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Elastic Constraints
^^^^^^^^^^^^^^^^^^^
.. currentmodule:: pulp
A constraint :math:`C(x) = c` (equality may be replaced by :math:`\le`
or :math:`\ge`)
can be elasticized to the form
.. math:: C(x) \in D
where :math:`D` denotes some interval containing the value
:math:`c`.
Define the constraint in two steps:
#. instantiate constraint (subclass of :class:`LpConstraint`) with target :math:`c`.
#. call its :meth:`~LpConstraint.makeElasticSubProblem` method which returns
an object of type :class:`FixedElasticSubProblem`
(subclass of :class:`LpProblem`) - its objective is the minimization
of the distance of :math:`C(x)` from :math:`D`.
.. code-block:: python
constraint = LpConstraint(..., rhs = c)
elasticProblem = constraint.makeElasticSubProblem(
penalty = <penalty_value>,
proportionFreeBound = <freebound_value>,
proportionFreeBoundList = <freebound_list_value>,
)
where:
* ``<penalty_value>`` is a real number
* ``<freebound_value>`` :math:`a \in [0,1]` specifies a symmetric
target interval :math:`D = (c(1-a),c(1+a))` about :math:`c`
* ``<freebound_list_value> = [a,b]``, a list of
proportions :math:`a, b \in [0,1]` specifying an asymmetric target
interval :math:`D = (c(1-a),c(1+b))` about :math:`c`
The penalty applies to the constraint at points :math:`x` where
:math:`C(x) \not \in D`.
The magnitude of ``<penalty_value>`` can be assessed by examining
the final objective function in the ``.lp`` file written by
:meth:`LpProblem.writeLP`.
Example:
>>> constraint_1 = LpConstraint('ex_1',sense=1,rhs=200)
>>> elasticProblem_1 = constraint_1.makeElasticSubproblem(penalty=1, proportionFreeBound = 0.01)
>>> constraint_2 = LpConstraint('ex_2',sense=0,rhs=500)
>>> elasticProblem_2 = constraint_2.makeElasticSubproblem(penalty=1,
proportionFreeBoundList = [0.02, 0.05])
#. constraint_1 has a penalty-free target interval of 1% either side of the rhs value, 200
#. constraint_2 has a penalty-free target interval of
- 2% on left and 5% on the right side of the rhs value, 500
.. image:: _static/freebound.*
:height: 5in
:alt: Freebound interval
Following are the methods of the return-value:
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