整数规划（linprog\optimproblem解法），01规划（背包问题）

姚安欣/intLP.m

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