Sparse sets in Pyomo Concrete Model

Question

I want to create a sparse set in a ConcreteModel in pyomo. Here is a minimum example:

import pyomo
import pyomo.environ as pe

m = pe.ConcreteModel

m.P = pe.Set(initialize=['A', 'B', 'C'])
m.Q = pe.Set(initialize=[1, 2, 3, 4, 5, 6, 9, 10, 11])

D1 = {'A': [1, 2, 3], 'B': [9, 10, 11], 'C': [4, 5, 6]}
m.E = pe.Set(initialize=D1)

m.x = pe.Var(m.Q)

m.obj = pe.Objective(expr=1, sense=pe.minimize)


def constraint_rule(m: pe.ConcreteModel, p: str):
    return sum(m.x[i] for i in m.E[p]) <= 1


m.add_constraint = pe.Constraint(m.P, rule=constraint_rule)

opt = pe.SolverFactory('gurobi')
opt.solve(m)

When I run this model, I get the following message:

TypeError: valid_problem_types() missing 1 required positional argument: 'self'

Is this a problem in the construction of the set m.E?

Answer 1

You're getting that error because you're not creating an instance of the pyomo.environ.ConcreteModel but using an alias to it. You need to use parenthesis in m = pe.ConcreteModel()

Now, I assume that you want to express your constraints something like this:

x[1] + x[2] + x[3] <= 1
x[9] + x[10] + x[11] <= 1
x[4] + x[5] + x[6] <= 1

using the actual sets created. Then you need to create model.E a a Subset of model.P, since the current values relays upong each value of model.P. Then you need to change it as follows:

m.E = pe.Set(m.P, initialize=D1)

The actual model will be something like this:

import pyomo
import pyomo.environ as pe

m = pe.ConcreteModel()

m.P = pe.Set(initialize=['A', 'B', 'C'])
m.Q = pe.Set(initialize=[1, 2, 3, 4, 5, 6, 9, 10, 11])

D1 = {'A': [1, 2, 3], 'B': [9, 10, 11], 'C': [4, 5, 6]}
m.E = pe.Set(m.P, initialize=D1)

m.x = pe.Var(m.Q)

m.obj = pe.Objective(expr=1, sense=pe.minimize)


def constraint_rule(m: pe.ConcreteModel, p: str):
    return sum(m.x[i] for i in m.E[p]) <= 1


m.add_constraint = pe.Constraint(m.P, rule=constraint_rule)

opt = pe.SolverFactory('gurobi')
opt.solve(m)

This will give you the following solution:

>>>m.x.display()
x : Size=9, Index=Q
    Key : Lower : Value : Upper : Fixed : Stale : Domain
      1 :  None :   1.0 :  None : False : False :  Reals
      2 :  None :   0.0 :  None : False : False :  Reals
      3 :  None :   0.0 :  None : False : False :  Reals
      4 :  None :   1.0 :  None : False : False :  Reals
      5 :  None :   0.0 :  None : False : False :  Reals
      6 :  None :   0.0 :  None : False : False :  Reals
      9 :  None :   1.0 :  None : False : False :  Reals
     10 :  None :   0.0 :  None : False : False :  Reals
     11 :  None :   0.0 :  None : False : False :  Reals

I assume that you understand that this only generate a feasible solution, since the OF is a constant