lingo11 求助贴
model:sets:city / 1.. 8/: u;link( city, city): dist, x;endsets n = @size( city);data:dist = ENDDATA min = @sum( link:dist * x); @FOR( city( K): @sum( city( I)| I #ne# K: x( I, K))= 1; @sum( city( J)| J #ne# K: x( K, J))= 1; ); @for(city(I)|I #gt# 1: @for( city( J)| J#gt#1 #and# I #ne#J: u(I)-u(J)+n*x(I,J)<=n-1); ); @for(city(I)| I #gt# 1: u(I)<=n-2 ); @for( link: @bin( x)); end表4.1 各个节点间的距离（单位：公里）
节点 1 2 3 4 5 6 7 8
1 0 2.7 2.0 1.5 1.8 2.7 3.0 4.0
2 0 1.3 2.2 3.7 5.1 5.8 6.4
3 0 2.2 2.5 4.0 4.9 5.9
4 0 3.3 4.0 4.0 4.3
5 0 1.8 3.2 4.7
6 0 1.8 3.6
7 0 1.9
8 0
表4.2 各个节点间的行车时间（单位：分钟）
节点 1 2 3 4 5 6 7 8
1 0 5.5 4.0 3.0 3.5 5.5 6.0 8.0
2 0 2.5 4.5 7.5 10 11.5 12.5
3 0 4.5 5.0 8.0 9.5 11.5
4 0 6.5 8.0 8.0 8.5
5 0 3.5 6.5 13.0
6 0 3.5 7.0
7 0 3.5
8 0
数据不对，略作更改就可运行：model:
sets:
city / 1.. 8/: u;
link( city, city): dist, x;
endsets
n = @size( city);
data:
dist =
0 2.7 2 1.5 1.8 2.7 3 4
2.7 0 1.3 2.2 3.7 5.1 5.8 6.4
2 1.3 0 2.2 2.5 4 4.9 5.9
1.5 2.2 2.2 0 3.3 4 4 4.3
1.8 3.7 2.5 3.3 0 1.8 3.2 4.7
2.7 5.1 4 4 1.8 0 1.8 3.6
3 5.8 4.9 4 3.2 1.8 0 1.9
4 6.4 5.9 4.3 4.7 3.6 1.9 0;
ENDDATA
min = @sum( link:dist * x);
@FOR( city( K):
@sum( city( I)| I #ne# K: x( I, K))= 1;
@sum( city( J)| J #ne# K: x( K, J))= 1;
);
@for(city(I)|I #gt# 1:
@for( city( J)| J#gt#1 #and# I #ne#J: u(I)-u(J)+n*x(I,J)<=n-1);
);
@for(city(I)| I #gt# 1: u(I)<=n-2);
@for( link: @bin( x));
end运行后结果： Global optimal solution found.
Objective value: 17.00000
Objective bound: 17.00000
Infeasibilities: 0.8881784E-15
Extended solver steps: 4
Total solver iterations: 710
Variable Value Reduced Cost
N 8.000000 0.000000
U( 1) 0.000000 0.000000
U( 2) 5.000000 0.000000
U( 3) 4.000000 0.000000
U( 4) 6.000000 0.000000
U( 5) 3.000000 0.000000
U( 6) 2.000000 0.000000
U( 7) 1.000000 0.000000
U( 8) 0.000000 0.000000
DIST( 1, 1) 0.000000 0.000000
DIST( 1, 2) 2.700000 0.000000
DIST( 1, 3) 2.000000 0.000000
DIST( 1, 4) 1.500000 0.000000
DIST( 1, 5) 1.800000 0.000000
DIST( 1, 6) 2.700000 0.000000
DIST( 1, 7) 3.000000 0.000000
DIST( 1, 8) 4.000000 0.000000
DIST( 2, 1) 2.700000 0.000000
DIST( 2, 2) 0.000000 0.000000
DIST( 2, 3) 1.300000 0.000000
DIST( 2, 4) 2.200000 0.000000
DIST( 2, 5) 3.700000 0.000000
DIST( 2, 6) 5.100000 0.000000
DIST( 2, 7) 5.800000 0.000000
DIST( 2, 8) 6.400000 0.000000
DIST( 3, 1) 2.000000 0.000000
DIST( 3, 2) 1.300000 0.000000
DIST( 3, 3) 0.000000 0.000000
DIST( 3, 4) 2.200000 0.000000
DIST( 3, 5) 2.500000 0.000000
DIST( 3, 6) 4.000000 0.000000
DIST( 3, 7) 4.900000 0.000000
DIST( 3, 8) 5.900000 0.000000
DIST( 4, 1) 1.500000 0.000000
DIST( 4, 2) 2.200000 0.000000
DIST( 4, 3) 2.200000 0.000000
DIST( 4, 4) 0.000000 0.000000
DIST( 4, 5) 3.300000 0.000000
DIST( 4, 6) 4.000000 0.000000
DIST( 4, 7) 4.000000 0.000000
DIST( 4, 8) 4.300000 0.000000
DIST( 5, 1) 1.800000 0.000000
DIST( 5, 2) 3.700000 0.000000
DIST( 5, 3) 2.500000 0.000000
DIST( 5, 4) 3.300000 0.000000
DIST( 5, 5) 0.000000 0.000000
DIST( 5, 6) 1.800000 0.000000
DIST( 5, 7) 3.200000 0.000000
DIST( 5, 8) 4.700000 0.000000
DIST( 6, 1) 2.700000 0.000000
DIST( 6, 2) 5.100000 0.000000
DIST( 6, 3) 4.000000 0.000000
DIST( 6, 4) 4.000000 0.000000
DIST( 6, 5) 1.800000 0.000000
DIST( 6, 6) 0.000000 0.000000
DIST( 6, 7) 1.800000 0.000000
DIST( 6, 8) 3.600000 0.000000
DIST( 7, 1) 3.000000 0.000000
DIST( 7, 2) 5.800000 0.000000
DIST( 7, 3) 4.900000 0.000000
DIST( 7, 4) 4.000000 0.000000
DIST( 7, 5) 3.200000 0.000000
DIST( 7, 6) 1.800000 0.000000
DIST( 7, 7) 0.000000 0.000000
DIST( 7, 8) 1.900000 0.000000
DIST( 8, 1) 4.000000 0.000000
DIST( 8, 2) 6.400000 0.000000
DIST( 8, 3) 5.900000 0.000000
DIST( 8, 4) 4.300000 0.000000
DIST( 8, 5) 4.700000 0.000000
DIST( 8, 6) 3.600000 0.000000
DIST( 8, 7) 1.900000 0.000000
DIST( 8, 8) 0.000000 0.000000
X( 1, 1) 0.000000 0.000000
X( 1, 2) 0.000000 2.700000
X( 1, 3) 0.000000 2.000000
X( 1, 4) 0.000000 1.500000
X( 1, 5) 0.000000 1.800000
X( 1, 6) 0.000000 2.700000
X( 1, 7) 0.000000 3.000000
X( 1, 8) 1.000000 4.000000
X( 2, 1) 0.000000 2.700000
X( 2, 2) 0.000000 0.000000
X( 2, 3) 0.000000 1.300000
X( 2, 4) 1.000000 2.200000
X( 2, 5) 0.000000 3.700000
X( 2, 6) 0.000000 5.100000
X( 2, 7) 0.000000 5.800000
X( 2, 8) 0.000000 6.400000
X( 3, 1) 0.000000 2.000000
X( 3, 2) 1.000000 1.300000
X( 3, 3) 0.000000 0.000000
X( 3, 4) 0.000000 2.200000
X( 3, 5) 0.000000 2.500000
X( 3, 6) 0.000000 4.000000
X( 3, 7) 0.000000 4.900000
X( 3, 8) 0.000000 5.900000
X( 4, 1) 1.000000 1.500000
X( 4, 2) 0.000000 2.200000
X( 4, 3) 0.000000 2.200000
X( 4, 4) 0.000000 0.000000
X( 4, 5) 0.000000 3.300000
X( 4, 6) 0.000000 4.000000
X( 4, 7) 0.000000 4.000000
X( 4, 8) 0.000000 4.300000
X( 5, 1) 0.000000 1.800000
X( 5, 2) 0.000000 3.700000
X( 5, 3) 1.000000 2.500000
X( 5, 4) 0.000000 3.300000
X( 5, 5) 0.000000 0.000000
X( 5, 6) 0.000000 1.800000
X( 5, 7) 0.000000 3.200000
X( 5, 8) 0.000000 4.700000
X( 6, 1) 0.000000 2.700000
X( 6, 2) 0.000000 5.100000
X( 6, 3) 0.000000 4.000000
X( 6, 4) 0.000000 4.000000
X( 6, 5) 1.000000 1.800000
X( 6, 6) 0.000000 0.000000
X( 6, 7) 0.000000 1.800000
X( 6, 8) 0.000000 3.600000
X( 7, 1) 0.000000 3.000000
X( 7, 2) 0.000000 5.800000
X( 7, 3) 0.000000 4.900000
X( 7, 4) 0.000000 4.000000
X( 7, 5) 0.000000 3.200000
X( 7, 6) 1.000000 1.800000
X( 7, 7) 0.000000 0.000000
X( 7, 8) 0.000000 1.900000
X( 8, 1) 0.000000 4.000000
X( 8, 2) 0.000000 6.400000
X( 8, 3) 0.000000 5.900000
X( 8, 4) 0.000000 4.300000
X( 8, 5) 0.000000 4.700000
X( 8, 6) 0.000000 3.600000
X( 8, 7) 1.000000 1.900000
X( 8, 8) 0.000000 0.000000
Row Slack or Surplus Dual Price
1 0.000000 0.000000
2 17.00000 -1.000000
3 0.000000 0.000000
4 0.000000 0.000000
5 0.000000 0.000000
6 0.000000 0.000000
7 0.000000 0.000000
8 0.000000 0.000000
9 0.000000 0.000000
10 0.000000 0.000000
11 0.000000 0.000000
12 0.000000 0.000000
13 0.000000 0.000000
14 0.000000 0.000000
15 0.000000 0.000000
16 0.000000 0.000000
17 0.000000 0.000000
18 0.000000 0.000000
19 6.000000 0.000000
20 0.000000 0.000000
21 5.000000 0.000000
22 4.000000 0.000000
23 3.000000 0.000000
24 2.000000 0.000000
25 0.000000 0.000000
26 9.000000 0.000000
27 6.000000 0.000000
28 5.000000 0.000000
29 4.000000 0.000000
30 3.000000 0.000000
31 6.000000 0.000000
32 5.000000 0.000000
33 4.000000 0.000000
34 3.000000 0.000000
35 2.000000 0.000000
36 1.000000 0.000000
37 9.000000 0.000000
38 0.000000 0.000000
39 10.00000 0.000000
40 6.000000 0.000000
41 5.000000 0.000000
42 4.000000 0.000000
43 10.00000 0.000000
44 9.000000 0.000000
45 11.00000 0.000000
46 0.000000 0.000000
47 6.000000 0.000000
48 5.000000 0.000000
49 11.00000 0.000000
50 10.00000 0.000000
51 12.00000 0.000000
52 9.000000 0.000000
53 0.000000 0.000000
54 6.000000 0.000000
55 12.00000 0.000000
56 11.00000 0.000000
57 13.00000 0.000000
58 10.00000 0.000000
59 9.000000 0.000000
60 0.000000 0.000000
61 1.000000 0.000000
62 2.000000 0.000000
63 0.000000 0.000000
64 3.000000 0.000000
65 4.000000 0.000000
66 5.000000 0.000000
67 6.000000 0.000000
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