I am struggling with "linked" variables in a cost optimization problem. Overall I have four variables: varX1, varX2, varY1 and varY2 which are paired in the following manner:
if 0 <= varX1 < 1 then varY1 = 0
if 1 <= varX1 <= 6 then varY1 = 1
and
if 0 <= varX2 < 1 then varY2 = 0
if 1 <= varX2 <= 5 then varY2 = 1
I have tried to model the relationship of varX1 and varY1as well asvarX2andvarY2` using pyomos piecewise trying to recreate the example from https://github.com/Pyomo/pyomo/blob/main/examples/pyomo/piecewise/step.py.
Full model code is:
import pyomo.environ as po
costsX1 = 4
costsX2 = 6
costsY1 = 2
costsY2 = 1
a1 = 4
a2 = 3
model = po.ConcreteModel()
model.VarX1 = po.Var(bounds=(0,6))
model.VarX2 = po.Var(bounds=(0,5))
model.VarY1 = po.Var(within=po.Binary)
model.VarY2 = po.Var(within=po.Binary)
model.cons1 = po.Constraint(expr=model.VarX1+model.VarX2==5)
model.cons2 = po.Constraint(expr=a1*model.VarY1+ a2*model.VarY2>=3)
model.obj = po.Objective(expr=costsX1*model.VarX1+costsY1*a1*model.VarY1+costsX2*model.VarX2+costsY2*a2*model.VarY2,
sense=po.minimize)
DOMAIN_PTS_X1 = [0, 1, 1, 6]
RANGE_PTS_Y1 = [0, 0, 1, 1]
DOMAIN_PTS_X2 = [0, 1, 1, 5]
RANGE_PTS_Y2 = [0, 0, 1, 1]
model.piece1 = po.Piecewise(model.VarX1, model.VarY1,
pw_pts=DOMAIN_PTS_X1,
pw_constr_type='LB',
f_rule=RANGE_PTS_Y1,
pw_repn='INC')
model.piece2 = po.Piecewise(model.VarX2, model.VarY2,
pw_pts=DOMAIN_PTS_X2,
pw_constr_type='LB',
f_rule=RANGE_PTS_Y2,
pw_repn='INC')
opt = po.SolverFactory('cbc')
result_obj = opt.solve(model, tee=True)
model.pprint()
I get the following result
4 Var Declarations
VarX1 : Size=1, Index=None
Key : Lower : Value : Upper : Fixed : Stale : Domain
None : 0 : 5.0 : 6 : False : False : Reals
VarX2 : Size=1, Index=None
Key : Lower : Value : Upper : Fixed : Stale : Domain
None : 0 : 0.0 : 5 : False : False : Reals
VarY1 : Size=1, Index=None
Key : Lower : Value : Upper : Fixed : Stale : Domain
None : 0 : 0.0 : 1 : False : False : Binary
VarY2 : Size=1, Index=None
Key : Lower : Value : Upper : Fixed : Stale : Domain
None : 0 : 1.0 : 1 : False : False : Binary
As one can see, there is no pairing of varX1 and varY1.
Can anyone help me with that?
With the help of AirSquid I was able to find a simple solution for my problem. I gave up on using pyomos piecewise function and introduced additional constraints to the model. The following model works as desired
import pyomo.environ as po
costsX1 = 4
costsX2 = 6
costsY1 = 2
costsY2 = 1
a1 = 4
a2 = 3
model = po.ConcreteModel()
model.VarX1 = po.Var(bounds=(0,6))
model.VarX2 = po.Var(bounds=(0,5))
model.VarY1 = po.Var(within=po.Binary)
model.VarY2 = po.Var(within=po.Binary)
model.cons1 = po.Constraint(expr=model.VarX1+model.VarX2==5)
model.cons2 = po.Constraint(expr=a1*model.VarY1+ a2*model.VarY2>=3)
model.con3 = po.Constraint(expr=model.VarY1 <= model.VarX1)
model.con4 = po.Constraint(expr=model.VarY1 >= model.VarX1/6)
model.con5 = po.Constraint(expr=model.VarY2 <= model.VarX2)
model.con6 = po.Constraint(expr=model.VarY2 >= model.VarX2/5)
model.obj = po.Objective(expr=costsX1*model.VarX1+costsY1*a1*model.VarY1+costsX2*model.VarX2+costsY2*a2*model.VarY2,
sense=po.minimize)
opt = po.SolverFactory('cbc')
result_obj = opt.solve(model, tee=True)
model.pprint()
Think about this differently. Consider y to be an "indicator" variable. In this case it indicates which range x is in, or more precisely, it indicates the upper and lower bounds on x. So, now the task is to do a little algebra with binary numbers to make that work...
Let's think about the low....
x >= 1 * y
Works for both values of y in {0, 1}
And the high ... if y=0 we want 1, if y=1, we want 6... A little algebra:
x <= 1 + 5 * y