Switching to Pyomo – Syntax issue with sets

I have used the algebraic modelling language AMPL but I’m now making the switch to python and Pyomo.

I’m struggling a bit with its syntax though. In AMPL I would have something like this:

param M; 
param n{i in 0..M};
var b{k in 0..M-1, j in 1..n[k+1]};

How can I implement the last line in Pyomo?

Any help is much appreciated, thank you!

Best regards, Johannes

Answer

Welcome to the site.

Below is an example that I think does what you want. There are many ways to build a sparse set in pyomo. You can do it “on the side” in pure python (like example below) using set comprehensions or whatever or you can create a rule that returns same. There is a decent example in the documentation.

# sparse set example

import pyomo.environ as pyo

M = 4

mdl = pyo.ConcreteModel('sparse set example')

mdl.A =  pyo.Set(initialize=range(M))
sparse_index = {(k, j) for k in mdl.A for j in range(1, k+1)}    # just a little helper set-comprehension
mdl.LT = pyo.Set(within=mdl.A * mdl.A, initialize=sparse_index)  # "within" is optional...good for error checking

mdl.x =  pyo.Var(mdl.LT, domain=pyo.NonNegativeReals)

mdl.pprint()

Yields:

3 Set Declarations
    A : Size=1, Index=None, Ordered=Insertion
        Key  : Dimen : Domain : Size : Members
        None :     1 :    Any :    4 : {0, 1, 2, 3}
    LT : Size=1, Index=None, Ordered=Insertion
        Key  : Dimen : Domain    : Size : Members
        None :     2 : LT_domain :    6 : {(2, 1), (3, 1), (1, 1), (3, 3), (2, 2), (3, 2)}
    LT_domain : Size=1, Index=None, Ordered=True
        Key  : Dimen : Domain : Size : Members
        None :     2 :    A*A :   16 : {(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3)}

1 Var Declarations
    x : Size=6, Index=LT
        Key    : Lower : Value : Upper : Fixed : Stale : Domain
        (1, 1) :     0 :  None :  None : False :  True : NonNegativeReals
        (2, 1) :     0 :  None :  None : False :  True : NonNegativeReals
        (2, 2) :     0 :  None :  None : False :  True : NonNegativeReals
        (3, 1) :     0 :  None :  None : False :  True : NonNegativeReals
        (3, 2) :     0 :  None :  None : False :  True : NonNegativeReals
        (3, 3) :     0 :  None :  None : False :  True : NonNegativeReals

4 Declarations: A LT_domain LT x