标题: 关于lingo软件的使用问题！ [打印本页] 作者: nanjiyulin 时间: 2008-9-14 19:16 标题: 关于lingo软件的使用问题！ 我看了很多关于lingo和lindo的书，其中很多题都是讲目标函数是min=x1+x2+4x3这种类型的题，那求解有西格玛符号的题怎么做啊，而且约束条件也没书上那么整齐？请高手帮帮忙啊~作者: madio 时间: 2008-9-14 19:17
求和用sum函数作者: chendaxiang9 时间: 2008-9-14 19:52
是@sum（）作者: nanjiyulin 时间: 2008-9-15 14:28
能具体点么~~作者: madio 时间: 2008-9-15 22:22
这个例子你能学到一些
In the traveling salesman problem (TSP), we have a network of cities connected by roads. We need to find a tour that visits each of the cities exactly once, minimizing the total distance traveled.
As it turns, large TSP models are difficult to solve using optimization and are best approached using some form of heuristic (see Lin and Kernighan, 1973). The problem lies in the fact that solutions to large models tend to contain subtours. A subtour is a tour of a subset of cities unconnected to the main tour. One can add constraints to break the subtours, but the number of constraints required grows dramatically as the number of cities increase.
MODEL:
! Traveling Salesman Problem for the cities of
Atlanta, Chicago, Cincinnati, Houston, LA,
Montreal;
SETS:
CITY / 1.. 6/: U; ! U( I) = sequence no. of city;
LINK( CITY, CITY):
DIST, ! The distance matrix;
X; ! X( I, J) = 1 if we use link I, J;
ENDSETS
DATA: !Distance matrix, it need not be symmetric;
DIST = 0 702 454 842 2396 1196
702 0 324 1093 2136 764
454 324 0 1137 2180 798
842 1093 1137 0 1616 1857
!The model:Ref. Desrochers & Laporte, OR Letters,
Feb. 91;
N = @SIZE( CITY);
MIN = @SUM( LINK: DIST * X);
@FOR( CITY( K):
! It must be entered;
@SUM( CITY( I)| I #NE# K: X( I, K)) = 1;
! It must be departed;
@SUM( CITY( J)| J #NE# K: X( K, J)) = 1;
! Weak form of the subtour breaking constraints;
! These are not very powerful for large problems;
@FOR( CITY( J)| J #GT# 1 #AND# J #NE# K:
U( J) >= U( K) + X ( K, J) -
( N - 2) * ( 1 - X( K, J)) +
( N - 3) * X( J, K)
);
);
! Make the X's 0/1;
@FOR( LINK: @BIN( X));
! For the first and last stop we know...;
@FOR( CITY( K)| K #GT# 1:
U( K) <= N - 1 - ( N - 2) * X( 1, K);
U( K) >= 1 + ( N - 2) * X( K, 1)
);
