|
|
|
|
|
|
|
|
|
|
|
%非线性规划
|
|
|
|
|
|
|
|
|
|
|
|
%P42例题
|
|
|
|
|
|
|
|
|
|
|
|
%求解
|
|
|
|
|
|
clc,clear,format long g,close all;
|
|
|
|
|
|
syms x1 x2;%符号变量(用于定义函数、求解方程、计算导数和积分)
|
|
|
|
|
|
f=(339-0.01*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000);
|
|
|
|
|
|
f=simplify(f);
|
|
|
|
|
|
f1=diff(f,x1),f2=diff(f,x2);
|
|
|
|
|
|
[x10,x20]=solve(f1,f2);%求驻点即使f1,f2为0的点
|
|
|
|
|
|
x10=round(double(x10));%四舍五入
|
|
|
|
|
|
x20=round(double(x20));
|
|
|
|
|
|
f0=subs(f,{x1,x2},{x10,x20});
|
|
|
|
|
|
f0=double(f0);
|
|
|
|
|
|
subplot(121);
|
|
|
|
|
|
fmesh(f,[0,10000,0,10000]);%3维
|
|
|
|
|
|
%xlabel('x1','Interpreter','latex');
|
|
|
|
|
|
%ylabel('y1','Interpreter','latex');
|
|
|
|
|
|
xlabel('x1');
|
|
|
|
|
|
ylabel('y1');
|
|
|
|
|
|
subplot(122);
|
|
|
|
|
|
L=fcontour(f,[0,10000,0,10000]);
|
|
|
|
|
|
contour(L.XData,L.YData,L.ZData,'ShowText','on');
|
|
|
|
|
|
xlabel('x1');
|
|
|
|
|
|
ylabel('y1');
|
|
|
|
|
|
p1=339-0.01*x10-0.003*x20;
|
|
|
|
|
|
p2=399-0.004*x10-0.01*x20;
|
|
|
|
|
|
c=195*x10+225*x20+400000;
|
|
|
|
|
|
rate=f0/c;
|
|
|
|
|
|
|
|
|
|
|
|
%灵敏性检验 分析 最优解 对 19村彩电价格下降幅度 的灵敏性
|
|
|
|
|
|
clc,clear,close all,format long g;
|
|
|
|
|
|
syms x1 x2 a;
|
|
|
|
|
|
X1=4735,X2=7043,AA=0.01,FF=553641;
|
|
|
|
|
|
f=(339-a*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000);
|
|
|
|
|
|
f1=diff(f,x1),f2=diff(f,x2);
|
|
|
|
|
|
[x10,x20]=solve(f1,f2);
|
|
|
|
|
|
|
|
|
|
|
|
subplot(121);
|
|
|
|
|
|
fplot(x10,[0.002,0.02]);
|
|
|
|
|
|
xlabel('a');
|
|
|
|
|
|
ylabel('x1');
|
|
|
|
|
|
|
|
|
|
|
|
subplot(122);
|
|
|
|
|
|
fplot(x20,[0.002,0.02]);
|
|
|
|
|
|
xlabel('a');
|
|
|
|
|
|
ylabel('x2');
|
|
|
|
|
|
|
|
|
|
|
|
dx1=diff(x10,a);
|
|
|
|
|
|
dx10=subs(dx1,a,0.01),dx10=double(dx10);
|
|
|
|
|
|
sx1a=dx10*AA/X1;
|
|
|
|
|
|
|
|
|
|
|
|
dx2=diff(x20,a);
|
|
|
|
|
|
dx20=subs(dx2,a,0.01),dx20=double(dx20);
|
|
|
|
|
|
sx2a=dx20*AA/X2;
|
|
|
|
|
|
|
|
|
|
|
|
F=subs(f,[x1,x2],[x10,x20]);
|
|
|
|
|
|
F=simplify(F);
|
|
|
|
|
|
figure,fplot(F,[0.002,0.02]);
|
|
|
|
|
|
xlabel('a');
|
|
|
|
|
|
ylabel('profit');
|
|
|
|
|
|
dpro=diff(F,a);
|
|
|
|
|
|
dpro0=subs(F,a,0.01);
|
|
|
|
|
|
sya=dpro0*AA/FF;
|
|
|
|
|
|
|
|
|
|
|
|
%当a提高10%
|
|
|
|
|
|
f3=subs(f,[x1,x2,a],[X1,X2,0.011]),f3=double(f3);
|
|
|
|
|
|
f4=subs(F,[a],0.011);
|
|
|
|
|
|
%相对误差
|
|
|
|
|
|
delta=(f4-f3)/f4;
|
|
|
|
|
|
delta=double(delta);
|
|
|
|
|
|
%相对误差很小，说明在19寸的价格下降幅度在一定范围内发生变化时，仍然按照不变时的最优解来确定生产方案，仍然可以获得几乎最优的利润。
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
%使用fmincon的简单例子
|
|
|
|
|
|
|
|
|
|
|
|
%蒙特卡罗确定初始值
|
|
|
|
|
|
clc,clear,close all;
|
|
|
|
|
|
n=10^7;
|
|
|
|
|
|
x1=unifrnd(0,12,[1,n]);
|
|
|
|
|
|
x2=unifrnd(0,12,[1,n]);
|
|
|
|
|
|
fmin=+inf;
|
|
|
|
|
|
for i=1:n
|
|
|
|
|
|
x=[x1(i),x2(i)];
|
|
|
|
|
|
if ((x1(i)-1)^2-x2(i)-6<=0) & (-2*x1(i)+3*x2(i)-6<=0)
|
|
|
|
|
|
temp=x(1)^2+x(2)^2-x(1)*x(2)-2*x(1)-5*x(2);
|
|
|
|
|
|
if temp<fmin
|
|
|
|
|
|
fmin=temp;
|
|
|
|
|
|
x0=x;
|
|
|
|
|
|
end
|
|
|
|
|
|
end
|
|
|
|
|
|
end
|
|
|
|
|
|
|
|
|
|
|
|
%[x,fval]= fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
|
|
|
|
|
|
|
|
|
|
|
|
A=[-2,3];
|
|
|
|
|
|
b=6;
|
|
|
|
|
|
[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1);
|
|
|
|
|
|
|
|
|
|
|
|
%option=optimoptions('fmincon','Algorithm','sqp');
|
|
|
|
|
|
%[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1,option);
|
|
|
|
|
|
|
|
|
|
|
|
disp('Thw optimal solution is:');
|
|
|
|
|
|
disp(x);
|
|
|
|
|
|
disp('The minimum value is:');
|
|
|
|
|
|
disp(fval);
|
|
|
|
|
|
figure;
|
|
|
|
|
|
fmesh(@(x1, x2) arrayfun(@(x1, x2) fun1([x1, x2]), x1, x2), [-4, 4, -4, 4]);%用法
|
|
|
|
|
|
|
|
|
|
|
|
xlabel('x1');
|
|
|
|
|
|
ylabel('x2');
|
|
|
|
|
|
zlabel('f(x1,x2)');
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
%非线性规划---料场选址
|
|
|
|
|
|
clc,clear,close all;
|
|
|
|
|
|
a=[1.25,8.75,0.5,5.75,3,7.25];
|
|
|
|
|
|
b=[1.25,0.75,4.75,5,6.5,7.25];
|
|
|
|
|
|
A=[1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0];
|
|
|
|
|
|
bb=[20;20];
|
|
|
|
|
|
Aeq=[eye(6),eye(6),zeros(6,4)];
|
|
|
|
|
|
beq=[3;5;4;7;6;11;];
|
|
|
|
|
|
lb=[zeros(12,1);-inf;-inf;-inf;-inf];
|
|
|
|
|
|
x0=[3,5,0,7,0,1,0,0,4,0,6,10,5,1,2,7];
|
|
|
|
|
|
[xans,fvans]=fmincon(@fun2,x0,A,bb,Aeq,beq,lb,[]);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
