How can I make an indicator function with Pyomo? - pyomo

Question

I'm looking to create a simple indicator variable in Pyomo. Assuming I have a variable x, this indicator function would take the value 1 if x > 0, and 0 otherwise.
Here's how I've tried to do it:
model = ConcreteModel()
model.A = Set(initialize=[1,2,3])
model.B = Set(initialize=['J', 'K'])
model.x = Var(model.A, model.B, domain = NonNegativeIntegers)
model.ix = Var(model.A, model.B, domain = Binary)
def ix_indicator_rule(model, a, b):
return model.ix[a, b] == int(model.x[a, b] > 0)
model.ix_constraint = Constraint(model.A, model.B,
rule = ix_indicator_rule)
The error message I get is along the lines of Avoid this error by using Pyomo-provided math functions, which according to this link are found at pyomo.environ...but I'm not sure how to do this. I've tried using validate_PositiveValues(), like this:
def ix_indicator_rule(model, a, b):
return model.ix[a, b] == validate_PositiveValues(model.x[a, b])
model.ix_constraint = Constraint(model.A, model.B,
rule = ix_indicator_rule)
with no luck. Any help is appreciated!

Answer 1

You can achieve this with a "big-M" constraint, like this:
model = ConcreteModel()
model.A = Set(initialize=[1, 2, 3])
model.B = Set(initialize=['J', 'K'])
# m must be larger than largest allowed value of x, but it should
# also be as small as possible to improve numerical stability
model.m = Param(initialize=1e9)
model.x = Var(model.A, model.B, domain=NonNegativeIntegers)
model.ix = Var(model.A, model.B, domain=Binary)
# force model.ix to be 1 if model.x > 0
def ix_indicator_rule(model, a, b):
return model.x <= model.ix[a, b] * model.m
model.ix_constraint = Constraint(
model.A, model.B, rule=ix_indicator_rule
)
But note that the big-M constraint is one-sided. In this example it forces model.ix on when model.x > 0, but doesn't force it off when model.x == 0. You can achieve the latter (but not the former) by flipping the inequality to model.x >= model.ix[a, b] * model.m. But you can't do both in the same model. Generally you just pick the version that suits your model, e.g., if setting model.ix to 1 worsens your objective function, then you would pick the version shown above, and the solver will take care of setting model.ix to 0 whenever it can.
Pyomo also offers disjunctive programming features (see here and here) which may suit your needs. And the cplex solver offers indicator constraints, but I don't know whether Pyomo supports them.

Answer 2

I ended up using the Piecewise function and doing something like this:
DOMAIN_PTS = [0,0,1,1000000000]
RANGE_PTS = [0,0,1,1]
model.ix_constraint = Piecewise(
model.A, model.B,
model.ix, model.x,
pw_pts=DOMAIN_PTS,
pw_repn='INC',
pw_constr_type = 'EQ',
f_rule = RANGE_PTS,
unbounded_domain_var = True)
def objective_rule(model):
return sum(model.ix[a,b] for a in model.A for b in model.B)
model.objective = Objective(rule = objective_rule, sense=minimize)
It seems to work okay.