最佳旅游线路-数学建模[1](7)

!@sum(jingdian(j):@sum(jingdian(i):r(i,j)))

!@sum(jingdian(j):@sum(jingdian(i):r2(i,j)))

!@sum(jingdian(j):@sum(jingdian(i):r2(i,j)))>n2-0.5;

@for(jingdian(i):@for(jingdian(j)|j#gt#1#and#j#ne#i:l(j)>=l(i)+r(i,j)-(n-2)*(1-r(i,j))+(n-3)*r(j,i)));

@for(jingdian(i):@for(jingdian(j)|j#gt#1#and#j#ne#i:l2(j)>=l2(i)+r2(i,j)-(n2-2)*(1-r2(i,j))+(n2-3)*r2(j,i)));

@for(jingdian(i)|i#gt#1:l(i)1+(n-2)*r(i,1));!这两个约束条件：为了控制不出现两个以上环形回路，保证有且仅有一条环形路线;

@for(jingdian(i)|i#gt#1:l2(i)1+(n2-2)*r2(i,1));

@for(jingdian(i)|1#eq#i:v(i)=1;b(i)=0);

!@for(jingdian(k)|1#lt#k#and#k#le#n:@for(jingdian(i):@for(jingdian(j):x(k,i,j)=@if(r(i,j)#eq#1#and#v(k-1)#eq#i,j,0)));!v(k)=@sum(jingdian(j):@sum(jingdian(i):x(k,i,j))));

@for(jingdian(k)|1#lt#k#and#k#le#n:@for(jingdian(i):@for(jingdian(j):x(k,i,j)=@if(0.5#le#r(i,j)#and#r(i,j)#le#1.5#and#(i-0.5)#le#v(k-1)#and#v(k-1)#le#(i+0.5),j,0)));v(k)=@sum(jingdian(j):@sum(jingdian(i):x(k,i,j))));

@for(jingdian(i)|1#eq#i:v2(i)=1;b2(i)=0);

!@for(jingdian(k)|1#lt#k#and#k#le#n2:@for(jingdian(i):@for(jingdian(j):x2(k,i,j)=@if(r(i,j)#eq#1#and#v2(k-1)#eq#i,j,0)));!v2(k)=@sum(jingdian(j):@sum(jingdian(i):x2(k,i,j))));

@for(jingdian(k)|1#lt#k#and#k#le#n2:@for(jingdian(i):@for(jingdian(j):x2(k,i,j)=@if(0.5#le#r2(i,j)#and#r2(i,j)#le#1.5#and#(i-0.5)#le#v2(k-1)#and#v2(k-1)#le#(i+0.5),j,0)));v2(k)=@sum(jingdian(j):@sum(jingdian(i):x2(k,i,j))));

@for(jingdian(i)|2#le#i#and#i#le#(n):@for(jingdian(k):@for(jingdian(j):bb(k,i,j)=@if(v(i)#eq#j#and#v(i-1)#eq#k,t(k)+tt(k,j),0)));b(i)=@sum(jingdian(j):@sum(jingdian(k):bb(k,i,j))));

@for(jingdian(k)|k#le#n:tv(k)=@sum(jingdian(i)|i#le#(k):b(i))/12); @for(jingdian(i)|2#le#i#and#i#le#(n2):@for(jingdian(k):@for(jingdian(j):bb2(k,i,j)=@if(v2(i)#eq#j#and#v2(i-1)#eq#k,t(k)+tt(k,j),0)));b2(i)=@sum(jingdian(j):@sum(jingdian(k):bb2(k,i,j))));

@for(jingdian(k)|k#ne#1#and#k#le#n2:tv2(k)=@sum(jingdian(i)|i#le#(k):b2(i))/12+4);

@for(jingdian(k)|k#eq#1#or#k#gt#n2:tv2(k)=0);

@for(jingdian(k)|k#le#n2:@for(jingdian(j)|j#le#n:rrr(j,k)=@if(v(j)#eq#v2(k)#and#(tv2(k)-tv(j))#lt#1#and#(tv(j)-tv2(k))#lt#1,1,0))); @for(links(j,k)|(j#gt#n#and#k#le#n2)#or#(j#le#n#and#k#gt#n)#or#(j#gt#n#and#k#gt#n):rrr(j,k)=0);

@for(jingdian(j)|j#ge#2#and#j#le#n2:rrv(j)=@sum(jingdian(k):rrr(j,k)));

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@for(jingdian(k)|k#eq#1#or#k#gt#n2:rrv(k)=0); End

第四问结果（以n=5为例）：

Local optimal solution found at iteration: 5831 Objective value: 1617.405

Variable Value Reduced Cost Z 0.9500000 0.000000 N2 5.000000 0.000000 N 5.000000 0.000000 FEIYONG 960.6000 0.000000 FEIYONG2 980.4500 0.000000 V( 1) 1.000000 0.000000 V( 2) 0.000000 0.000000 V( 3) 0.000000 0.000000 V( 4) 0.000000 0.000000 V( 5) 0.000000 0.000000 V( 6) 0.000000 0.000000 V( 7) 0.000000 0.000000 V( 8) 0.000000 0.000000 V( 9) 0.000000 0.000000 V( 10) 0.000000 0.000000 V( 11) 0.000000 0.000000 V2( 1) 1.000000 0.000000 V2( 2) 0.000000 0.000000 V2( 3) 0.000000 0.000000 V2( 4) 0.000000 0.000000 V2( 5) 0.000000 0.000000 V2( 6) 0.000000 0.000000 V2( 7) 0.000000 0.000000 V2( 8) 0.000000 0.000000 V2( 9) 0.000000 0.000000 V2( 10) 0.000000 0.000000 V2( 11) 0.000000 0.000000 第五问程序：（以n=5为例） sets:

jingdian/1..11/:c,t,w,l,v,b,y,tv;!其中：1,2,...,11分别代表成都、九寨沟、黄龙、乐山、峨嵋、四姑娘山、丹巴、都江堰、青城山、海螺、沟康定；c，t分别表示旅行团在各景点的吃住消费和逗留时间；w表示各景点选择性权重；l是为了控制不出现两个以上环形回路而设的一个变量; gailv/1..10/;

links(jingdian,jingdian):r,cc,tt;!其中：r为0-1变量（0表示两景点不相连，1表示两景点相通）；cc为两景点之间的交通费用；tt为两景点之间的交通时间; links2(jingdian,gailv):pp,pv;

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links1(jingdian,jingdian,jingdian):x,bb,ppv; endsets data:

t=7 24 18 12 36 30 12 9 15 24 17;!其中:t(1)=0,表示在成都的逗留时间为0，因为相对旅行团而言，由于成都既是起点又是终点，并未在成都游玩;

c=120 423 300 135 378 390 175 90 148 303 241;!其中：c(1)=0，表示在成都的吃住费用算做，理由同上;

w= 0 0.185 0.185 0.217 0.217 0.196 0.196 0.206 0.206 0.196 0.196; tt=0 8.54 4.74 2.82

3.44

5.08

8.4 1.32

1.54 6.14

8.54 0 1.22

11.52 12.14 10.9

13.1 8.84 8.98 14.84 4.74 1.22 0 11.22 11.82 9.38 11.58 7.66

7.46 13.44 2.82 11.52 11.22 0 0.88 7.78

8.08

4.02 4.24 5.84 3.44

12.14 11.82 0.88

0 8.42

8.24

4.66 4.88

6 5.08 10.9 9.38 7.78

8.42 0 2.18

4.24 4.04 5.98 8.4 13.1 11.58 8.08

8.24

2.18

0 6.08

6.22

3.86

1.32 8.84 7.66 4.02 4.66 4.24 6.08 0 0.3 6.28 1.54 8.98

7.46

4.24

4.88 4.04 6.22 0.3 0 6.08

6.14

14.84 13.44 5.84

6 5.98 3.86 6.28 6.08 0 6.6 15.54 13.9

6.3 6.46

6.74

2.86

6.74

6.54

2.08

!其中：主对角线为零,表示各景点到自身交通费用为零;

cc=0 128 71 42 52 77 126 20 23 92 99 128 0 18 173

182 164

197 133 135 223 233

71 18 0 168 177 141 174 115 112 202 209 42 173 168 0 13 117 121 60. 64 88 95 52 182 177 13 0 126 124 70 73 90 97 76 164 141 117 126 0 33 64 61 90 101 126 197

174 121 124 33 0 91 93 58 43

20 133 115 60 70 64 91 0 5 94 101 23 135 112 64 73 61 93 5 0 91 98 92 223 202 88 90 90 58 94 91 0 31 99 233 209 95 97 101 43 101 98 31 0; !其中：主对角线为零,表示各景点到自身的交通时间为零; n=5;!其中：n表示计划游玩的景点数目; pp=0.15 0.1 0.3 0.8 0.7 0.5 0.6 0.3 0.1 0 1 0.8 0.8 0.5 0.5 0.4 0.5 0.6 0.3 0.2 0.5 1 0.9 1 0.3 0 0.2 0 0.4 0.4 0.1 0 0.1 0.5 0.5 0.7 0.3 0.3 0.1 0.1 0.3 0.4 0.4 0.6 0.3 0.3 0.2 0.4 0.6 0.6 0.6 0.6 0.6 0.5 0.8 0.3 0.1 0.1 0.1 1 0.3 0.2 0.2 0.1 0 0.1 0.1 0.2 0.2 0.3 0.4 0.3 0.3 0.2 0.4 0.9 0.9 0.9 0.8 0.8 0.5 0.3 0.3 0.4 0.3 0.8 1 0.9 0.9 0.9 0.2 0.6 0.6 0.4 0.1 0 0.8 0.7 0.6 0.4 0.1 0.1 0.3 0.3 0.5 0.6 0.8 0.7 0.63

0.4;

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6.6

15.54 13.9 6.3 6.46

6.74 2.86 6.74 6.54 2.08

0; enddata

min=0*(p-0.9)/3.3+0.9*(quan- 137)/173;!目标函数：表示计划游玩的景点数目为n时的最小费用;

quan=@sum(jingdian(j):@sum(jingdian(i):w(j)*r(i,j)*(cc(i,j)+0.45*(c(i)+c(j)))));

q=@sum(jingdian(j):@sum(jingdian(i):r(i,j)*(cc(i,j)+0.45*(c(i)+c(j)))));

@for(jingdian(i):r(i,i)=0);!约束条件：表示各景点到自身没有路线相连的约束条件; @for(jingdian(i)|i#ge#2:@for(jingdian(j)|j#ge#2:r(i,j)+r(j,i)<1));!约束条件：表示除起点（成都）外，若旅行团从景点i到景点j去游玩（即r(i,j)=1），则不会再从景点j到景点i去游玩（即r(j,i)=0），也就是说除起点外每个景点只游玩一次;

@sum(jingdian(j):@sum(jingdian(i):r(i,j)*(tt(i,j)+0.5*(t(i)+t(j)))))<120;!约束条件:表示总的旅行时间（交通时间和景点逗留时间）不超过给定时间10天;

@for(jingdian(i):@sum(jingdian(j):r(i,j))=@sum(jingdian(j):r(j,i))); @for(jingdian(i)|i#eq#1:@sum(jingdian(j):r(i,j))=1);

@for(jingdian(i)|i#ne#1:@sum(jingdian(j):r(i,j))<1);!这三个约束条件：表示起点（成都）有且仅有一条路线出去和一条路线进来，其它景点要么有且仅有一条路线出去和一条路线进来，要么既没有路线出去也没有路线进来; @for(links:@bin(r));!约束条件:表示0-1变量约束;

@sum(jingdian(j):@sum(jingdian(i):r(i,j)))=n;!约束条件:表示旅游景点的数目为n的约束;

@for(jingdian(i):@for(jingdian(j)|j#gt#1#and#j#ne#i:l(j)>=l(i)+r(i,j)-(n-2)*(1-r(i,j))+(n-3)*r(j,i)));

@for(jingdian(i)|i#gt#1:l(i)1+(n-2)*r(i,1));!这两个约束条件：为了控制不出现两个以上环形回路，保证有且仅有一条环形路线; @for(jingdian(i)|1#eq#i:v(i)=1;b(i)=0);

@for(jingdian(k)|1#lt#k#and#k#le#n:@for(jingdian(i):@for(jingdian(j):x(k,i,j)=@if(0.5#le#r(i,j)#and#r(i,j)#le#1.5#and#(i-0.5)#le#v(k-1)#and#v(k-1)#le#(i+0.5),j,0)));v(k)=@sum(jingdian(j):@sum(jingdian(i):x(k,i,j))));

@for(jingdian(i)|2#le#i#and#i#le#(n):@for(jingdian(k):@for(jingdian(j):bb(k,i,j)=@if(v(i)#eq#j#and#v(i-1)#eq#k,t(k)+tt(k,j),0))));

@for(jingdian(i)|2#le#i#and#i#le#(n):b(i)=@sum(jingdian(j):@sum(jingdian(k):bb(k,i,j))));

@for(jingdian(k)|k#le#n:tv(k)=@sum(jingdian(i)|1#le#i#and#i#le#(k):b(i)/12));

!@for(jingdian(j)|j#le#n:@for(jingdian(i):ssv(i,j)=@if(v(j)#eq#i,t(i),0)));

!@for(jingdian(j)|j#le#n:sv(j)=@sum(jingdian(i):ssv(i,j)));

@for(jingdian(j)|2#le#j#and#j#le#n:@for(gailv(k):@for(jingdian(i):ppv(i,j,k)=@if(v(j)#eq#i#and#(tv(j))#le#k#and#k#le#(tv(j)+t(i)/12),pp(i,k),0))));

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@for(links2(j,k)|2#le#j#and#j#le#n:pv(j,k)=@sum(jingdian(i):ppv(i,j,k)));

@for(links2(j,k)|j#lt#2#or#j#gt#n:pv(j,k)=0); p=@sum(links2(j,k):pv(j,k)); end

第五问结果：

Variable Value Reduced Cost

N 5.000000 0.000000 P 1.600000 0.000000 QUAN 157.8990 0.000000 Q 927.2000 0.000000 V( 1) 1.000000 0.000000 V( 2) 7.000000 0.000000 V( 3) 9.000000 0.000000 V( 4) 8.000000 0.000000 V( 5) 4.000000 0.000000 V( 6) 0.000000 0.000000 V( 7) 0.000000 0.000000 V( 8) 0.000000 0.000000 V( 9) 0.000000 0.000000 V( 10) 0.000000 0.000000 V( 11) 0.000000 0.000000

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