An objective is a function of variables that returns a value that an optimization package attempts to maximize or minimize. The Objective function in Pyomo declares an objective. Although other mechanisms are possible, this function is typically passed the name of another function that gives the expression. Here is a very simple version of such a function that assumes model.x has previously been declared as a Var:

>>> def ObjRule(model):
...     return 2*model.x[1] + 3*model.x[2]
>>> model.obj1 = pyo.Objective(rule=ObjRule)

It is more common for an objective function to refer to parameters as in this example that assumes that model.p has been declared as a Param and that model.x has been declared with the same index set, while model.y has been declared as a singleton:

>>> def ObjRule(model):
...     return pyo.summation(model.p, model.x) + model.y
>>> model.obj2 = pyo.Objective(rule=ObjRule, sense=pyo.maximize)

This example uses the sense option to specify maximization. The default sense is minimize.