p3itgm2rp
/
mycode
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Merge pull request '三人三个文件夹' (#2) from 盘荣博 into main

Browse Source
王朝群
p3itgm2rp 5 months ago
parent 371c0c70c3 19262e6ef2
commit aa9c8889bd
11 changed files with 564 additions and 536 deletions
Show Stats Download Patch File Download Diff File

80
LPej1_3.m → 姚安欣/LPej1_3.m
Unescape View File

@ -1,40 +1,40 @@
clc; clear; close all; format long g; clc; clear; close all; format long g;
prob=optimproblem; prob=optimproblem;
x=optimvar('x',9,1,'LowerBound',0,'Type','integer'); x=optimvar('x',9,1,'LowerBound',0,'Type','integer');
p=[0.25,0.35,0.50]; p=[0.25,0.35,0.50];
r=[1.25,2.00,2.80]; r=[1.25,2.00,2.80];
ot=[5,10,0;7,9,12;6,8,0;4,0,11;7,0,0]; ot=[5,10,0;7,9,12;6,8,0;4,0,11;7,0,0];
total=1000:200:3000; total=1000:200:3000;
odp=[300/6000,321/10000,250/4000,783/7000,200/4000]; odp=[300/6000,321/10000,250/4000,783/7000,200/4000];
X=[]; X=[];
Q=[]; Q=[];
for i=1:length(total) for i=1:length(total)
% prob.Objective=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1)+(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2)+(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3)+(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4)+(ot(5,1)*(x(3)+x(6)))*odp(5)-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9); % prob.Objective=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1)+(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2)+(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3)+(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4)+(ot(5,1)*(x(3)+x(6)))*odp(5)-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9);
dp1=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1); dp1=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1);
dp2=(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2); dp2=(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2);
dp3=(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3); dp3=(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3);
dp4=(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4); dp4=(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4);
dp5=(ot(5,1)*(x(3)+x(6)))*odp(5); dp5=(ot(5,1)*(x(3)+x(6)))*odp(5);
dp=dp1+dp2+dp3+dp4+dp5; dp=dp1+dp2+dp3+dp4+dp5;
prob.Objective=dp-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9); prob.Objective=dp-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9);
prob.Constraints.con1=p(1)*ones(1,6)*x(1:6)+p(2)*ones(1,2)*x(7:8)+p(3)*x(9)+dp<=total(i);%总费用 prob.Constraints.con1=p(1)*ones(1,6)*x(1:6)+p(2)*ones(1,2)*x(7:8)+p(3)*x(9)+dp<=total(i);%总费用
prob.Constraints.con2=ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7)<=6000;%A1 prob.Constraints.con2=ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7)<=6000;%A1
prob.Constraints.con3=ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9)<=10000; prob.Constraints.con3=ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9)<=10000;
prob.Constraints.con4=ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8))<=4000; prob.Constraints.con4=ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8))<=4000;
prob.Constraints.con5=ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9)<=7000; prob.Constraints.con5=ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9)<=7000;
prob.Constraints.con6=ot(5,1)*(x(3)+x(6))<=4000; prob.Constraints.con6=ot(5,1)*(x(3)+x(6))<=4000;
[sol,fval,flag,out]=solve(prob); [sol,fval,flag,out]=solve(prob);
xx=sol.x; xx=sol.x;
X=[X,xx]; X=[X,xx];
Q=[Q,-fval]; Q=[Q,-fval];
end end
plot(total,Q,'*-'); plot(total,Q,'*-');

122
Mengtkl.m → 姚安欣/Mengtkl.m
Unescape View File

@ -1,61 +1,61 @@
%27页例题 %27页例题
clc; clear; close all; clc; clear; close all;
n = 10000; % 使用较小的 n 值以便更容易可视化 n = 10000; % 使用较小的 n 值以便更容易可视化
x = unifrnd(0, 12, [1, n]); x = unifrnd(0, 12, [1, n]);
y = unifrnd(0, 9, [1, n]); y = unifrnd(0, 9, [1, n]);
ans=sum(y < x.^2 & x <= 3)+sum(y < 12 - x & x >= 3); ans=sum(y < x.^2 & x <= 3)+sum(y < 12 - x & x >= 3);
ans=ans/n; ans=ans/n;
% 找出满足条件的点 % 找出满足条件的点
condition1 = y < x.^2 & x <= 3; condition1 = y < x.^2 & x <= 3;
condition2 = y < 12 - x & x >= 3; condition2 = y < 12 - x & x >= 3;
condition_met = condition1 | condition2; % 满足任一条件的点 condition_met = condition1 | condition2; % 满足任一条件的点
condition_not_met = ~condition_met; % 不满足任何条件的点 condition_not_met = ~condition_met; % 不满足任何条件的点
% 创建图形窗口 % 创建图形窗口
figure; figure;
hold on;%在同一张图上绘图 hold on;%在同一张图上绘图
% 绘制不满足任何条件的点 % 绘制不满足任何条件的点
scatter(x(condition_not_met), y(condition_not_met), 'k.'); % k----黑色 .----绘制样式 scatter(x(condition_not_met), y(condition_not_met), 'k.'); % k----黑色 .----绘制样式
%scatter绘制散点图 %scatter绘制散点图
%x(condition_not_met) 会返回一个新的向量，其中只包含 x 中对应 condition_not_met 为 true 的元素。 %x(condition_not_met) 会返回一个新的向量，其中只包含 x 中对应 condition_not_met 为 true 的元素。
% 绘制满足第一个条件的点 % 绘制满足第一个条件的点
scatter(x(condition1), y(condition1), 'r.'); % 红色 scatter(x(condition1), y(condition1), 'r.'); % 红色
% 绘制满足第二个条件的点 % 绘制满足第二个条件的点
scatter(x(condition2), y(condition2), 'b.'); % 蓝色 scatter(x(condition2), y(condition2), 'b.'); % 蓝色
% 添加图例和标签 % 添加图例和标签
legend('不满足任何条件的点', '满足 y < x^2 且 x <= 3 的点', '满足 y < 12 - x 且 x >= 3 的点'); legend('不满足任何条件的点', '满足 y < x^2 且 x <= 3 的点', '满足 y < 12 - x 且 x >= 3 的点');
xlabel('x'); xlabel('x');
ylabel('y'); ylabel('y');
title('随机生成的点和满足条件的点'); title('随机生成的点和满足条件的点');
hold off; hold off;
%蒙特卡洛法求圆周率qw %蒙特卡洛法求圆周率qw
clc;clear;close all; clc;clear;close all;
n=10^5; n=10^5;
x=unifrnd(-1,1,[1,n]); x=unifrnd(-1,1,[1,n]);
y=unifrnd(-1,1,[1,n]); y=unifrnd(-1,1,[1,n]);
con1=x.^2+y.^2<=1; con1=x.^2+y.^2<=1;
con2=~con1; con2=~con1;
ans=sum(x.^2+y.^2<=1); ans=sum(x.^2+y.^2<=1);
ans=ans/n*4; ans=ans/n*4;
figure ; figure ;
hold on; hold on;
scatter(x(con1),y(con1),'r.'); scatter(x(con1),y(con1),'r.');
scatter(x(con2),y(con2),'k.'); scatter(x(con2),y(con2),'k.');
hold off; hold off;

270
NLP.m → 姚安欣/NLP.m
Unescape View File

@ -1,135 +1,135 @@
%非线性规划 %非线性规划
%P42例题 %P42例题
%求解 %求解
clc,clear,format long g,close all; 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) 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=(339-0.01*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000);
f=simplify(f); f=simplify(f);
f1=diff(f,x1),f2=diff(f,x2); 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,x20]=solve(f1,f2);%求驻点即使f1,f2为0的点
x10=round(double(x10));%四舍五入 x10=round(double(x10));%四舍五入
x20=round(double(x20)); x20=round(double(x20));
f0=subs(f,{x1,x2},{x10,x20}); f0=subs(f,{x1,x2},{x10,x20});
f0=double(f0); f0=double(f0);
subplot(121); subplot(121);
fmesh(f,[0,10000,0,10000]);%3维 fmesh(f,[0,10000,0,10000]);%3维
%xlabel('x1','Interpreter','latex'); %xlabel('x1','Interpreter','latex');
%ylabel('y1','Interpreter','latex'); %ylabel('y1','Interpreter','latex');
xlabel('x1'); xlabel('x1');
ylabel('y1'); ylabel('y1');
subplot(122); subplot(122);
L=fcontour(f,[0,10000,0,10000]); L=fcontour(f,[0,10000,0,10000]);
contour(L.XData,L.YData,L.ZData,'ShowText','on'); contour(L.XData,L.YData,L.ZData,'ShowText','on');
xlabel('x1'); xlabel('x1');
ylabel('y1'); ylabel('y1');
p1=339-0.01*x10-0.003*x20; p1=339-0.01*x10-0.003*x20;
p2=399-0.004*x10-0.01*x20; p2=399-0.004*x10-0.01*x20;
c=195*x10+225*x20+400000; c=195*x10+225*x20+400000;
rate=f0/c; 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 %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; clc,clear,close all,format long g;
syms x1 x2 a; syms x1 x2 a;
X1=4735,X2=7043,AA=0.01,FF=553641; 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); 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); f1=diff(f,x1),f2=diff(f,x2);
[x10,x20]=solve(f1,f2); [x10,x20]=solve(f1,f2);
subplot(121); subplot(121);
fplot(x10,[0.002,0.02]); fplot(x10,[0.002,0.02]);
xlabel('a'); xlabel('a');
ylabel('x1'); ylabel('x1');
subplot(122); subplot(122);
fplot(x20,[0.002,0.02]); fplot(x20,[0.002,0.02]);
xlabel('a'); xlabel('a');
ylabel('x2'); ylabel('x2');
dx1=diff(x10,a); dx1=diff(x10,a);
dx10=subs(dx1,a,0.01),dx10=double(dx10); dx10=subs(dx1,a,0.01),dx10=double(dx10);
sx1a=dx10*AA/X1; sx1a=dx10*AA/X1;
dx2=diff(x20,a); dx2=diff(x20,a);
dx20=subs(dx2,a,0.01),dx20=double(dx20); dx20=subs(dx2,a,0.01),dx20=double(dx20);
sx2a=dx20*AA/X2; sx2a=dx20*AA/X2;
F=subs(f,[x1,x2],[x10,x20]); F=subs(f,[x1,x2],[x10,x20]);
F=simplify(F); F=simplify(F);
figure,fplot(F,[0.002,0.02]); figure,fplot(F,[0.002,0.02]);
xlabel('a'); xlabel('a');
ylabel('profit'); ylabel('profit');
dpro=diff(F,a); dpro=diff(F,a);
dpro0=subs(F,a,0.01); dpro0=subs(F,a,0.01);
sya=dpro0*AA/FF; sya=dpro0*AA/FF;
%当a提高10% %当a提高10%
f3=subs(f,[x1,x2,a],[X1,X2,0.011]),f3=double(f3); f3=subs(f,[x1,x2,a],[X1,X2,0.011]),f3=double(f3);
f4=subs(F,[a],0.011); f4=subs(F,[a],0.011);
%相对误差 %相对误差
delta=(f4-f3)/f4; delta=(f4-f3)/f4;
delta=double(delta); 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。 %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 %使用fmincon的简单例子
%蒙特卡罗确定初始值 %蒙特卡罗确定初始值
clc,clear,close all; clc,clear,close all;
n=10^7; n=10^7;
x1=unifrnd(0,12,[1,n]); x1=unifrnd(0,12,[1,n]);
x2=unifrnd(0,12,[1,n]); x2=unifrnd(0,12,[1,n]);
fmin=+inf; fmin=+inf;
for i=1:n for i=1:n
x=[x1(i),x2(i)]; x=[x1(i),x2(i)];
if ((x1(i)-1)^2-x2(i)-6<=0) & (-2*x1(i)+3*x2(i)-6<=0) 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); temp=x(1)^2+x(2)^2-x(1)*x(2)-2*x(1)-5*x(2);
if temp<fmin if temp<fmin
fmin=temp; fmin=temp;
x0=x; x0=x;
end end
end end
end end
%[x,fval]= fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options) %[x,fval]= fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
A=[-2,3]; A=[-2,3];
b=6; b=6;
[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1); [x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1);
%option=optimoptions('fmincon','Algorithm','sqp'); %option=optimoptions('fmincon','Algorithm','sqp');
%[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1,option); %[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1,option);
disp('Thw optimal solution is:'); disp('Thw optimal solution is:');
disp(x); disp(x);
disp('The minimum value is:'); disp('The minimum value is:');
disp(fval); disp(fval);
figure; figure;
fmesh(@(x1, x2) arrayfun(@(x1, x2) fun1([x1, x2]), x1, x2), [-4, 4, -4, 4]);%用法 fmesh(@(x1, x2) arrayfun(@(x1, x2) fun1([x1, x2]), x1, x2), [-4, 4, -4, 4]);%用法
xlabel('x1'); xlabel('x1');
ylabel('x2'); ylabel('x2');
zlabel('f(x1,x2)'); zlabel('f(x1,x2)');
%非线性规划---料场选址 %非线性规划---料场选址
clc,clear,close all; clc,clear,close all;
a=[1.25,8.75,0.5,5.75,3,7.25]; a=[1.25,8.75,0.5,5.75,3,7.25];
b=[1.25,0.75,4.75,5,6.5,7.25]; 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]; 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]; bb=[20;20];
Aeq=[eye(6),eye(6),zeros(6,4)]; Aeq=[eye(6),eye(6),zeros(6,4)];
beq=[3;5;4;7;6;11;]; beq=[3;5;4;7;6;11;];
lb=[zeros(12,1);-inf;-inf;-inf;-inf]; 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]; 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,[]); [xans,fvans]=fmincon(@fun2,x0,A,bb,Aeq,beq,lb,[]);

0
README.md → 姚安欣/README.md
Unescape View File

6
fun1.m → 姚安欣/fun1.m
Unescape View File

@ -1,3 +1,3 @@
function f=fun1(x) function f=fun1(x)
f=x(1)*x(1)+x(2)*x(2)-x(1)*x(2)-2*x(1)-5*x(2); f=x(1)*x(1)+x(2)*x(2)-x(1)*x(2)-2*x(1)-5*x(2);
end end

28
fun2.m → 姚安欣/fun2.m
Unescape View File

@ -1,15 +1,15 @@
function f=fun2(x) function f=fun2(x)
a=[1.25,8.75,0.5,5.75,3,7.25]; a=[1.25,8.75,0.5,5.75,3,7.25];
b=[1.25,0.75,4.75,5,6.5,7.25]; b=[1.25,0.75,4.75,5,6.5,7.25];
f1 = 0; % 初始化f1 f1 = 0; % 初始化f1
f2 = 0; % 初始化f2 f2 = 0; % 初始化f2
for i=1:6 for i=1:6
s=sqrt((a(i)-x(13))^2+(b(i)-x(14))^2); s=sqrt((a(i)-x(13))^2+(b(i)-x(14))^2);
f1=x(i)*s+f1; f1=x(i)*s+f1;
end end
for i=7:12 for i=7:12
s=sqrt((a(i-6)-x(15))^2+(b(i-6)-x(16))^2); s=sqrt((a(i-6)-x(15))^2+(b(i-6)-x(16))^2);
f2=s*x(i)+f2; f2=s*x(i)+f2;
end end
f=f1+f2; f=f1+f2;
end end

98
intLP.m → 姚安欣/intLP.m
Unescape View File

@ -1,49 +1,49 @@
%整数规划 %整数规划
%P23 ej2.5 %P23 ej2.5
%optimproblem解法 %optimproblem解法
clc; clear; close all; format long g; clc; clear; close all; format long g;
prob=optimproblem; prob=optimproblem;
x=optimvar('x',6,'LowerBound',0,'Type','integer'); x=optimvar('x',6,'LowerBound',0,'Type','integer');
prob.Objective=sum(x); prob.Objective=sum(x);
cnt=[35,40,50,45,55,30]; cnt=[35,40,50,45,55,30];
con=optimconstr(6); con=optimconstr(6);
con(1)=x(1)+x(6)>=35; con(1)=x(1)+x(6)>=35;
for i=1:5 for i=1:5
con(i+1)=x(i)+x(i+1)>=cnt(i+1); con(i+1)=x(i)+x(i+1)>=cnt(i+1);
end end
prob.Constraints.con=con; prob.Constraints.con=con;
[sol,fval,flag,out]=solve(prob); [sol,fval,flag,out]=solve(prob);
X=sol.x; X=sol.x;
%linprog解法 %linprog解法
clc; clear; close all; format long g; clc; clear; close all; format long g;
f=[1,1,1,1,1,1]; f=[1,1,1,1,1,1];
intcon=[1:6]; intcon=[1:6];
A=zeros(6,6); A=zeros(6,6);
A(1,1)=-1; A(1,1)=-1;
A(1,6)=-1; A(1,6)=-1;
for i=1:5 for i=1:5
A(i+1,i)=-1; A(i+1,i)=-1;
A(i+1,i+1)=-1; A(i+1,i+1)=-1;
end end
lb=zeros(6,1);%注意不是lb=0 lb=zeros(6,1);%注意不是lb=0
b=[-35;-40;-50;-45;-55;-30]; b=[-35;-40;-50;-45;-55;-30];
[x,fval]=intlinprog(f,intcon,A,b,[],[],lb); [x,fval]=intlinprog(f,intcon,A,b,[],[],lb);
%01规划 %01规划
%背包问题 %背包问题
f=-[540,200,180,350,60,150,280,450,320,120]; f=-[540,200,180,350,60,150,280,450,320,120];
intcon=1:10; intcon=1:10;
lb=zeros(10); lb=zeros(10);
ub=ones(10); ub=ones(10);
A=[6,3,4,5,1,2,3,5,4,2]; A=[6,3,4,5,1,2,3,5,4,2];
b=30; b=30;
[x,fval]=intlinprog(f,intcon,A,b,[],[],lb,ub); [x,fval]=intlinprog(f,intcon,A,b,[],[],lb,ub);

280
mm1.m → 姚安欣/mm1.m
Unescape View File

@ -1,140 +1,140 @@
%投资利益与风险1998A题 %投资利益与风险1998A题
%模型一 给定风险承受程度，求最大利益 %模型一 给定风险承受程度，求最大利益
f=[-0.05,-0.27,-0.19,-0.185,-0.185]; f=[-0.05,-0.27,-0.19,-0.185,-0.185];
%A矩阵 %A矩阵
%A=[0,0.025,0.015,0.055,0.026]; %错误 %A=[0,0.025,0.015,0.055,0.026]; %错误
%b=[1,1,1,1,1]; %b=[1,1,1,1,1];
A=[zeros(4,1),diag([0.025,0.015,0.055,0.026])];%不等式约束条件矩阵 A=[zeros(4,1),diag([0.025,0.015,0.055,0.026])];%不等式约束条件矩阵
%Aeq、beq %Aeq、beq
Aeq=[1,1.01,1.02,1.045,1.065]; Aeq=[1,1.01,1.02,1.045,1.065];
beq=1; beq=1;
%lb %lb
%lb=0; %错误 %lb=0; %错误
lb=zeros(5,1); lb=zeros(5,1);
%可承担风险率a %可承担风险率a
a=(0:0.001:0.05); a=(0:0.001:0.05);
%保存最优解 %保存最优解
Q=zeros(1,length(a)); Q=zeros(1,length(a));
xx=[];%空矩阵存放最优解对应x的值 xx=[];%空矩阵存放最优解对应x的值
for i=1:length(a) for i=1:length(a)
b=a(i)*ones(4,1); b=a(i)*ones(4,1);
[x,y]=linprog(f,A,b,Aeq,beq,lb); [x,y]=linprog(f,A,b,Aeq,beq,lb);
Q(i)=-y;%注意取负！！！ Q(i)=-y;%注意取负！！！
xx=[xx;x']; xx=[xx;x'];
end end
plot(a,Q,'*r'); plot(a,Q,'*r');
xlabel("风险率"); xlabel("风险率");
ylabel("最大收益"); ylabel("最大收益");
%模型二 收益、风险按权重组合 %模型二 收益、风险按权重组合
% f0=[-0.05,-0.27,-0.19,-0.185,-0.185]; % f0=[-0.05,-0.27,-0.19,-0.185,-0.185];
% w=(0:0.1:1); % w=(0:0.1:1);
% Aeq=[1,1.01,1.02,1.045,1.065,0]; % Aeq=[1,1.01,1.02,1.045,1.065,0];
% beq=1; % beq=1;
% lb=0; % lb=0;
% xx=[]; % xx=[];
% Q=zeros(1,length(w)); % Q=zeros(1,length(w));
% A=[zeros(5,1),diag([0.025,0.025,0.055,0.065,0])]; % A=[zeros(5,1),diag([0.025,0.025,0.055,0.065,0])];
% b=ones(5,1); % b=ones(5,1);
% for i=1:length(w) % for i=1:length(w)
% f=[-w(i)*f0,1-w(i)]; % f=[-w(i)*f0,1-w(i)];
% b=x(end)*b; % b=x(end)*b;
% [x,y]=linprog(f,A,b,Aeq,beq,lb); % [x,y]=linprog(f,A,b,Aeq,beq,lb);
% Q(i)=-y; % Q(i)=-y;
% xx=[xx,x']; % xx=[xx,x'];
% end % end
% plot(w,Q,'*r'); % plot(w,Q,'*r');
%模型二 收益、风险按权重组合 %模型二 收益、风险按权重组合
clc; clear; close all; format long g; clc; clear; close all; format long g;
M = 10000; M = 10000;
prob = optimproblem; prob = optimproblem;
x = optimvar('x', 6, 1, 'LowerBound', 0); x = optimvar('x', 6, 1, 'LowerBound', 0);
r = [0.05, 0.28, 0.21, 0.23, 0.25]; r = [0.05, 0.28, 0.21, 0.23, 0.25];
p = [0, 0.01, 0.02, 0.045, 0.065]; p = [0, 0.01, 0.02, 0.045, 0.065];
q = [0, 0.025, 0.015, 0.055, 0.026]'; q = [0, 0.025, 0.015, 0.055, 0.026]';
%w = 0:0.1:1; %w = 0:0.1:1;
w = 0.7:0.03:1; w = 0.7:0.03:1;
V = []; V = [];
Q = []; Q = [];
X = []; X = [];
prob.Constraints.con1 = (1 + p) * x(1:end-1) == M; prob.Constraints.con1 = (1 + p) * x(1:end-1) == M;
prob.Constraints.con2 = (q(2:end).* x(2:end-1))<= x(end); %下标从1开始 prob.Constraints.con2 = (q(2:end).* x(2:end-1))<= x(end); %下标从1开始
for i = 1:length(w) for i = 1:length(w)
prob.Objective = w(i) * x(end) - (1 - w(i)) * (r - p) * x(1:end-1); %注意大小写 prob.Objective = w(i) * x(end) - (1 - w(i)) * (r - p) * x(1:end-1); %注意大小写
[sol, fval, flag, out] = solve(prob); [sol, fval, flag, out] = solve(prob);
xx = sol.x; xx = sol.x;
V = [V, max(q.* xx(1:end-1))]; V = [V, max(q.* xx(1:end-1))];
Q = [Q, (r - p) * xx(1:end-1)]; Q = [Q, (r - p) * xx(1:end-1)];
X = [X, xx]; X = [X, xx];
plot(V, Q, '*-'); plot(V, Q, '*-');
grid on; grid on;
xlabel('风险'); xlabel('风险');
ylabel('收益'); ylabel('收益');
end end
%模型三：达到一定盈利水平，极小化风险 %模型三：达到一定盈利水平，极小化风险
clc; clear; close all; format long g; clc; clear; close all; format long g;
M=10000; M=10000;
k=1500:100:3000; k=1500:100:3000;
prob = optimproblem; prob = optimproblem;
x = optimvar('x', 5, 1, 'LowerBound', 0);%下界为0 x = optimvar('x', 5, 1, 'LowerBound', 0);%下界为0
r = [0.05, 0.28, 0.21, 0.23, 0.25]; r = [0.05, 0.28, 0.21, 0.23, 0.25];
p = [0, 0.01, 0.02, 0.045, 0.065]; p = [0, 0.01, 0.02, 0.045, 0.065];
q = [0, 0.025, 0.015, 0.055, 0.026]'; q = [0, 0.025, 0.015, 0.055, 0.026]';
V = []; V = [];
Q = []; Q = [];
X = []; X = [];
t = optimvar('t', 'LowerBound', 0); t = optimvar('t', 'LowerBound', 0);
%prob.Objective=max(q.*x);%极小化风险 %prob.Objective=max(q.*x);%极小化风险
for i=1:length(k) for i=1:length(k)
prob.Objective = t; % 极小化风险 prob.Objective = t; % 极小化风险
prob.Constraints.con1 = (1 + p) * x == M; prob.Constraints.con1 = (1 + p) * x == M;
prob.Constraints.con2=((r-p)*x>=k(i));%达到一定盈利水平 prob.Constraints.con2=((r-p)*x>=k(i));%达到一定盈利水平
prob.Constraints.con3=(q.*x<=t); prob.Constraints.con3=(q.*x<=t);
[sol,fval,flag,out]=solve(prob); [sol,fval,flag,out]=solve(prob);
if flag==1 if flag==1
xx=sol.x; xx=sol.x;
X=[X,xx]; X=[X,xx];
Q=[Q,(r-p)*xx]; Q=[Q,(r-p)*xx];
V=[V,fval]; V=[V,fval];
else else
xx=-1*ones(5,1); xx=-1*ones(5,1);
X=[X,xx]; X=[X,xx];
Q=[Q,-1]; Q=[Q,-1];
V=[V,-1]; V=[V,-1];
end end
end end
plot(k,V,'*-'); plot(k,V,'*-');

188
mm2_graph.m → 姚安欣/mm2_graph.m
Unescape View File

@ -1,94 +1,94 @@
%ej.4.10仓库选址 %ej.4.10仓库选址
clc; clear; close all; format long g; clc; clear; close all; format long g;
a=zeros(6); a=zeros(6);
a(1,[2,5])=[20,15]; a(1,[2,5])=[20,15];
a(2,[1,3,4,5])=[20,20,60,25]; a(2,[1,3,4,5])=[20,20,60,25];
a(3,[2,4,5])=[20,30,18]; a(3,[2,4,5])=[20,30,18];
a(4,[2,3])=[60,30]; a(4,[2,3])=[60,30];
a(5,[1,2,3,6])=[15,25,18,15]; a(5,[1,2,3,6])=[15,25,18,15];
a(6,5)=15; a(6,5)=15;
s = cellstr(strcat('销售点',int2str([1:6]'))); s = cellstr(strcat('销售点',int2str([1:6]')));
G=graph(a,s); G=graph(a,s);
P = plot(G,'layout','force','EdgeColor','k','NodeFontSize',12); P = plot(G,'layout','force','EdgeColor','k','NodeFontSize',12);
D=[]; D=[];
for i=1:6 for i=1:6
temp=0; temp=0;
for j=1:6 for j=1:6
[path,d]=shortestpath(G,i,j); [path,d]=shortestpath(G,i,j);
if d>temp; if d>temp;
temp=d; temp=d;
end end
end end
D=[D,temp]; D=[D,temp];
end end
[minVal,minInd]=min(D); [minVal,minInd]=min(D);
disp('仓库应建在销售点'); disp('仓库应建在销售点');
disp(minInd); disp(minInd);
%答案版 %答案版
clc; clear; close all; clc; clear; close all;
% 初始化邻接矩阵 % 初始化邻接矩阵
a = zeros(6); a = zeros(6);
a(1, [2, 5]) = [20, 15]; a(1, [2, 5]) = [20, 15];
a(2, 3:5) = [20, 60, 25]; a(2, 3:5) = [20, 60, 25];
a(3, [4, 5]) = [30, 18]; a(3, [4, 5]) = [30, 18];
a(5, 6) = 15; a(5, 6) = 15;
% 创建节点标签 % 创建节点标签
s = cellstr(strcat('V', int2str([1:6]'))); s = cellstr(strcat('V', int2str([1:6]')));
% 创建图 % 创建图
G = graph(a, s, 'upper'); G = graph(a, s, 'upper');
% 计算所有节点之间的最短路径距离矩阵 % 计算所有节点之间的最短路径距离矩阵
d = distances(G); d = distances(G);
% 计算从每个节点到其他节点的最大最短路径距离 % 计算从每个节点到其他节点的最大最短路径距离
D = max(d, [], 2)'; %第三个参数 2 指定沿着矩阵的第二个维度（即列）进行操作。 D = max(d, [], 2)'; %第三个参数 2 指定沿着矩阵的第二个维度（即列）进行操作。
% 找到最大最短路径距离中的最小值及其下标 % 找到最大最短路径距离中的最小值及其下标
[minD, minIndex] = min(D); [minD, minIndex] = min(D);
% 绘制图 % 绘制图
plot(G, 'EdgeLabel', G.Edges.Weight, 'Layout', 'force');%设置边的标签 plot(G, 'EdgeLabel', G.Edges.Weight, 'Layout', 'force');%设置边的标签
% 显示结果 % 显示结果
fprintf('从每个节点到任意其他节点的最大最短路径距离: \n'); fprintf('从每个节点到任意其他节点的最大最短路径距离: \n');
disp(D); disp(D);
fprintf('最大最短路径距离中的最小值为: %f\n', minD); fprintf('最大最短路径距离中的最小值为: %f\n', minD);
fprintf('对应的节点为: V%d\n', minIndex); fprintf('对应的节点为: V%d\n', minIndex);
%设备更新问题； %设备更新问题；
clc;clear;close all; clc;clear;close all;
a=zeros(6); a=zeros(6);
a(1,[2:6])=[15,20,27,37,54]; a(1,[2:6])=[15,20,27,37,54];
a(2,[3:6])=[15,20,27,37]; a(2,[3:6])=[15,20,27,37];
a(3,[4:6])=[16,21,28]; a(3,[4:6])=[16,21,28];
a(4,[5:6])=[16,21]; a(4,[5:6])=[16,21];
a(5,6)=17; a(5,6)=17;
s=cellstr(strcat(int2str((1:6)'),'年初')); s=cellstr(strcat(int2str((1:6)'),'年初'));
G=digraph(a,s); G=digraph(a,s);
P = plot(G,'layout','force','EdgeColor','k','NodeFontSize',12); P = plot(G,'layout','force','EdgeColor','k','NodeFontSize',12);
[path,d]=shortestpath(G,1,6);%注意参数个数 [path,d]=shortestpath(G,1,6);%注意参数个数
highlight(P,path,"EdgeColor","red",'LineWidth',3.5); highlight(P,path,"EdgeColor","red",'LineWidth',3.5);
%最小生成树 %最小生成树
clc;clear; clc;clear;
a=zeros(9); a=zeros(9);
a(1,[2:9])=[2 1 3 4 4 2 5 4]; % 顶点1到其他顶点的边的权重 a(1,[2:9])=[2 1 3 4 4 2 5 4]; % 顶点1到其他顶点的边的权重
a(2,[3 9])=[4 1]; % 顶点2到顶点3、顶点9的边的权重 a(2,[3 9])=[4 1]; % 顶点2到顶点3、顶点9的边的权重
a(3,4)=1; % 同上。因为写过1到3，和2到3的边的权重，无需重复设 a(3,4)=1; % 同上。因为写过1到3，和2到3的边的权重，无需重复设
a(4,5)=1; a(4,5)=1;
a(5,6)=5; a(5,6)=5;
a(6,7)=2; a(6,7)=2;
a(7,8)=3; a(7,8)=3;
a(8,9)=5; a(8,9)=5;
s=cellstr(strcat('节点',int2str([1:9]'))); s=cellstr(strcat('节点',int2str([1:9]')));
G=graph(a,s,'upper'); G=graph(a,s,'upper');
P=plot(G,'layout','force'); P=plot(G,'layout','force');
T=minspantree(G,'Method','sparse'); T=minspantree(G,'Method','sparse');
L=sum(T.Edges.Weight); L=sum(T.Edges.Weight);
highlight(P,T,"EdgeColor","red",'LineWidth',2.5); highlight(P,T,"EdgeColor","red",'LineWidth',2.5);

BIN
盘荣博/图/figure10_9.png
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 47 KiB

28
盘荣博/图/例10.py
Unescape View File

@ -0,0 +1,28 @@
import networkx as nx
import pylab as plt
import numpy as np
p=[25,26,28,31] ;a=[10,14,18,26] ; r=[20,16,13,11]
b= np.zeros((5,5))
for i in range(5):
for j in range(i+1,5):
b[i,j]=p[i]+np.sum(a[0:j-i])-r[j-i-1]
G=nx.DiGraph(b)
print(G)
p=nx.dijkstra_path(G,source=0,target=4,weight='weight')
print("最短路径为：",np.array(p)+1)#下标从零开始
d=nx.dijkstra_path_length(G,source=0,target=4,weight="weight")
print("所求的费用最小值为：",d)
s=dict(zip(range(5),range(1,6)))
plt.rc("font",size=16)
pos=nx.shell_layout((G))#设置布局
print(type(pos),'\npos=',pos)
w=nx.get_edge_attributes(G,"weight")
print(type(w),'\nw=',w)
nx.draw(G,pos,font_weight='bold',labels=s,node_color='r')#绘制点和边
nx.draw_networkx_edge_labels(G,pos,edge_labels=w)#绘制标签
#绘制最短路径
path_edges=list(zip(p,p[1:]))
print(type(path_edges),"\npath_edges=",path_edges)
nx.draw_networkx_edges(G,pos,edgelist=path_edges,edge_color="r",width=1)
plt.savefig("figure10_9.png");plt.show()
Write Preview
Loading…
Cancel
Save