Download LP Example

Introduc)onto
Python,Cplexand
Gurobi
Introduc)on
•  Pythonisawidelyused,highlevel
programminglanguagedesignedby
GuidovanRossumandreleasedon1991.
•  Twostablereleases:
– Python2.7
– Python3.5
Python
•  ToopenStartMenu->Python27->IDLE
•  PythonisaninteracAveinterpretedlanguage,
soyoucaninteractdirectlywiththePython
prompttowriteaprogram.
•  Forexample,writeontheprompt
–  Print(‘HelloWorld!’)
–  2+4or2<4
Python
•  Pythonpromptcanbeusedtowritea
programdirectly
OR
•  APythonscriptcanbecreated.
–  File->NewFile
–  Writetheprogramandsaveitwiththe
extension.py
–  Run->RunModule
BasicSyntax
•  Printstatement
–  Elementsseparatedbycommasareprintedwitha
spaceinthemiddle.
–  Operatorssuchas\nor\tindicatenewlineor
newtab
–  All‘–“–‘’’or“””indicatethesamething.
BasicSyntax
•  CommentsareiniAalizedby#
•  Pythoniden)fiershavetostartwithalePerA
toZ(atoz)oranunderscore(_)followedby
lePersornumbers.
•  Reservedwords
And
Assert
Break
Class ConAnue def
del
elif
exec
finally
for
from global
if
import in
Not
or
pass
print raise
return try
while
else
except
is
lambda
with
yield
BasicSyntax
•  Blocksofcodearedenotedbyline
indentaAon,nobracesareused.
OK
ERROR
VariableTypes
•  Fivestandarddatatypes:numbers,string,list,
tupleanddicAonary.
•  AssignValuestoVariables
•  MulApleassignment
VariableTypes
•  Numbers:fournumericaltypesaresupported
–  Int(integers),long(longintegers),float(floaAng
pointrealvalues)andcomplex(complexnumbers)
•  Toconvertfromonetoother.
VariableTypes
•  SomefuncAonswithnumbers
Func)on
Descrip)on
Func)on
Descrip)on
abs(x)
Absolutevalueofx
acos(x)
Arccosineofx,radians
ceil(x)
Smallestintegernotlessx asin(x)
Arcsineofx,randians
exp(x)
e^x
atan(x)
Arctangentofx,radians
log(x)
Naturallogarithmofx
cos(x)
Cosineofx,radians
log10(x)
Base10logarithmofx
sin(x)
Sineofx,radians
max(x1,…,xn)
Maxvalueofarguments
tan(x)
Tangentofx,radians
min(x1,…,xn)
Minvalueofarguments
degrees(x) Convertfromradianstodegre
pow(x,y)
x^y
radians(x)
Convertfromdegreetorad
sqrt(x)
Squarerootofx
pie
Constantspiande
VariableTypes
•  Strings:createthemenclosingcharactersin
quotes
VariableTypes
•  Lists:containsitemsseparatedbycommas
andenclosedwithinbrackets[]
VariableTypes
•  SomefuncAonsoflists
Func)on
Descrip)on
len(A)
Returnslengthofthelist
max(A)
ReturnsitemfromlistAwiththemaxvalue
min(A)
ReturnsitemfromlistAwiththeminvalue
A.append(x)
AppendsxtolistA
A.count(x)
ReturnshowmanyAmesxisinlistA
A.insert(i,x)
InsertsxinlistAinposiAoni
A.remove(x)
RemovesxfromlistA
A.reverse()
ReverseslistA
A.sort()
SortsobjectsoflistA
VariableTypes
•  Tuples:similartoalistbutisenclosedin
parentheses()andcannotbeupdated.(Readonlylists)
•  ListvsTuple:Onalistanassignmentcanbe
done,butnotonatuple.Atuplecanbe
convertedtoalistbylist(A).
VariableTypes
•  DicAonaries:likehashtables.Areenclosedby
curlybraces{}
•  DATATYPECOVERSION:Toconvertbetween
typesyouonlyusethetypenameasa
funcAon.
BasicOperators
•  ArithmeAcOperators
+
AddiAon
/
Division
-
SubstracAon
%
Module
*
MulAplicaAon
**
Exponent
•  ComparisonOperators
a==b Trueifvaluesareequal
a<b
Trueifalessthanb
a!=b Trueifvaluesarenotequal
a>=b
Trueifagreaterorequalthanb
a>b
a<=b
Trueifaislessorequalthanb
Trueifagreaterthanb
BasicOperators
•  AssignmentOperators
a=b
Assignvalueofbtoa
a*=b
MulApliesawithb,assignstoa
a+=b
Addsbtoa,assigntoa
a/=b
Dividesawithb,assignstoa
a-=b
Subtractsbtoa,assigntoa a**=b a^bandassignstoa
•  LogicalOperators
and
Trueifbothoperatorsaretrue
or
TrueifONEoftheoperatorsistrue
not
NegaAonoperator
DecisionMaking
•  CondiAonalstatements
Example:
Loops
•  StatementsareexecutedsequenAally.
LoopType
Descrip)on
while
RepeatsastatementwhileagivencondiAonistrue
for
ExecutesasequenceofstatementmulApleAmes
while:
Loops
•  StatementsareexecutedsequenAally.
LoopType
Descrip)on
while
RepeatsastatementwhileagivencondiAonistrue
for
ExecutesasequenceofstatementmulApleAmes.
for:
•  Forallowstoiteratealongtheitemsofanysequence,that
canbealist.AlsorangefuncAoncanbeused.
Loops
For:
Loops
•  Controlstatements.
Statement
Descrip)on
break
TerminatestheloopandtransfertheexecuAontothe
followingstatementatertheloop
conAnue
Causesthelooptoskiptheremainderofitsbodyand
immediatelyretestitscondiAonpriortoreiteraAng.
pass
Usedwhenastatementisrequiredbutnotwantto
executeanythingonit.
Func)ons
•  FuncAonscanbedefinedtoprovidethe
requiredfuncAonality
–  Blocksbeginwithdeffollowedbythenameand
parentheses()
–  Anyinputshouldbeplacedwithinthe
parentheses
–  Thestatementreturn[]exitsafuncAon.
•  TocallthefuncAonjustwritethenameofthe
funcAonandtheinputparameters.
Func)ons
•  Example
Func)ons
•  Allparametersarepassedbyreference.Ifyou
changethevalueofanargumentthatwasan
inputinsidethefuncAon,itwillbechanged
alsooutside.
•  Butifavariable(withthesamename)is
redefinedinsidethefuncAonthatwillnot
changethevalueoutsidethefuncAon
Func)ons
FilesI/O
•  PythonprovidesbasicfuncAonstoreadand
writefiles.
•  OPEN:beforeyoucanreadorwriteafileit
needstobeopened.
Modes
Descrip)on
r
Opensafilereadingonly.
r+
OpensafileforbothreadingandwriAng.
w
OpensafileforwriAngonly.
w+
OpensafileforbothwriAngandreading.
FilesI/O
•  Close()closesthefileandnomorewriAngcan
bedone.
•  Write()writesanystringtoanopenfile.
•  Read()readsastringfromanopenfile.
–  readline()
Modules
•  Amoduleallowsyoutologicallyorganizeyour
Pythoncode.
•  Themodules,suchasCplexorGurobimodule
arecalledasfollows
Gurobi
•  IsacommercialopAmizaAonsolver.
•  Itisnamedateritsfounders:ZonghaoGu,
EdwardRothbergandRobertBixby.
•  Itsupportsavarietyofprogrammingand
modellinglanguagesincludingPython,C++,
etc.
•  InstallaAonfromwww.gurobi.comandan
accademicfreelicensecanberequested.
LPExample
LPExample
•  Firstweneedtoimportthegurobimodule
•  WeneedtodefinethemodelwithModel().
Insidetheparenthesesyoucanaddanameto
themodel.Andthevariablemwillbeused
everyAmewerefertothemodelonPython.
LPExample
•  Createthevariableswithmodel.addVar()
•  model.addVar(),takesthefollowing
arguments
•  vtypecanbeGRB.BINARY,GRB.CONTINUOUS,
GRB.INTEGER,GRB.SEMICONTor
GRB.SEMIINT
LPExample
•  Tointegratenewvariables,model.update()
•  SetthemodelobjecAvewith
model.setObjecAve(‘EXPRESION’,‘SENSE’)
•  Senses:GRB.MAXIMIZEandGRB.MINIMIZE
LPExample
•  Addtheconstraintswith
model.addConstr(‘LHS’,sense,‘RHS’,name=‘’)
ormodel.addConstr(‘expression’,“name”)
•  Sense:GRB.EQUAL,GRB.LESS_EQUALor
GRB.GREATER_EQUAL
LPExample
•  WecanwritetheformulaAonona.lpfilewith
model.write()
•  FinallywewanttosolvetheopAmizaAon
modelwithmodel.opAmize()
LPExample
•  Oncetheproblemissolved,wecanaccessto
–  ObjecAveFuncAonValue.
m.objval
–  Variablevalues
m.getVars()
LPExample
•  OtherwayofsolvingaproblemwithGurobiis
wriAngintoa.lpfileandreadingthefileand
solvingit.
Cplex
•  IBMILOGCPLEXOpAmizaAonStudioisan
opAmizaAonsotwarepackage.
•  Cplexwasnamedforthesimplexmethodas
implementedintheCprogramminglanguage.
•  ItwasoriginallydevelopedbyRobertE.Bixby
andreleasedon1998forthefirstAme.
LPExample
LPExample
•  Firstweneedtoimportthecplexmodule
•  Weneedtodefinethemodelwith
cplex.Cplex().Insidetheparenthesesyoucan
addanametothemodel.Andthevariablem
willbeusedeveryAmewerefertothemodel
onPython.
LPExample
•  Createthevariableswithm.variables.add()
•  model.variables.add(),takesthefollowing
arguments
•  typescanbebinary,conAnuous,integer,
semi_conAnuousorsemi_integer.
LPExample
•  SetthemodelobjecAvem.objecAve.set_linear
whereeachvariableneedstobefollowedby
thecoefficient.
•  TosettheobjecAvesense,m.objecAve.set_sense()
wherethesensescanbe
m.objecAve.sense.maximize/minimize
LPExample
•  Addtheconstraintswith
m.linear_constraints.add(lin_expr=[],senses=[],rhs=[],
names=‘’)
•  Tocreatetheexpressioncplex.SparsePair()
funcAonisneeded.
•  Senses:‘G’,‘L’or‘E’
LPExample
•  WecanwritetheformulaAonona.lpfilewith
model.write()
•  FinallywewanttosolvetheopAmizaAon
modelwithmodel.solve()
LPExample
•  Oncetheproblemissolved,wecanaccessto
–  ObjecAvefuncAonvalue:
m.soluAon.get_objecAve_value()
–  Variablevalues:
m.soluAon.get_values([‘variablesnames’])
LPExample
•  OtherwayofsolvingaproblemwithCplexis
wriAngintoa.lpfileandreadingthefileand
solvingit.
Exercise