Matlab:一种有效的差分进化算法解决多目标优化问题（MODEA）

%% %%%%%%%%%%%%%%%%多目标测试函数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %SCH、FON、POL、KUR、ZDT来自文献---A Fast and Elitist Multiobjective Genetic Algorithm:NSGA-II %DTLZ来自文献--Scalable Multi-Objective Optimization Test Problems %MOP来自文献---Decomposition of a Multiobjective Optimization Probleminto a Number of Simple Multiobjective Subproblems function y=muti_fun(x,type) global D if type==1 %SCH----维度1---边界范围[-10^3,10^3] y(1)=x.^2; y(2)=(x-2).^2; elseif type==2 %FON-------维度3----边界范围[-4,4] L=3; sumFON1=0; sumFON2=0; for i=1:L sumFON1=sumFON1+(x(i)-1/sqrt(3)).^2; sumFON2=sumFON2+(x(i)+1/sqrt(3)).^2; end y(1)=1-exp(-sumFON1); y(2)=1-exp(-sumFON2); elseif type==3 %POL-----维度2-----边界范围[-pi,pi] A1=0.5*sin(1)-2*cos(1)+sin(2)-1.5*cos(2); A2=1.5*sin(1)-cos(1)+2*sin(2)-0.5*cos(2); B1=0.5*sin(x(1))-2*cos(x(1))+sin(x(2))-1.5*cos(x(2)); B2=1.5*sin(x(1))-cos(x(1))+2*sin(x(2))-0.5*cos(x(2)); y(1)=1+(A1-B1).^2+(A2-B2).^2; y(2)=(x(1)+3).^2+(x(2)+1).^2; elseif type==4 %KUR-----------维度3-----边界范围[-5,5] sumKUR1=0; sumKUR2=0; for i=1:D-1 sumKUR1=sumKUR1+(-10*exp(-0.2*sqrt(x(i).^2+x(i+1).^2))); end for i=1:D sumKUR2=sumKUR2+abs(x(i)).^(0.8)+5*sin(x(i).^3); end y(1)=sumKUR1; y(2)=sumKUR2; elseif type==5 %ZDT1----维度30----边界范围[0,1] y(1)=x(1); y(2)=1-sqrt(y(1)/g(x)); elseif type==6 %ZDT2----维度30----边界范围[0,1] y(1)=x(1); y(2)=1-(y(1)/g1(x)).^2; elseif type==7 %ZDT3----维度30----边界范围[0,1] y(1)=x(1); y(2)=1-sqrt(y(1)/g1(x))-(y(1)/g1(x))*sin(10*pi*y(1)); elseif type==8 %ZDT4----维度10----边界范围x1=[0,1],x(2,...,10)=[-5,5] y(1)=x(1); y(2)=1-sqrt(y(1)/g2(x)); elseif type==9 %ZDT6----维度10----边界范围[0,1] y(1)=1-exp(-4*x(1))*sin(6*pi*x(1)).^6; y(2)=1-(y(1)/g3(x)).^2; elseif type==10 %MOP1----维度10----边界范围[0,1] y(1)=(1+g4(x))*x(1); y(2)=(1+g4(x))*(1-sqrt(x(1))); elseif type==11 %MOP2----维度10----边界范围[0,1] y(1)=(1+g5(x))*x(1); y(2)=(1+g5(x))*(1-x(1).^2); elseif type==12 %MOP3----维度10----边界范围[0,1] y(1)=(1+g6(x))*cos((pi*x(1))/2); y(2)=(1+g6(x))*sin((pi*x(1))/2); elseif type==13 %MOP4----维度10----边界范围[0,1] y(1)=(1+g7(x))*x(1); y(2)=(1+g7(x))*(1-x(1).^2*cos(2*pi*x(1)).^2); elseif type==14 %MOP5----维度10----边界范围[0,1] y(1)=(1+g8(x))*x(1); y(2)=(1+g8(x))*(1-sqrt(x(1))); elseif type==15 %MOP6----三目标----维度10----边界范围[0,1] y(1)=(1+g9(x))*x(1)*x(2); y(2)=(1+g9(x))*x(1)*(1-x(2)); y(3)=(1+g9(x))*(1-x(1)); elseif type==16 %MOP7----三目标----维度10----边界范围[0,1] y(1)=(1+g10(x))*cos((x(1)*pi)/2)*cos((x(2)*pi)/2); y(2)=(1+g10(x))*cos((x(1)*pi)/2)*sin((x(2)*pi)/2); y(3)=(1+g10(x))*sin((x(1)*pi)/2); elseif type==17 %DTLZ1----三目标----维度7----边界范围[0,1]---定义k=5 y(1)=(1/2)*x(1)*x(2)*(1+g11(x)); y(2)=(1/2)*x(1)*(1-x(2))*(1+g11(x)); y(3)=(1/2)*(1-x(1))*(1+g11(x)); elseif type==18 %DTLZ2----三目标----维度7----边界范围[0,1]---定义k=10 y(1)=(1+g12(x))*cos((pi/2)*x(1))*cos((pi/2)*x(2)); y(2)=(1+g12(x))*cos((pi/2)*x(1))*sin((pi/2)*x(2)); y(3)=(1+g12(x))*sin((pi/2)*x(1)); elseif type==19 %DTLZ3----三目标----维度12----边界范围[0,1]---定义k=5--k=n-m+1 y(1)=(1+g11(x))*cos((pi/2)*x(1))*cos((pi/2)*x(2)); y(2)=(1+g11(x))*cos((pi/2)*x(1))*sin((pi/2)*x(2)); y(3)=(1+g11(x))*sin((pi/2)*x(1)); elseif type==20 %DTLZ4----三目标----维度12----边界范围[0,1]---定义k=10 a=100; y(1)=(1+g12(x))*cos((pi/2)*x(1).^a)*cos((pi/2)*x(2).^a); y(2)=(1+g12(x))*cos((pi/2)*x(1).^a)*sin((pi/2)*x(2).^a); y(3)=(1+g12(x))*sin((pi/2)*x(1).^a); elseif type==21 %DTLZ5----三目标----维度12----边界范围[0,1]---定义k=10 y(1)=(1+g12(x))*cos(x(1)*(pi/2))*cos((pi/(4*(1+g12(x))))*(1+2*g12(x)*x(2))*(pi/2)); y(2)= (1+g12(x))*cos(x(1)*(pi/2))*sin((pi/(4*(1+g12(x))))*(1+2*g12(x)*x(2))*(pi/2)); y(3)=(1+g12(x))*sin(x(1)*(pi/2)); elseif type==22 %DTLZ6----三目标----维度12----边界范围[0,1]---定义k=20 y(1)=(1+g13(x))*cos(x(1)*(pi/2))*cos((pi/(4*(1+g13(x))))*(1+2*g13(x)*x(2))*(pi/2)); y(2)= (1+g13(x))*cos(x(1)*(pi/2))*sin((pi/(4*(1+g13(x))))*(1+2*g13(x)*x(2))*(pi/2)); y(3)=(1+g13(x))*sin(x(1)*(pi/2)); elseif type==23 %DTLZ7--三目标---边界范围[0,1]---k=28 y(1)=x(1); y(2)=x(2); y(3)=(1+g14(x))*h(x); end end %% 下面是各测试集函数子函数 function f=g(x) global D f=1+9*(sum(x(2:D))/(D-1)); end function f=g1(x) global D f=1+9*(sum(x(2:D))/(D-1)); end function f=g2(x) global D D=10; f=0; for i=2:D f=f+x(i).^2-10*cos(4*pi*x(i)); end f=f+1+10*(D-1); end function f=g3(x) global D f=1+9*(sum(x(:,2:D))/(D-1)).^0.25; end function f=g4(x) %MOP1 global D f=0; for i=2:D t(i)=x(i)-sin(0.5*pi*x(1)); f=-0.9*t(i).^2+abs(t(i)).^0.6+f; end f=f*2*sin(pi*x(1)); end function f=g5(x) %MOP2 global D f=0; for i=2:D t(i)=x(i)-sin(0.5*pi*x(1)); f=(abs(t(i))/(1+exp(5*abs(t(i)))))+f; end f=f*10*sin(pi*x(1)); end function f=g6(x) %MOP3 global D f=0; for i=2:D t(i)=x(i)-sin(0.5*pi*x(1)); f=(abs(t(i))/(1+exp(5*abs(t(i)))))+f; end f=f*10*sin(pi*x(1)*(1/2)); end function f=g7(x) %MOP4 global D f=0; for i=2:D t(i)=x(i)-sin(0.5*pi*x(1)); f=(abs(t(i))/(1+exp(5*abs(t(i)))))+f; end f=f*10*sin(pi*x(1)); end function f=g8(x) %MOP5 global D f=0; for i=2:D t(i)=x(i)-sin(0.5*pi*x(1)); f=-0.9*t(i).^2+abs(t(i)).^0.6+f; end f=f*2*abs(cos(pi*x(1))); end function f=g9(x) %MOP6 global D f=0; for i=2:D t(i)=x(i)-x(1)*x(2); f=-0.9*t(i).^2+abs(t(i)).^0.6+f; end f=f*2*sin(pi*x(1)); end function f=g10(x) %MOP7 global D f=0; for i=3:D t(i)=x(i)-x(1)*x(2); f=-0.9*t(i).^2+abs(t(i)).^0.6+f; end f=f*2*sin(pi*x(1)); end function f=g11(x) %DTLZ1 DTLZ3 global D k f=0; for i=3:D f=(x(i)-0.5).^2-cos(20*pi*(x(i)-0.5))+f; end f=(f+k)*100; end function f=g12(x) %DTLZ2 DTLZ4 DTLZ5 global D f=0; for i=3:D f=f+(x(i)-0.5).^2; end end function f=g13(x) % DTLZ6 global D f=0; for i=3:D f=f+x(i).^0.1; end end function f=g14(x) %DTLZ7 global D k f=0; for i=3:D f=f+x(i); end f=1+(9/k)*f; end function g=h(x) global f_num g=0; for i=1:f_num-1 g=g+(x(i)/(1+g14(x)))*(1+sin(3*pi*x(i))); end g=f_num-g; end