j)=x_min(j); 45 end 46 end 47 %计算子代个体的目标函数值 48 off_1(1,(x_num+1):(x_num+f_num))=object_fun(off_1,f_num,x_num,fun); 49 end 50 chromo_offspring=off_1; 51 end