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 – the name of the file to be created.

return variables Side Effects:

  • The file is created.

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, indexs, lowBound=None, upBound=None, cat='Continuous', indexStart=[])

Creates a dictionary of LP variables

This function creates a dictionary of LP Variables with the specified

associated parameters.

Parameters

  • name – The prefix to the name of each LP variable created

  • indexs – 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 LP Variables

fixValue()

changes lower bound and upper bound to the initial value if exists. :return:

setInitialValue(val, check=True)

sets the initial value of the Variable to val may of may not be supported by the solver if check is True: we confirm the value is really possible

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: collections.OrderedDict

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

  1. e = None: an empty Expression

  2. e = dict: gives an expression with the values being the coefficients of the keys (order of terms is undetermined)

  3. e = list or generator of 2-tuples: equivalent to dict.items()

  4. e = LpElement: an expression of length 1 with the coefficient 1

  5. 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.

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: pulp.pulp.LpAffineExpression

An LP constraint

Parameters
makeElasticSubProblem(*args, **kwargs)

Builds an elastic subproblem by adding variables to a hard constraint

uses FixedElasticSubProblem

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

Bases: pulp.pulp.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]

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(orgset, k=None)

returns an iterator that lists the combinations of orgset of length k

Parameters

  • orgset – the list to be iterated

  • k – the cardinality of the subsets

Returns

an iterator of the subsets

example:

>>> c = combination([1,2,3,4],2)
>>> for s in c:
...     print(s)
(1, 2)
(1, 3)
(1, 4)
(2, 3)
(2, 4)
(3, 4)
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(orgset, k=None)

returns an iterator that lists the permutations of orgset of length k

Parameters

  • orgset – the list to be iterated

  • k – the cardinality of the subsets

Returns

an iterator of the subsets

example:

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