LINGO???????

1
LINGO???????
2
???????
3
0-1?????

• ??????????????????(???)??,????????????0-1?????
• ?? ???????? ?

4

• ????,??LINGO????
• model
• sets
• cities/A,B,C,D,E,F,G/ !??7???
• roads(cities,cities)/
• A,B A,C B,D B,E B,F C,D C,E C,F
• D,G E,G F,G/ W, X
• !????????????,W???,X?0-1?????
• endsets
• data
• W2 4 3 3 1 2 3 1 1 3 4
• enddata

5

• N_at_SIZE(CITIES)
• MIN_at_SUM(roadsWX)
• _at_FOR(cities(i) i GT 1 AND i LT N
• _at_SUM(roads(i,j) X(i,j))_at_SUM(roads(j,i)
  X(j,i)))
• _at_SUM(roads(i,j)i EQ 1X(i,j))1
• _at_SUM(roads(i,j)j EQ NX(i,j))1
• end

6

• ????????????.????????????????,????????????(?n-1?
  ????)????????????,???????????n-1?????????.???????,
  LINGO????????????,??LINGO??????????.
• ???????????,?????,????????????????????,??????,????
  ?????????.

7
?? ???????

• ???????(???????,Traveling Salesman Problem
  ??TSP??),????????????
• ????????,???????,??????????????
  ,??????????????i?j????Cij,???????????????,????????
  
• ?????????????????????(?)?

8

• TSP??????????,?????NP?????
• ??????n????(n-1)!?????,??????????????,?n???,??????
  ??,??????????????
• ??,??????????????????
• ???TSP?????0-1??,???LINGO????

9

• 1. ?????????????????
• ??0-1????xij(?i?j)xij1?????i?j,??i-j??????,?xij
  0?????i-j??
• ????
• ???????????????????????????i????(??????),???

10

• ??0-1????xij(?i?j)xij1?????i?j,xij0?????i-j??
• ????
• ???????????????????????????i????(??????),???
• ???????j??????,???
• ?????????????????,?TSP????????,?????

11

• ??,???????????,??????????,??????????????,??????,??
  ????????
• ????????????????????????????????
• ????ui,i2,3,,n,(??????????????????????u2,????)
  ?

12

• ??????
• ui-ujnxijn-1,i1,,n,j2,,n,?i?j ?

13

• TSP?????????

14

• TSP???LINGO??
• !???????
• model
• sets
• city / 1..6/ u! ??6???
• link( city, city)
• dist, ! ????
• x !????
• endsets
• n _at_size( city)

15

• data !????
• 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
• 2396 2136 2180 1616 0 2900
• 1196 764 798 1857 2900 0
• !???????????????
• enddata
• !????
• min _at_sum( link dist x)

16

• _at_FOR( city( K)
• !????K
• _at_sum( city( I) I ne K x( I, K)) 1
• !????K
• _at_sum( city( J) J ne K x( K, J)) 1
• )
• !???????
• _at_for(city(I)I gt 1
• _at_for( city( J) Jgt1 and I ne J
• u(I)-u(J)nx(I,J)ltn-1)
• )
• !??u???????????,???????????TSP??????
• _at_for(city(I) u(I)ltn-1 )
• _at_for( link _at_bin( x))!??X?0\1??
• end

17

• ????
• ?????6610
• ??1-3-6-2-5-4-1

18

• 2. ????????,??????
• ???????????,???????????,?????,?????????????,??????
  ??????(?????),????????????Cij????????,????????????
  ??(????????????????),????????????????????????????

19

• ???????????????(????????),????????????n??????????,
  ?????????????????n?,????????(?n1??????),?????????
  ???n????????,n?????n!??????????????(???)????,???(?
  ???)??????????????????

20

• ??0-1?????Xkj,??k???????,??j?????????,Xkj1??????k
  ????(???)???j,Xkj0??????lj???????????,?Cij????i??
  ?j???????
• ??????1??????
• ???????????????

21

• ????k???????i,??k1?????j,?XkiXk1,j1,???????
• CijXkiXk1,j
• ??1???n????????
• ?????

22

• ???????2?
• (1) ?????????,?
• (2) ???????????????,?

23

• ????,???TSP??????????0-1 ??

24

• ????????????????
• ?LINGO???????,?????
• ?????10????????????????,?????????????????????(????
  ??)??????????????,???????????????????,??????,?????
  ???????

25

• ??LINGO????
• MODEL
• SETS
• CITY/1..10/ JL
• STEP/1..10/
• LINE( STEP, CITY) X
• LINKS(CITY,CITY)C
• ENDSETS

26

• DATA
• JL71,56,27,30,28,26,15,9,30,27
• C 0,15,44,47,64,83,86,75,93,98
• 15,0,29,32,49,68,71,60,78,83
• 44,29,0,20,37,53,42,31,49,54
• 47,32,20,0,17,36,42,39,60,57
• 64,49,37,17,0,19,37,37,58,55
• 83,68,53,36,19,0,18,35,56,47
• 86,71,42,42,37,18,0,24,38,29
• 75,60,31,39,37,35,24,0,21,26
• 93,78,49,60,58,56,38,21,0,29
• 98,83,54,57,55,47,29,26,29,0
• ENDDATA

27

• _at_FOR( LINE _at_BIN( X))
• M1_at_SIZE(STEP)
• _at_FOR(CITY(I) _at_SUM(STEP(N) X(N,I)) 1)
• _at_FOR(STEP(N)_at_SUM(CITY(I)X(N,I))1)
• L1_at_SUM(CITY(I)(X(1,I)X(M1,I))JL(I))
• LX_at_SUM(STEP(N)NLTM1_at_SUM(LINKS(I,J)C(I,J)X(N
  ,I)X(N1,J)))
• MINL1LX
• END

28

• ?????????LINGO??????????
• ???????,LINGO????????,???Global
  Solver(?????????),????Multistart
  Solver(???????),???????????????????,?????????????
  ????????????????,????????????????,????????????????
  ????
• ????Options,??????????Global
  Solver??,??????Global Solver,????????Multistar
  t Solver?,???????,???Solver Decides???LINGO???

29

• ?????,????Global Solver,????Options,????????G
  lobal Solver?????v,??????
• ??????,??4???,?????
• ?????(???)260??
• ????????
• ???8?9?10?7?6?5?4?1?2?3???