Introduc)ontoPython,Cplexand

Gurobi

•  Pythonisawidelyused,highlevelprogramminglanguagedesignedbyGuidovanRossumandreleasedon1991.

•  Twostablereleases:– Python2.7– Python3.5

Introduc)on

Python•  ToopenStartMenu->Python27->IDLE•  PythonisaninteracAveinterpretedlanguage,soyoucaninteractdirectlywiththePythonprompttowriteaprogram.

•  Forexample,writeontheprompt– Print(‘HelloWorld!’)– 2+4or2<4

Python•  Pythonpromptcanbeusedtowriteaprogramdirectly

OR•  APythonscriptcanbecreated.– File->NewFile– Writetheprogramandsaveitwiththeextension.py

– Run->RunModule

BasicSyntax•  Printstatement– Elementsseparatedbycommasareprintedwithaspaceinthemiddle.

– Operatorssuchas\nor\tindicatenewlineornewtab

– All‘–“–‘’’or“””indicatethesamething.

BasicSyntax•  CommentsareiniAalizedby#

•  Pythoniden)fiershavetostartwithalePerAtoZ(atoz)oranunderscore(_)followedbylePersornumbers.

•  ReservedwordsAnd Assert Break Class ConAnue def del elif else except

exec finally for from global if import in is lambda

Not or pass print raise return try while with yield

BasicSyntax•  BlocksofcodearedenotedbylineindentaAon,nobracesareused.

OK

ERROR

VariableTypes•  Fivestandarddatatypes:numbers,string,list,tupleanddicAonary.

•  AssignValuestoVariables

•  MulApleassignment

VariableTypes•  Numbers:fournumericaltypesaresupported–  Int(integers),long(longintegers),float(floaAngpointrealvalues)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:createthemenclosingcharactersinquotes

VariableTypes•  Lists:containsitemsseparatedbycommasandenclosedwithinbrackets[]

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:similartoalistbutisenclosedinparentheses()andcannotbeupdated.(Read-onlylists)

•  ListvsTuple:Onalistanassignmentcanbedone,butnotonatuple.Atuplecanbeconvertedtoalistbylist(A).

VariableTypes•  DicAonaries:likehashtables.Areenclosedbycurlybraces{}

•  DATATYPECOVERSION:ToconvertbetweentypesyouonlyusethetypenameasafuncAon.

BasicOperators•  ArithmeAcOperators

•  ComparisonOperators

+ AddiAon / Division

- SubstracAon % Module

* MulAplicaAon ** Exponent

a==b Trueifvaluesareequal a<b Trueifalessthanb

a!=b Trueifvaluesarenotequal a>=b Trueifagreaterorequalthanb

a>b Trueifagreaterthanb a<=b Trueifaislessorequalthanb

BasicOperators•  AssignmentOperators

•  LogicalOperators

a=b Assignvalueofbtoa a*=b MulApliesawithb,assignstoa

a+=b Addsbtoa,assigntoa a/=b Dividesawithb,assignstoa

a-=b Subtractsbtoa,assigntoa a**=b a^bandassignstoa

and Trueifbothoperatorsaretrue

or TrueifONEoftheoperatorsistrue

not NegaAonoperator

DecisionMaking•  CondiAonalstatements

Example:

Loops•  StatementsareexecutedsequenAally.

while:

LoopType Descrip)on

while RepeatsastatementwhileagivencondiAonistrue

for ExecutesasequenceofstatementmulApleAmes

Loops•  StatementsareexecutedsequenAally.

for:

•  Forallowstoiteratealongtheitemsofanysequence,thatcanbealist.AlsorangefuncAoncanbeused.

LoopType Descrip)on

while RepeatsastatementwhileagivencondiAonistrue

for ExecutesasequenceofstatementmulApleAmes.

LoopsFor:

Loops•  Controlstatements.

Statement Descrip)on

break TerminatestheloopandtransfertheexecuAontothefollowingstatementatertheloop

conAnue CausesthelooptoskiptheremainderofitsbodyandimmediatelyretestitscondiAonpriortoreiteraAng.

pass Usedwhenastatementisrequiredbutnotwanttoexecuteanythingonit.

Func)ons•  FuncAonscanbedefinedtoprovidetherequiredfuncAonality– Blocksbeginwithdeffollowedbythenameandparentheses()

– Anyinputshouldbeplacedwithintheparentheses

– Thestatementreturn[]exitsafuncAon.•  TocallthefuncAonjustwritethenameofthefuncAonandtheinputparameters.

Func)ons•  Example

Func)ons•  Allparametersarepassedbyreference.IfyouchangethevalueofanargumentthatwasaninputinsidethefuncAon,itwillbechangedalsooutside.

•  Butifavariable(withthesamename)isredefinedinsidethefuncAonthatwillnotchangethevalueoutsidethefuncAon

Func)ons

FilesI/O•  PythonprovidesbasicfuncAonstoreadandwritefiles.

•  OPEN:beforeyoucanreadorwriteafileitneedstobeopened.

Modes Descrip)on

r Opensafilereadingonly.

r+ OpensafileforbothreadingandwriAng.

w OpensafileforwriAngonly.

w+ OpensafileforbothwriAngandreading.

FilesI/O•  Close()closesthefileandnomorewriAngcanbedone.

•  Write()writesanystringtoanopenfile.

•  Read()readsastringfromanopenfile.–  readline()

Modules•  AmoduleallowsyoutologicallyorganizeyourPythoncode.

•  Themodules,suchasCplexorGurobimodulearecalledasfollows

Gurobi•  IsacommercialopAmizaAonsolver.•  Itisnamedateritsfounders:ZonghaoGu,EdwardRothbergandRobertBixby.

•  ItsupportsavarietyofprogrammingandmodellinglanguagesincludingPython,C++,etc.

•  InstallaAonfromwww.gurobi.comandanaccademicfreelicensecanberequested.

LPExample

LPExample•  Firstweneedtoimportthegurobimodule

•  WeneedtodefinethemodelwithModel().Insidetheparenthesesyoucanaddanametothemodel.AndthevariablemwillbeusedeveryAmewerefertothemodelonPython.

LPExample•  Createthevariableswithmodel.addVar()

•  model.addVar(),takesthefollowingarguments

•  vtypecanbeGRB.BINARY,GRB.CONTINUOUS,GRB.INTEGER,GRB.SEMICONTorGRB.SEMIINT

LPExample•  Tointegratenewvariables,model.update()

•  SetthemodelobjecAvewithmodel.setObjecAve(‘EXPRESION’,‘SENSE’)

•  Senses:GRB.MAXIMIZEandGRB.MINIMIZE

LPExample•  Addtheconstraintswithmodel.addConstr(‘LHS’,sense,‘RHS’,name=‘’)ormodel.addConstr(‘expression’,“name”)

•  Sense:GRB.EQUAL,GRB.LESS_EQUALorGRB.GREATER_EQUAL

LPExample•  WecanwritetheformulaAonona.lpfilewithmodel.write()

•  FinallywewanttosolvetheopAmizaAonmodelwithmodel.opAmize()

LPExample•  Oncetheproblemissolved,wecanaccessto– ObjecAveFuncAonValue.

m.objval– Variablevaluesm.getVars()

LPExample•  OtherwayofsolvingaproblemwithGurobiiswriAngintoa.lpfileandreadingthefileandsolvingit.

Cplex•  IBMILOGCPLEXOpAmizaAonStudioisanopAmizaAonsotwarepackage.

•  CplexwasnamedforthesimplexmethodasimplementedintheCprogramminglanguage.

•  ItwasoriginallydevelopedbyRobertE.Bixbyandreleasedon1998forthefirstAme.

LPExample

LPExample•  Firstweneedtoimportthecplexmodule

•  Weneedtodefinethemodelwithcplex.Cplex().Insidetheparenthesesyoucanaddanametothemodel.AndthevariablemwillbeusedeveryAmewerefertothemodelonPython.

LPExample•  Createthevariableswithm.variables.add()

•  model.variables.add(),takesthefollowingarguments

•  typescanbebinary,conAnuous,integer,semi_conAnuousorsemi_integer.

LPExample•  SetthemodelobjecAvem.objecAve.set_linearwhereeachvariableneedstobefollowedbythecoefficient.

•  TosettheobjecAvesense,m.objecAve.set_sense()wherethesensescanbem.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.lpfilewithmodel.write()

•  FinallywewanttosolvetheopAmizaAonmodelwithmodel.solve()

LPExample•  Oncetheproblemissolved,wecanaccessto– ObjecAvefuncAonvalue:m.soluAon.get_objecAve_value()

– Variablevalues:m.soluAon.get_values([‘variablesnames’])

LPExample•  OtherwayofsolvingaproblemwithCplexiswriAngintoa.lpfileandreadingthefileandsolvingit.

Exercise