How to use if conditions which contain variables in Pyomo constraint - if-statement

Question

I am trying to add a simple constraint to my Pyomo model:
maximum{x[1]-a,b}+maximum{x[2]-a,b} >= c
where a,b,c are given predefined parameters and x is the decision variable indexed by set model.I which is initialize to [1,2].
In order to achieve this, I tried the following method with no success:
from pyomo.environ import *
from pyomo.opt import SolverFactory
from pyomo.environ import *
model = AbstractModel()
model.I = Set()
model.a = Param()
model.b = Param()
model.c = Param()
model.x = Var(model.I)
def my_rule(model):
total = 0
for i in model.I:
val = model.x[i] - model.a
if val < model.b:
val = model.b
total = total + val
return total >= model.c
model.my_constraint = Constraint(rule=my_rule)
data = {None:{
'I': {None: [1,2]},
'a': {None: 3},
'b': {None: 5},
'c': {None: 4}}
}
real_model = model.create_instance(data)
The error given is:
WARNING: DEPRECATED: Chained inequalities are deprecated. Use the inequality()
function to express ranged inequality expressions.
ERROR: Rule failed when generating expression for constraint my_constraint:
TypeError: Attempting to form a compound inequality with two lower bounds
The inequality expression:
x[1] - 3 < 5.0
contains non-constant terms (variables) that were evaluated in an
unexpected Boolean context at
File '<ipython-input-11-e3a6c44c5b8e>', line 14:
if val < model.b:
Evaluating Pyomo variables in a Boolean context, e.g.
if expression <= 5:
is generally invalid. If you want to obtain the Boolean value of
the expression based on the current variable values, explicitly
evaluate the expression using the value() function:
if value(expression) <= 5:
or
if value(expression <= 5):
Could any one help me with this? Thanks a lot.

Answer 1

Couple problems...
You can't bury an "if" statement inside of the constraint construction where the condition depends on the evaluation of variables.
max and min functions can't be directly represented in a LP/IP if that is what you are trying to do. There may be ways to reformulate...however...
Your constraint is somewhat nonsensical. If b and c are fixed values then the constraint you presented is ALWAYS true because b>c as stated, so:
max(anything, b) + max(anything else, b) > c is always true.
Time to re-examine your problem formulation. :)