数学建模优化与LINGO.ppt

1、优化与LINGO软件分类程序模版,指派问题,model: sets: pel/1,2,3,4/; link(pel,pel):x,t; endsets data: t=15 18 21 24 19 23 22 18 26 18 16 19 19 21 23 17; enddata min=sum(link(i,j):x(i,j)*t(i,j); for(link(i,j):bin(x(i,j); for(pel(i):sum(pel(j):x(i,j)=1); for(pel(i):sum(pel(j):x(j,i)=1); end,二次指派问题,model: sets: p/1.10/; l

2、ink(p,p):x; link1(p,p)|,二次指派,c= 7 4 6 8 8 8 6 6 5 7 8 2 6 5 6 8 3 6 4 8 10 4 4 7 2 6 7 6 2 10 6 6 9 3 2 6 8 6 4 6 6 4 8 8 6 8 5 4 6 6 3 8 3 2 8 6 7 9 4 3 6 7 8 6 8 2 3 8 8 6 8 8 6 3 6 2 8 3 7 8 9 5 6 7 6 6 2 8 8 9 ; enddata min=sum(link1(i,j):t(i,j)*sum(link2(k,m):c(k,m)*x(i,k)*x(j,m); for(link(i,j)

3、:bin(x(i,j); for(p(i):sum(p(j):x(i,j)=1); for(p(i):sum(p(j):x(j,i)=1); end,供水问题,MODEL: SETS: shuiku/1.3/:c; quyu/1.4/:b,a; link(shuiku,quyu):x,d; ENDSETS data: b=30,70,10,10; a=50,70,20,40; c=100,120,100; d=160,130,220,170,140,130,190,150,190,200,230,0; x= , , , , , , , , , , ,0;,供水,enddata objectiv

4、e max=sum(link(i,j):x(i,j)*(900-450-d(i,j); FOR (quyu(j): sum(shuiku(i):x(i,j)=b(j); sum(shuiku(i):x(i,j)=b(j)+a(j); ); for (shuiku(i): sum(quyu(j):x(i,j)=c(i); ); end,售书问题,model: sets: id/1.7/; link(id,id)|,售书,enddata max=sum(link(i,j):x(i,j)*s(i,j); for(link(i,j):bin(x(i,j);); for(id(i): sum(link(

5、i,j):x(i,j) +sum(link(j,i):x(j,i)=1; ); sum(link(i,j):x(i,j)=2; end,售书点确定,model: sets: a/1.7/; b(a,a)| enddata,售书点,max=sum(b(i,j):x(i,j)*s(i,j); sum(b(i,j):x(i,j)=2; for(b(i,j):bin(x(i,j); sum(a(j)|j#gt#2:x(1,j)=1; x(1,2)+sum(a(j)|j#gt#3:x(2,j)=1; x(1,3)+x(2,3)+x(3,4)+x(3,5)+x(3,6)+x(3,7)=1; x(1,4)+

6、x(2,4)+x(3,4)+x(4,5)+x(4,6)+x(4,7)=1; x(1,5)+x(2,5)+x(3,5)+x(4,5)+x(5,6)+x(5,7)=1; x(1,6)+x(2,6)+x(3,6)+x(4,6)+x(5,6)+x(6,7)=1; sum(a(i)|i#lt#7:x(i,7)=1; end,最大流问题1,model: sets: id/s,1,2,3,4,t/; link(id,id):p,f,c; endsets data: p=0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0

7、0; c=0 8 7 0 0 0 0 0 5 9 0 0 0 0 0 0 9 0 0 0 2 0 0 5 0 0 0 6 0 10 0 0 0 0 0 0;,最大流问题1,enddata max=flow; for(link(i,j):bnd(0,f(i,j),c(i,j); for(id(i)|i#gt#1#and#i#lt#6: sum(id(j):p(i,j)*f(i,j)=sum(id(j):p(j,i)*f(j,i); flow=sum(id(i):p(1,i)*f(1,i); flow=sum(id(i):p(i,6)*f(i,6); end,最大流问题2,MODEL: sets:

8、 nodes/s,1,2,3,4,t/; arcs(nodes,nodes)/s,1 s,2 1,2 1,3 2,4 3,2 3,t 4,3 4,t/:c,f; endsets data: c=8 7 5 9 9 2 5 6 10; enddata max=flow; for(nodes(i)|i#ne#1#and#i#ne#size(nodes): sum(arcs(i,j):f(i,j)-sum(arcs(j,i):f(j,i)=0); sum(arcs(i,j)|i#eq#1:f(i,j)=flow; for(arcs:bnd(0,f,c); end,最小生成树问题,model: set

9、s: cities/1.10/:level; link(cities,cities):distance,x; endsets data: distance=0 8 5 9 12 14 12 16 17 22 8 0 9 15 16 8 11 18 14 22 5 9 0 7 9 11 7 12 12 17 9 15 7 0 3 17 10 7 15 15 12 16 9 3 0 8 10 6 15 15 14 8 11 17 8 0 9 14 8 16 12 11 7 10 10 9 0 8 6 11 16 18 12 7 6 14 8 0 11 11 17 14 12 15 15 8 6 1

10、1 0 10 22 22 17 15 15 16 11 11 10 0; enddata,最小生成树问题,n=size(cities); min=sum(link(i,j)|i#ne#j:distance(i,j)*x(i,j); sum(cities(i)|i#gt#1:x(1,i)=1; for(cities(i)|i#gt#1: sum(cities(j)|j#ne#i:x(j,i)=1; for(cities(j)|j#gt#1 #and# j#ne#i: level(j)=level(i)+x(i,j)-(n-2)*(1-x(i,j)+(n-3)*x(j,i); ); bnd(1,l

11、evel(i),999999); level(i)=n-1-(n-2)*x(1,i); ); for(link:bin(x); end,最小费用最大流问题,model: sets: id/s,1,2,3,4,t/; link(id,id):p,f,c,e; endsets data: p=0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0; c=0 8 7 0 0 0 0 0 5 9 0 0 0 0 0 0 9 0 0 0 2 0 0 5 0 0 0 6 0 10 0 0 0 0 0 0;,最小费用最大

12、流,e=100 2 8 100 100 100 100 100 5 2 100 100 100 100 100 100 3 100 100 100 1 100 100 6 100 100 100 4 100 7 100 100 100 100 100 100; enddata min=sum(link(i,j):e(i,j)*f(i,j); for(link(i,j):bnd(0,f(i,j),c(i,j); for(id(i)|i#gt#1#and#i#lt#6: sum(id(j):p(i,j)*f(i,j)=sum(id(j):p(j,i)*f(j,i); sum(id(i):p(1,i

13、)*f(1,i)=14; sum(id(i):p(i,6)*f(i,6)=14; end,泳姿指派,model: sets: p/1.5/;!5个运动员; q/1.4/;!4个泳姿; link(p,q):c,x;!c表示第i个人的第j种泳姿的最好成绩，x表示第i个人指定第j种泳姿; endsets data: c=66.8 75.6 87 58.6 57.2 66 66.4 53 78 67.8 84.6 59.4 70 74.2 69.6 57.2 67.4 71 83.8 62.4; enddata min=sum(link(i,j):c(i,j)*x(i,j); for(p(i):sum

14、(q(j):x(i,j)=1); for(q(j):sum(p(i):x(i,j)=1); for(link(i,j):bin(x(i,j); end,运输问题,model: sets: p/1.3/:a;!a表示产地的产量; q/1.4/:b;!b表示销地的销量; link(p,q):x,y;!x表示产地到销地的运费单价，y表示产地到销地的运输量; endsets data: a=30 25 21; b=15 17 22 12; x=6 2 6 7 4 9 5 3 8 8 1 5; enddata min=sum(link(i,j):x(i,j)*y(i,j); for(p(i):sum(q

15、(j):y(i,j)=0); end,转运问题,model: sets: p/1,2/:g;!g表示两个工厂的产量; q/1.3/;!三个仓库; w/1.4/:n;!n表示四个顾客的需求量; link1(p,q):a,b;!a表示第i个工厂第j个仓库的运输单价，b表示第i个工厂第j个仓库的运输量; link2(q,w):c,d;!c表示第j个仓库第k个顾客的运输单价，d表示第j个仓库第k个顾客的运输量; endsets data: g=9 8; n=3 5 4 5; a=1 2 100 3 1 2; c=5 7 100 100 9 6 7 100 100 6 7 4;,转运问题,enddata

16、 min=sum(link1(i,j):a(i,j)*b(i,j)+sum(link2(j,k):c(j,k)*d(j,k); for(p(i):sum(q(j):b(i,j)=0); for(link2(j,k):d(j,k)=0); end,选课问题,MODEL: SETS: a/1.18/:x,fen; endsets data: fen=5 5 4 4 3 3 3 2 3 3 3 2 2 2 1 1 1 1; enddata objective min=sum(a(i):x(i); y1=sum(a(i)|i#LE#8:x(i)*fen(i); y2=sum(a(i)|i#GE#9:x

17、(i)*fen(i); y=y1+y2+2;,选课,for(a(i):bin(x(i); y=20; y=3*y2; x(1)=x(5); x(2)=x(7); x(8)=x(9); x(6)=x(10); x(4)=x(11); x(5)=x(12); x(7)=x(13); x(6)=x(14); end,钢管选料问题,model: sets: m/1.3/:x; q/1.4/:c,z; link(q,m):r; endsets data: c=4 5 6 8; z=50 10 20 15; enddata min=sum(m(i):x(i); for(q(i):sum(m(j):r(i,

18、j)*x(j)=z(i); for(m(j):sum(q(i):r(i,j)*c(i)=16); for(m(j):sum(q(i):r(i,j)*c(i)=0; for(m(i):gin(x(i); for(link(i,j):gin(r(i,j); end,订单选择问题,model: sets: r/1.9/:d,p,v,w; endsets data: p=7 6 3 6 3 1 1 2 4; v=6 2 7 5 2 3 7 9 4; w=7 7 2 4 2 7 8 6 7; enddata max=sum(r(i):d(i)*p(i); sum(r(i):d(i)*v(i)=1000; sum(r(i):d(i)*w(i)=1200; for(r