`pulp`: Pulp classes

`LpProblem`([name, sense])	An LP Problem
`LpVariable`(name[, lowBound, upBound, cat, e])	This class models an LP Variable with the specified associated parameters
`LpAffineExpression`([e, constant, name])	A linear combination of `LpVariables`.
`LpConstraint`([e, sense, name, rhs])	An LP constraint
`LpConstraint.makeElasticSubProblem`(*args, ...)	Builds an elastic subproblem by adding variables to a hard constraint
`FixedElasticSubProblem`(constraint[, ...])	Contains the subproblem generated by converting a fixed constraint \(\sum_{i}a_i x_i = b\) into an elastic constraint.

Todo

LpFractionConstraint, FractionElasticSubProblem

The LpProblem Class

class pulp.LpProblem(name='NoName', sense=1)

Bases: object

An LP Problem

Creates an LP Problem

This function creates a new LP Problem with the specified associated parameters

Parameters:

name – name of the problem used in the output .lp file
sense – of the LP problem objective. Either LpMinimize (default) or LpMaximize.

Returns:

An LP Problem

Three important attributes of the problem are:

objective: The objective of the problem, an LpAffineExpression

constraints: An ordered dictionary of constraints of the problem - indexed by their names.

status: The return status of the problem from the solver.

Some of the more important methods:

solve(solver=None, **kwargs)

Solve the given Lp problem.

This function changes the problem to make it suitable for solving then calls the solver.actualSolve() method to find the solution

Parameters:: solver – Optional: the specific solver to be used, defaults to the default solver.

Side Effects:

The attributes of the problem object are changed in actualSolve() to reflect the Lp solution

roundSolution(epsInt=1e-05, eps=1e-07)

Rounds the lp variables

Inputs:

none

Side Effects:

The lp variables are rounded

setObjective(obj)

Sets the input variable as the objective function. Used in Columnwise Modelling

Parameters:: obj – the objective function of type LpConstraintVar

Side Effects:

The objective function is set

writeLP(filename, writeSOS=1, mip=1, max_length=100)

Write the given Lp problem to a .lp file.

This function writes the specifications (objective function, constraints, variables) of the defined Lp problem to a file.

Parameters:: filename (str) – the name of the file to be created.
Returns:: variables

Side Effects:

The file is created

writeMPS(filename, mpsSense=0, rename=0, mip=1, with_objsense: bool = False)

Writes an mps files from the problem information

Parameters:

filename (str) – name of the file to write
mpsSense (int)
rename (bool) – if True, normalized names are used for variables and constraints
mip – variables and variable renames

Returns:

Side Effects:

The file is created

toJson(filename, *args, **kwargs)

Creates a json file from the LpProblem information

Parameters:

filename (str) – filename to write json
args – additional arguments for json function
kwargs – additional keyword arguments for json function

Returns:

None

classmethod fromJson(filename)

Creates a new Lp Problem from a json file with information

Parameters:: filename (str) – json file name
Returns:: a tuple with a dictionary of variables and an LpProblem
Return type:: (dict, LpProblem)

variables()

Returns the problem variables

Returns:: A list containing the problem variables
Return type:: (list, LpVariable)

Variables and Expressions

class pulp.LpElement(name): Base class for LpVariable and LpConstraintVar

class pulp.LpVariable(name, lowBound=None, upBound=None, cat='Continuous', e=None)

This class models an LP Variable with the specified associated parameters

Parameters:

name – The name of the variable used in the output .lp file
lowBound – The lower bound on this variable’s range. Default is negative infinity
upBound – The upper bound on this variable’s range. Default is positive infinity
cat – The category this variable is in, Integer, Binary or Continuous(default)
e – Used for column based modelling: relates to the variable’s existence in the objective function and constraints

addVariableToConstraints(e): adds a variable to the constraints indicated by the LpConstraintVars in e

classmethod dicts(name, indices=None, lowBound=None, upBound=None, cat='Continuous', indexStart=[])

This function creates a dictionary of LpVariable with the specified associated parameters.

Parameters:

name – The prefix to the name of each LP variable created
indices – A list of strings of the keys to the dictionary of LP variables, and the main part of the variable name itself
lowBound – The lower bound on these variables’ range. Default is negative infinity
upBound – The upper bound on these variables’ range. Default is positive infinity
cat – The category these variables are in, Integer or Continuous(default)

Returns:

A dictionary of LpVariable

fixValue(): changes lower bound and upper bound to the initial value if exists. :return: None

classmethod fromDict(dj=None, varValue=None, **kwargs)

Initializes a variable object from information that comes from a dictionary (kwargs)

Parameters:

dj – shadow price of the variable
varValue (float) – the value to set the variable
kwargs – arguments to initialize the variable

Returns:

a LpVariable

Return type:

:LpVariable

classmethod from_dict(dj=None, varValue=None, **kwargs)

Initializes a variable object from information that comes from a dictionary (kwargs)

Parameters:

dj – shadow price of the variable
varValue (float) – the value to set the variable
kwargs – arguments to initialize the variable

Returns:

a LpVariable

Return type:

:LpVariable

isFixed()

Returns:: True if upBound and lowBound are the same
Return type:: bool

setInitialValue(val, check=True)

sets the initial value of the variable to val May be used for warmStart a solver, if supported by the solver

Parameters:

val (float) – value to set to variable
check (bool) – if True, we check if the value fits inside the variable bounds

Returns:

True if the value was set

Raises:

ValueError – if check=True and the value does not fit inside the bounds

toDict()

Exports a variable into a dictionary with its relevant information

Returns:: a dictionary with the variable information
Return type:: dict

to_dict()

Exports a variable into a dictionary with its relevant information

Returns:: a dictionary with the variable information
Return type:: dict

Example:

>>> x = LpVariable('x',lowBound = 0, cat='Continuous')
>>> y = LpVariable('y', upBound = 5, cat='Integer')

gives \(x \in [0,\infty)\), \(y \in (-\infty, 5]\), an integer.

class pulp.LpAffineExpression(e=None, constant=0, name=None)

Bases: OrderedDict

A linear combination of LpVariables. Can be initialised with the following:

e = None: an empty Expression
e = dict: gives an expression with the values being the coefficients of the keys (order of terms is undetermined)
e = list or generator of 2-tuples: equivalent to dict.items()
e = LpElement: an expression of length 1 with the coefficient 1
e = other: the constant is initialised as e

Examples:

>>> f=LpAffineExpression(LpElement('x'))
>>> f
1*x + 0
>>> x_name = ['x_0', 'x_1', 'x_2']
>>> x = [LpVariable(x_name[i], lowBound = 0, upBound = 10) for i in range(3) ]
>>> c = LpAffineExpression([ (x[0],1), (x[1],-3), (x[2],4)])
>>> c
1*x_0 + -3*x_1 + 4*x_2 + 0

In brief, \(\textsf{LpAffineExpression([(x[i],a[i]) for i in I])} = \sum_{i \in I} a_i x_i\) where (note the order):

x[i] is an LpVariable

a[i] is a numerical coefficient.

addInPlace(other, sign=1)

Parameters:: sign (int) – the sign of the operation to do other. if we add other => 1 if we subtract other => -1

asCplexLpAffineExpression(name, constant=1): returns a string that represents the Affine Expression in lp format

asCplexVariablesOnly(name): helper for asCplexLpAffineExpression

copy(): Make a copy of self except the name which is reset

sorted_keys(): returns the list of keys sorted by name

toDict()

exports the LpAffineExpression into a list of dictionaries with the coefficients it does not export the constant

Returns:: list of dictionaries with the coefficients
Return type:: list

to_dict()

exports the LpAffineExpression into a list of dictionaries with the coefficients it does not export the constant

Returns:: list of dictionaries with the coefficients
Return type:: list

pulp.lpSum(vector)

Calculate the sum of a list of linear expressions

Parameters:: vector – A list of linear expressions

Constraints

class pulp.LpConstraint(e=None, sense=0, name=None, rhs=None)

Bases: LpAffineExpression

An LP constraint

Parameters:

e – an instance of LpAffineExpression
sense – one of LpConstraintEQ, LpConstraintGE, LpConstraintLE (0, 1, -1 respectively)
name – identifying string
rhs – numerical value of constraint target

addInPlace(other, sign=1)

Parameters:: sign (int) – the sign of the operation to do other. if we add other => 1 if we subtract other => -1

asCplexLpConstraint(name): Returns a constraint as a string

changeRHS(RHS): alters the RHS of a constraint so that it can be modified in a resolve

copy(): Make a copy of self

classmethod fromDict(_dict)

Initializes a constraint object from a dictionary with necessary information

Parameters:: _dict (dict) – dictionary with data
Returns:: a new LpConstraint

classmethod from_dict(_dict)

Initializes a constraint object from a dictionary with necessary information

Parameters:: _dict (dict) – dictionary with data
Returns:: a new LpConstraint

makeElasticSubProblem(*args, **kwargs)

Builds an elastic subproblem by adding variables to a hard constraint

uses FixedElasticSubProblem

toDict()

exports constraint information into a dictionary

Returns:: dictionary with all the constraint information

class pulp.FixedElasticSubProblem(constraint, penalty=None, proportionFreeBound=None, proportionFreeBoundList=None)

Bases: LpProblem

Contains the subproblem generated by converting a fixed constraint \(\sum_{i}a_i x_i = b\) into an elastic constraint.

Parameters:

constraint – The LpConstraint that the elastic constraint is based on
penalty – penalty applied for violation (+ve or -ve) of the constraints
proportionFreeBound – the proportional bound (+ve and -ve) on constraint violation that is free from penalty
proportionFreeBoundList – the proportional bound on constraint violation that is free from penalty, expressed as a list where [-ve, +ve]

Creates an LP Problem

This function creates a new LP Problem with the specified associated parameters

Parameters:

name – name of the problem used in the output .lp file
sense – of the LP problem objective. Either LpMinimize (default) or LpMaximize.

Returns:

An LP Problem

alterName(name): Alters the name of anonymous parts of the problem

deElasticize(): de-elasticize constraint

findDifferenceFromRHS(): The amount the actual value varies from the RHS (sense: LHS - RHS)

findLHSValue(): for elastic constraints finds the LHS value of the constraint without the free variable and or penalty variable assumes the constant is on the rhs

isViolated(): returns true if the penalty variables are non-zero

reElasticize(): Make the Subproblem elastic again after deElasticize

Combinations and Permutations

pulp.combination(iterable, r)

Return successive r-length combinations of elements in the iterable.

combinations(range(4), 3) –> (0,1,2), (0,1,3), (0,2,3), (1,2,3)

pulp.allcombinations(orgset, k)

returns all combinations of orgset with up to k items

Parameters:

orgset – the list to be iterated
k – the maxcardinality of the subsets

Returns:

an iterator of the subsets

example:

>>> c = allcombinations([1,2,3,4],2)
>>> for s in c:
...     print(s)
(1,)
(2,)
(3,)
(4,)
(1, 2)
(1, 3)
(1, 4)
(2, 3)
(2, 4)
(3, 4)

pulp.permutation(iterable, r=None)

Return successive r-length permutations of elements in the iterable.

permutations(range(3), 2) –> (0,1), (0,2), (1,0), (1,2), (2,0), (2,1)

pulp.allpermutations(orgset, k)

returns all permutations of orgset with up to k items

Parameters:

orgset – the list to be iterated
k – the maxcardinality of the subsets

Returns:

an iterator of the subsets

example:

>>> c = allpermutations([1,2,3,4],2)
>>> for s in c:
...     print(s)
(1,)
(2,)
(3,)
(4,)
(1, 2)
(1, 3)
(1, 4)
(2, 1)
(2, 3)
(2, 4)
(3, 1)
(3, 2)
(3, 4)
(4, 1)
(4, 2)
(4, 3)

pulp.value(x): Returns the value of the variable/expression x, or x if it is a number

pulp: Pulp classes

The LpProblem Class

Variables and Expressions

Constraints

Combinations and Permutations

`pulp`: Pulp classes