Pyomo "OR* Constraints?

[Jonathan Nowacki]

Is there a way to make constraints to be 0 or >=8?   In other words, the number can be 0,8,9,10...to infinity?

[Solver Max]

Pyomo includes the Generalized Disjunctive Programming (GDP) extension, which does OR constraints (amongst many other things).

Or you can create OR constraints yourself, using the BigM method.

We've recently published a couple of articles using both of those techniques, which might be useful:

https://www.solvermax.com/blog/optimal-but-not-practical-either-or-bigm

https://www.solvermax.com/blog/optimal-but-not-practical-either-or-disjunction

[Tomasz Gorecki]

strictly speaking bigM will not work if you really want you variable (say x) to have no upper bound. if you have a known upper bound M

you would use

x<=M*delta

x>= 8*delta

delta in [0,1] so that delta =0 gives x=0 and delta=1 gives 8<=x<=M

The lower M the better to avoid numerical issues

I am not sure what GDP would actually do to enforce the same, curious if someone can explain !

[Yohan Fleuriot]

Hi!

I would introduce a binary variable and an integer variable and combine them in an expression:

m = ConcreteModel()

m.bin = Var(within=Binary)

m.z = Var(within=NonNegativeIntegers)

m.x = Expression(expr= lambda A: A.bin*(A.z + 8))

Yohan Fleuriot 

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