Variable Replacement

There are a number of cases where it can be convenient to replace one variable for another. IDAES offers a convenient variable replacement transformation. This transformation is not reversible and can significantly alter the model structure.

An example use of this transformation, is a parameter estimation problem where a model contains several instances of a particular sub-model and each model contains a variable (\(\beta\)) for a model parameter to be estimated. In many cases \(\beta\) should be the same across all sub-models. One approach to this problem would be to add equality constraints to equate all the \(\beta\)’s. Another approach would be to use the variable replacement transformation to replace the individual \(\beta\)’s with a single global \(\beta\) variable.


The following example demonstrates the basic usage of the transformation.

import idaes # Load IDAES plugins including the replacement transformation
import pyomo.environ as pyo

# Use Pyomo's transformation factory to create the transformation object
rp = pyo.TransformationFactory("replace_variables")

# Create an example model
m = pyo.ConcreteModel()
m.x = pyo.Var({1,2,3}, initialize=2)
m.new_x = pyo.Var({1,2,3}, initialize=3)
m.e1 = pyo.Expression(expr=sum(m.x[i] for i in m.x))

# Apply the transformation to the model, the substitute argument contains a list
# of replacements, each element is a list-like object where the first element is
# a variable to be replaced by the second element.
rp.apply_to(m, substitute=[(m.x, m.new_x)])

# See that the variable was replaced
print(pyo.value(m.e1)) # since new_x has a value of 3 the expression value is 9




There are three basic steps to using the variable replacement transformation.

  1. Import anything from the idaes package; this will cause the IDAES plugins to be loaded.
  2. Use Pyomo’s transformation factory to create a variable replacement transformation object (e.g. rp = TransformationFactory("replace_variables").
  3. Call the transformation object’s apply_to() method to apply the transformation.

The apply_to(instance, substitute) method takes two arguments instance and substitute. The instance argument is a model or block to apply the transformation to. The substitute argument is a list-like object with substitutions. Each element is a two-element list-like object where the first element is a Pyomo Var, IndexedVar element or Reference to the variable to replace and the second element is a Pyomo Var, IndexedVar element or Reference to replace the first element with.

Indexed variables are allowed. The index set of the variable to replace must be a subset of the index set of the variable to replace it with. It can also be useful to use a Pyomo Reference to emulate an indexed variable, so this is also supported.

ReplaceVariables Class

The transformation object class is ReplaceVariables.

class idaes.plugins.variable_replace.ReplaceVariables(**kwds)[source]

Replace variables in a model or block with other variables.

Keyword arguments below are specified for the apply_to(instance, **kwargs) method.

Keyword Arguments:
 substitute – List-like of tuples where the first item in a tuple is a Pyomo variable to be replaced and the second item in the tuple is a Pyomo variable to replace it with. This transformation is not reversible.