?????LINDO/LINGO????

1
??????(2004?7?8????) ?????LINDO/LINGO????
??? ????????? Tel [phone] Emailjxie_at_math.
tsinghua.edu.cn http//faculty.math.tsinghua.edu.
cn/jxie
2
????

• ??????
• LINDO??????????????
• LINDO???????
• LINGO???????
• ???????(??????)

3
????
????? ?????
gi(x)?0????
x????
f(x)????
????
????(LP) ????(QP) ?????(NLP)
?????(PIP) ??????(MIP)
0-1???? ??????
????(IP)
????
4
LINDO ??????????
?????(Chicago)???Linus Schrage???1980?????, ????
LINDO????(LINDO Systems Inc.), ??http//www.lindo
.com
LINDO Linear INteractive and Discrete Optimizer
(V6.1) LINGO Linear INteractive
General Optimizer (V8.0) LINDO
API LINDO Application Programming Interface
(V2.0) Whats Best! (SpreadSheet e.g. EXCEL)
(V7.0)
??(??)????????????????????? (???????????)
5
LINDO?LINGO??????????
????
????(IP)
????

LINGO
LINDO
???? (LP)
???? (QP)
????? (NLP)
6
LINDO/LINGO???????
LINDO/LINGO?????
1. ???? 2. ????
LP QP NLP IP ????(?)
ILP
IQP INLP

????????
????????
?????????
1????????(SLP) 2????????(GRG) (?)
3?????(Multistart) (?)
1. ????? 2. ????(?)
7
??????????????
1?????????,??????????? 2?????????,??????????
??????????????????????/?????????????? 3????????
?,???????????????? (?x/y lt5
??xlt5y) 4??????????,?????????? 5???????????????
(???103)
8
???????????
1?LINDO ????????(??????????) 2?LINGO
????(SETS)??? ???????? ??????????
???????????(OPTIONS) ??????????????
9
?1 ??????????
50???
??480??
????100??A1
??
??????,???????

• 35????1???,?????,????????

• ???????,??????????????

• A1?????? 30?/??,?????????

10
??480??
????100??A1
x1?????A1
x2?????A2
????
?? 243x1
?? 164 x2
????
????
??????(LP)
????
????
????
????
????
11
????
max 72x164x2 st 2)x1x2lt50 3)12x18x2lt480 4)3x1lt1
00 end
OBJECTIVE FUNCTION VALUE 1)
3360.000 VARIABLE VALUE
REDUCED COST X1 20.000000
0.000000 X2 30.000000
0.000000 ROW SLACK OR SURPLUS
DUAL PRICES 2) 0.000000
48.000000 3) 0.000000
2.000000 4)
40.000000 0.000000 NO.
ITERATIONS 2
DO RANGE (SENSITIVITY) ANALYSIS?
No
20?????A1, 30???A2,??3360??
12
????
reduced cost????????????????(??????????)????????(?
max???)
OBJECTIVE FUNCTION VALUE 1)
3360.000 VARIABLE VALUE
REDUCED COST X1 20.000000
0.000000 X2 30.000000
0.000000 ROW SLACK OR SURPLUS
DUAL PRICES 2) 0.000000
48.000000 3) 0.000000
2.000000 4)
40.000000 0.000000 NO.
ITERATIONS 2
????? ?????????????,??????????????
13
????
max 72x164x2 st 2)x1x2lt50 3)12x18x2lt480 4)3x1lt1
00 end
OBJECTIVE FUNCTION VALUE 1)
3360.000 VARIABLE VALUE REDUCED
COST X1 20.000000
0.000000 X2 30.000000
0.000000 ROW SLACK OR SURPLUS DUAL
PRICES 2) 0.000000
48.000000 3) 0.000000
2.000000 4)
40.000000 0.000000
?????
????
?????
??????40
?? ???????????(????)
14
????
OBJECTIVE FUNCTION VALUE 1)
3360.000 VARIABLE VALUE REDUCED
COST X1 20.000000
0.000000 X2 30.000000
0.000000 ROW SLACK OR SURPLUS DUAL
PRICES 2) 0.000000
48.000000 3) 0.000000
2.000000 4)
40.000000 0.000000
????????1????????
????
???1??, ???48
???1??, ???2
?????????

• 35????1???,????

35 lt48, ???!

• ???????????????????

2?!
15
????
????????????????
DO RANGE(SENSITIVITY) ANALYSIS?
Yes
RANGES IN WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 72.000000 24.000000
8.000000 X2 64.000000
8.000000 16.000000
RIGHTHAND SIDE RANGES ROW
CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE
DECREASE 2 50.000000
10.000000 6.666667 3
480.000000 53.333332
80.000000 4 100.000000
INFINITY 40.000000
(??????)
x1????(64,96)
x2????(48,72)
x1???24?3 72 ???30?3 90,??????
??!

• A1????? 30?/??,????????

16
????
???????????????????
RANGES IN WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 72.000000 24.000000
8.000000 X2 64.000000
8.000000 16.000000
RIGHTHAND SIDE RANGES ROW
CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE
DECREASE 2 50.000000
10.000000 6.666667 3
480.000000 53.333332
80.000000 4 100.000000
INFINITY 40.000000
(??????)
?? ????????
??????10
??????53
???10??

• 35????1???,????????

17
??LINDO???????

• gt(?lt)??gt(?lt)????
• ??????????(????), ?????
• ????????,????8???
• ?????????(??LINDO?????)
• ???????????,?????????
• ??(??)?????????????)??
• ????!????????????
• ! Its Comment.
• ????????????TITLE ?????(??72???),?
• TITLE This Model is only an Example

18
??LINDO???????

• ????????????????
• ?????????( )???,?????, ? 400(X1X2)???400X14
  00X2
• ??????,?2X13X2- 4X1??? -2X13X2
• ???????????????END????FREE name???name???????
  
• ?? END??SUB ?SLB ???????
• ?? sub x1 10??????x1lt10
• ??SUB?SLB????????????????,?????????????
  ????
• 14. END??0-1????INT n ? INT name
• 15. END????????GIN n ? GIN name

19
????(QP)??

• LINDO???????(QP)??,????????,???LINDO???????????
• ??????????????????(LAGRANGE??),???????????????????
  ,???????
• END????QCP?????????????,??????
• ?????LINGO?QP
• ???QP?IP ?????????

20
????(LINDO Solver Status)

• ?????????
• ????18?
• ???????(??????)0
• ??????94
• ??????94
• ??????93.5
• ???1
• ????0.00?(???,???0.005?)
• ????????1(?)

21
????

• Preprocess???(?????)
• Preferred Branch???????
• Default(????)?
• Up(??????)?
• Down(??????)
• IP Optimality TolIP??????????(?????,?5?0.05)
• IP Objective HurdleIP????????,?????????????(????
  ?????????????,????????)
• IP Var Fixing Tol??????????????????(????????????
  (REDUCED COST)????,?????,????????????????)?

Nonzero Limit ????????? Iteration
Limit ?????? Initial Contraint
Tol ????????? Final Contraint
Tol ????????? Entering Var Tol ?????REDUCED
COST???? Pivot Size Tol ???????
22
Report/Statistics
ROWS 5 VARS 4 INTEGER VARS 2(
0 0/1) QCP 4 NONZEROS 19
CONSTRAINT NONZ 12( 6 -1)
DENSITY0.760 SMALLEST AND LARGEST ELEMENTS IN
ABSOLUTE VALUE 0.300000
277.000 OBJMIN, NO. lt,,gt 2 0 2,
GUBS lt 1 VUBS gt 0 SINGLE COLS 0
REDUNDANT COLS 0
??????5?(??4?),4???,??????(??0-1??),??4??????????
???? ???????19?,???????12?(??6??1?-1),?????0.760(
??????/??(???1)) ? ???????????,??????????0.3
?277? ???????????????????????????????2?0?2?????
??(GUBS)???1???????(VUBS)???0????GUBS,???????????
?????VUBS,?????????????,????X1X2-X30????,?X30,
?X10,X20(???????),??X1X2-X30???VUBS??? ??????
??1????????0??????0?
23
LINDO??????????
WINDOWS???????????
???????????(?????)
Example ??
FILE / SAVE??
SAVE???
?FILE / TAKE COMMANDS (F11) ????
????LINDO PACKED??(??)?????
24
LINGO????
LINGO?????

• ???LINDO?????
• ??????????(?????)

LINGO?????4??

• ??????
• ???(SETS ENDSETS)
• ???(DATA ENDDATA)
• ???(INIT ENDINIT)

25
LINGO?? ?????
????6?????,?????(ai, bi) (????),?????di (???)
??????????????
26
????ci j (??j???i???)12?
??????
???????,????
??????136.2
27
????NLP
2)???????,?????????(xj,yj)???cij
,?????????????????
???? ci j,(xj,yj)16?
???????
28
LINGO?????4??
???(SETS ENDSETS)
???(DATA ENDDATA)
???(INIT ENDINIT)
LP?????
??? ???
????89.8835(??? )
29
??
30
?????
setname(parent_set_list) /member_list/
attribute_list
setname /member_list/ attribute_list
??
???? ????
???? ???? ????? ????? ?????
?????
SETS CITIES /A1,A2,A3,B1,B2/ ROADS(CITIES,
CITIES)/ A1,B1 A1,B2 A2,B1 A3,B2/D
ENDSETS
SETS STUDENTS /S1..S8/ PAIRS( STUDENTS,
STUDENTS) 2 GT 1 BENEFIT, MATCH ENDSETS
31
?????????
?? ?????? ?? ???????
??? 1..n 1..5 1, 2, 3, 4, 5
??-??? stringM..stringN Car101..car208 Car101, car102, , car208
??? dayM..dayN MON..FRI MON, TUE, WED, THU, FRI
??? monthM..monthN OCT..JAN OCT, NOV, DEC, JAN
??-??? monthYearM..monthYearN OCT2001..JAN2002 OCT2001, NOV2001, DEC2001, JAN2002
32
???????
????? ????? ????? ?????
??? ???
?? NOT (??)

/
(??)
EQ NE GT GE LT LE
AND OR
?? lt() gt()
33
??????
????????FOR?SUM ? MAX?MIN _at_function( setname (
set_index_list) condition expression_list)
Example
objective MAX _at_SUM( PAIRS( I, J) BENEFIT( I,
J) MATCH( I, J)) _at_FOR(STUDENTS( I)
constraints _at_SUM( PAIRS( J, K) J EQ I
OR K EQ I MATCH( J, K)) 1) _at_FOR(PAIRS( I,
J) _at_BIN( MATCH( I, J))) MAXB_at_MAX(PAIRS( I,
J) BENEFIT( I, J)) MINB_at_MIN(PAIRS( I, J)
BENEFIT( I, J))
34
????
Model Class LP, QP,ILP, IQP,PILP,
PIQP,NLP,INLP,PINLP

• State
• Global Optimum
• Local Optimum
• Feasible
• Infeasible
• Unbounded
• Interrupted
• Undetermined

• Solver Type
• B-and-B
• Global
• Multistart

35
7????(???80-90?????)
36
????????

• Cut (or Copy) Paste ??
• _at_FILE ?????_at_TEXT????(????)
• _at_OLE?????????(?EXCEL)??
• _at_ODBC????????
• LINGO??????

???????

• LG4 (LONGO????)
• LNG (LONGO????)
• LTF (LONGO????)
• LDT (LONGO????)
• LRP (LONGO????)

? ? ? ?
??????
37
_at_FILE?_at_TEXT????????
MODEL SETS MYSET / _at_FILE(myfile.txt) /
_at_FILE(myfile.txt) ENDSETS MIN _at_SUM( MYSET(
I) SHIP( I) COST( I)) _at_FOR(
MYSET( I) CON1 SHIP( I) gt NEED(
I) CON2 SHIP( I) lt SUPPLY(
I)) DATA COST _at_FILE(myfile.txt) NEED
_at_FILE(myfile.txt) SUPPLY
_at_FILE(myfile.txt) _at_TEXT(result.txt)SHIP,
_at_DUAL(SHIP), _at_DUAL(CON1) ENDDATA END
myfile.txt?? ?????? Seattle,Detroit,Chicago,Denv
er COST,NEED,SUPPLY,SHIP 12,28,15,20 1600,1800,
1200,1000 1700,1900,1300,1100
?? MyfileExample.lg4
38
_at_OLE ?EXCEL??
MODEL SETS MYSET COST,SHIP,NEED,SUPPLY ENDSE
TS MIN _at_SUM( MYSET( I) SHIP( I) COST(
I)) _at_FOR( MYSET( I) CON1 SHIP(
I) gt NEED( I) CON2 SHIP( I) lt
SUPPLY( I)) DATA MYSET _at_OLE('D\JXIE\BJ2004M
CM\mydata.xls','CITIES') COST,NEED,SUPPLY
_at_OLE(mydata.xls) _at_OLE(mydata.xls,'SOLUTION')
SHIP ENDDATA END
mydata.xls??????????(???) CITIES,
COST,NEED,SUPPLY,SOLUTION
?? MydataExample.lg4

• ?EXCEL???????????LINGO(?)
• ????EXCEL?????LINGO???(?)

39
_at_ODBC ??????
???????,??????ODBC?????
??????DBMS (???????,????????) ACCESS,
DBASE,EXCEL,FOXPRO,ORACLE, PARADOX,SQL SERVER,
TEXE FILES
???????? setname/_at_ODBC(datasource ,
tablename , columnname)/ ???????? setnam
e/_at_ODBC(source,table , column1,
column2)/
???? Attr_list_at_ODBC(source,table ,
column1, column2) ???? _at_ODBC(source
,table , column1, column2) Attr_list
?????
40
???????
????? ???? ???????? ??????
41
?????
????T????
42
? ????
??1. ??????? ?
?????????
??2. ??????
????????????,??????????,??????????3??????????
43
????
????
????????????????????????
???????????????????????
44
??????
??????1
???????,?????????,?????????????,?????
????
1. ???????????
2. ???????????
45
????
xi ??i ????????????(i1,2,7)
??1(???)
??
????
???? xi ???
???x212, x515, ???0 ???27
???2??12?,???5??15?,??27?
46
??????1
??2(???)
??????
???x215, x55, x75, ???0 ???25?
???2??15?,???5??5?,???7??5?,?25?,??35?
???1??????27?,??27? ??
?????8?,????2?
????????,???????????
47
??????2
??????5?10????????3??
??4???4?50?,5?10?,6?20?,8?15?,????????????,?????
??????,??????????????
????
xi ??i ????????????(i1,2,3)
r1i, r2i, r3i, r4i ?i ??????,????????4??5??6??8?
???????
48
??????2
????(???)
???????????3?
????
????
???? xi ,r1i, r2i, r3i, r4i (i1,2,3)???
?????????
49
??????2
????,?????,????
??4?50?,5?10?,6?20?,8?15?
???????19?
?????????
????????????? ??1???4?4???,?13? ??2???1?5??2?6
???,?10? ??3???2?8???,?8?? ?????????31
?????????
50
LINGO???????????
Local optimal solution found at iteration
12211 Objective value
28.00000 Variable Value Reduced Cost X1
10.00000 0.000000 X2
10.00000 2.000000 X3 8.000000
1.000000 R11 3.000000
0.000000 R12 2.000000
0.000000 R13 0.000000
0.000000 R21 0.000000
0.000000 R22 1.000000 0.000000
R23 0.000000
0.000000 R31
1.000000 0.000000
R32 1.000000 0.000000
R33 0.000000
0.000000 R41
0.000000 0.000000
R42 0.000000 0.000000
R43 2.000000
0.000000
??cut02a.lg4 cut02b.lg4
??1?????????3?4??1?6???,?10? ??2?????????2?4??1
?5??1?6???,?10? ??3?????????2?8???,?8?? ????????
28??
51
??????????(CUMCM-2003B)
?????????????? ????????25????,??????????????????
,??????????(????)??????????????????,????????5??
??????????????29.5?1(????),????????(8??)????????
???????????????????154?,????28km,???????3???
???????????????????,???????????????????
????????,??????????????,?????????????? ?
52
?????
53
????
?? ??1 ??2 ??3 ??4 ??5 ??6 ??7 ??8 ??9 ??10
??? 5.26 5.19 4.21 4.00 2.95 2.74 2.46 1.90 0.64 1.27
??? 1.90 0.99 1.90 1.13 1.27 2.25 1.48 2.04 3.09 3.51
?? 5.89 5.61 5.61 4.56 3.51 3.65 2.46 2.46 1.06 0.57
??? 0.64 1.76 1.27 1.83 2.74 2.60 4.21 3.72 5.05 6.10
??? 4.42 3.86 3.72 3.16 2.25 2.81 0.78 1.62 1.27 0.50
??1 ??2 ??3 ??4 ??5 ??6 ??7 ??8 ??9 ??10
??? 0.95 1.05 1.00 1.05 1.10 1.25 1.05 1.30 1.35 1.25
??? 1.25 1.10 1.35 1.05 1.15 1.35 1.05 1.15 1.35 1.25
??? 30 28 29 32 31 33 32 31 33 31
54
????

• ???????????????
• ????????????????
• ????????????????
• ????????,???????
• ????????????????
• ????????,??????,154?/??
• ????????????????????7?????????????
• ???????????????????

• ????
• ?????????????????(MIP??)
• ??????????????????

55
????

• ????????????????????????
• ???????????????????????,???????????????,??????????
  ???????
• ??????????28km/h,??????
• ?????????,???

?????????,??????????? ??????????? (?)
56
??

• xij ?i???j???????? (?) ?? ?
• cij ?i????j??????
  ??
• Tij ?i?????j??????????????? ?
• Aij ??????????????????? ?
• Bij ?????????????????????? ?
• pii????????? p(30,28,29,32,31,33,32,31,33,31)
  
• qj j???????,q(1.2,1.3,1.3,1.9,1.3)10000
  ?
• cki i?????????
  ??
• cyi i????????
  ??
• fi ???i????????0-1??,?1???0????

(??)
57
????
(1)????(???)?? (2)?????? (3)?????? (4)?????? (
5)?????? (6)????? (7)?????? (8)????
.
xij????? fi ?0-1??
58
????(LINGO??)
??1 ??2 ??3 ??4 ??5 ??6 ??7 ??8 ??9 ??10
?? 13 54 11
?? 42 43
?? 70 15
?? 81 43
?? 13 2 70
??1 ??2 ??3 ??4 ??5 ??6 ??7 ??8 ??9 ??10
??? 0.867 1.862 0.314
??? 1.077 1.162
?? 1.892 0.326
??? 1.841 1.229
??? 0.684 0.1 1.489
59
????(??)
??1 ??2 ??3 ??4 ??5 ??6 ??7 ??8 ??9 ??10
??? 1 (29)
??? 1 (39) 1 (37)
?? 1 (37)
??? 1(44) 1 (35)
??? 1 (47)
??6?????(???)
?? ??1?2?3?4?8?9?10????????? ?????13???????85628
.62??? ?????32186??????38192??
60
?????
?????? ??????(20?)??(???????????)
?? (?)
61
??????(CUMCM-2000B)
?????
?? 300 301350 351400 401450 451500
?? 20 23 26 29 32
62
??????(CUMCM-2000B)

• ???? ????
• ?????????
• ??????(??/??)???????
• ???????????,????????

63
??????(CUMCM-2000B)

• fi????i????xij????i????j????
• yj????j????????zj?????????

• LINDO/LINGO??????matlab????

64
??????
?????? ?????? ?????? ?????? ??
65

????!
Thats all. Any Questions?