The word “parameters” is used in many settings. When discussing a Pyomo model, we use the word to refer to data that must be provided in order to find an optimal (or good) assignment of values to the decision variables. Parameters are declared as instances of a Param class, which takes arguments that are somewhat similar to the Set class. For example, the following code snippet declares sets model.A and model.B, and then a parameter model.P that is indexed by model.A and model.B:

model.A = pyo.RangeSet(1,3)
model.B = pyo.Set()
model.P = pyo.Param(model.A, model.B)

In addition to sets that serve as indexes, Param takes the following options:

  • default = The parameter value absent any other specification.
  • doc = A string describing the parameter.
  • initialize = A function (or Python object) that returns data used to initialize the parameter values.
  • mutable = Boolean value indicating if the Param values are allowed to change after the Param is initialized.
  • validate = A callback function that takes the model, proposed value, and indices of the proposed value; returning True if the value is valid. Returning False will generate an exception.
  • within = Set used for validation; it specifies the domain of valid parameter values.

These options perform in the same way as they do for Set. For example, given model.A with values {1, 2, 3}, then there are many ways to create a parameter that represents a square matrix with 9, 16, 25 on the main diagonal and zeros elsewhere, here are two ways to do it. First using a Python object to initialize:

v[1,1] = 9
v[2,2] = 16
v[3,3] = 25
model.S1 = pyo.Param(model.A, model.A, initialize=v, default=0)

And now using an initialization function that is automatically called once for each index tuple (remember that we are assuming that model.A contains {1, 2, 3})

def s_init(model, i, j):
    if i == j:
        return i*i
        return 0.0
model.S2 = pyo.Param(model.A, model.A, initialize=s_init)

In this example, the index set contained integers, but index sets need not be numeric. It is very common to use strings.


Data specified in an input file will override the data specified by the initialize option.

Parameter values can be checked by a validation function. In the following example, the every value of the parameter T (indexed by model.A) is checked to be greater than 3.14159. If a value is provided that is less than that, the model instantation will be terminated and an error message issued. The validation function should be written so as to return True if the data is valid and False otherwise.

t_data = {1: 10, 2: 3, 3: 20}

def t_validate(model, v, i):
    return v > 3.14159

model.T = pyo.Param(model.A, validate=t_validate, initialize=t_data)

This example will prodice the following error, indicating that the value provided for T[2] failed validation:

Traceback (most recent call last):
ValueError: Invalid parameter value: T[2] = '3', value type=<class 'int'>.
    Value failed parameter validation rule