Mixed Integer Linear Programming with pyomo or PuLP - optimization

Question

I am new to optimization programming using python and I have a problem with defining a variable in both pyomo and PuLP for a MILP problem. I am using gene expression data and I am confused about how to define a variable as a MXN matrix. I am trying to use either pyomo or PuLP. I know how to use MATLAB and define it so I am putting it make it more helpful to anyone to understand.
y = optimvar('y',M,N,'Type','integer','LowerBound',0,'UpperBound',1)
Also If you think there are better python package please give me your suggestion.
Thank you very much in advance !!

Answer 1

I'd pick pyomo. I think it is more expressive and easier to read/work with. You'll need to install a solver separately. If that is daunting, pulp comes with CBC built in.
This should get you started. There are a decent number of examples in the pyomo documentation to get you started.
import pyomo.environ as pe
m = pe.ConcreteModel('example')
m.M = pe.Set(initialize=[1, 2, 3], name='the M set')
m.N = pe.Set(initialize=['A', 'B', 'C'], name='the N set')
m.X = pe.Var(m.M, m.N, domain=pe.NonNegativeReals)
m.pprint()
Yields:
3 Set Declarations
M : Size=1, Index=None, Ordered=Insertion
Key : Dimen : Domain : Size : Members
None : 1 : Any : 3 : {1, 2, 3}
N : Size=1, Index=None, Ordered=Insertion
Key : Dimen : Domain : Size : Members
None : 1 : Any : 3 : {'A', 'B', 'C'}
X_index : Size=1, Index=None, Ordered=True
Key : Dimen : Domain : Size : Members
None : 2 : M*N : 9 : {(1, 'A'), (1, 'B'), (1, 'C'), (2, 'A'), (2, 'B'), (2, 'C'), (3, 'A'), (3, 'B'), (3, 'C')}
1 Var Declarations
X : Size=9, Index=X_index
Key : Lower : Value : Upper : Fixed : Stale : Domain
(1, 'A') : 0 : None : None : False : True : NonNegativeReals
(1, 'B') : 0 : None : None : False : True : NonNegativeReals
(1, 'C') : 0 : None : None : False : True : NonNegativeReals
(2, 'A') : 0 : None : None : False : True : NonNegativeReals
(2, 'B') : 0 : None : None : False : True : NonNegativeReals
(2, 'C') : 0 : None : None : False : True : NonNegativeReals
(3, 'A') : 0 : None : None : False : True : NonNegativeReals
(3, 'B') : 0 : None : None : False : True : NonNegativeReals
(3, 'C') : 0 : None : None : False : True : NonNegativeReals
4 Declarations: M N X_index X
[Finished in 1.5s]
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Edit: Making crossed sets
Some variation of below should work fine. You can either make a full x-set by initializing to the cross of two sets, or if your model is sparse, and it makes sense, I'd encourage you to use the within keyword to control the domain and only populated necessary pairs with initialize as shown.
import pyomo.environ as pe
m = pe.ConcreteModel('example')
m.M = pe.Set(initialize=[1, 2, 3], name='the M set')
m.N = pe.Set(initialize=['A', 'B', 'C'], name='the N set')
m.cross = pe.Set(within=m.M*m.N, initialize = [(1,'A'), (3,'B')])