youhua.m

优化灵巧手的各节长度,适用于多指灵巧手的手指结构优化设计的多目标优化函数。

function [f,g]=youhua(x)  
% obtain the objective function
V0=4*pi*(x(1)+x(2)+x(3))^3/3;S0=8*pi*(x(1)+x(2)+x(3))^2;
Va=8*pi^2*x(1)*x(2)*x(3);Sa=4*pi^2*x(1)*((x(2)+x(3))+abs(x(2)-x(3)));
Vb=8*pi^2*x(1)*x(2)*x(3)+2*pi*x(1)*(x(1)*sqrt((x(2)+x(3))^2-x(1)^2)-(x(2)+x(3))^2*acos(x(1)/(x(2)+x(3))))+4*pi*((x(2)+x(3))^2-x(1)^2-x(1)^2*sqrt((x(2)+x(3))^2-x(1)^2))/3;
Sb=4*pi^2*x(1)*(x(2)+x(3))-4*pi*x(1)*(x(2)+x(3))*acos(x(1)/(x(2)+x(3)))+4*pi*(x(2)+x(3))*sqrt((x(2)+x(3))^2-x(1)^2)+4*pi^2*x(1)*abs(x(2)-x(3));
Vc=8*pi^2*x(1)*x(2)*x(3)+2*pi*x(1)*(((x(2)-x(3))^2*acos(x(1)/abs(x(2)-x(3)))-x(1)*sqrt((x(2)-x(3))^2-x(1)^2))-((x(2)+x(3))^2*acos(x(1)/(x(2)+x(3)))-x(1)*sqrt((x(2)+x(3))^2-x(1)^2)))+4*pi*(((x(2)+x(3))^2-x(1)^2)*sqrt((x(2)+x(3))^2-x(1)^2)-((x(2)-x(3))^2-x(1)^2)*sqrt((x(2)-x(3))^2-x(1)^2))/3;
Sc=4*pi^2*x(1)*(x(2)+x(3))-4*pi*x(1)*(x(2)+x(3))*acos(x(1)/(x(2)+x(3)))+4*pi*(x(2)+x(3))*sqrt((x(2)+x(3))^2-x(1)^2)+4*pi^2*x(1)*abs(x(2)-x(3))-4*pi*x(1)*abs(x(2)-x(3))*acos(x(1)/abs(x(2)-x(3))+4*pi*abs(x(2)-x(3))*sqrt(x(2)-x(3))^2-x(1)^2);
if x(1)>=x(2)+x(3)
    V=Va;S=Sa;
else if abs(x(2)-x(3))<=x(1)&x(1)<x(2)+x(3)
        V=Vb;S=Sb;
    else if 0<x(1)&x(1)<abs(x(2)-x(3))
            V=Vc;S=Sc;
        end
    end
end
f1=V0/V;f2=S/S0;f3=f1;f4=(x(1)+x(2)+x(3))/V^(1/3);
f=0.25*f1+0.25*f2+0.25*f3+0.25*f4;