Pyomo: is possible to assign to a design variable only defined values?

Question

I want that a design variable assumes only specified values during optimization process.

For example: Let x be the variable which can assume only specific value, e.g.:

x = [0.1,0.5,1.0,1.7,2.3]

How can be written in python using pyomo (if it's possible)?

I hope I was clear.

Answer 1

You have to do this with integer variables. For example, if there are N possible values of x, then let x[n] = 1 if x equals the nth possible value, and 0 otherwise. Any time you have an x in your original model, replace it with

sum {n=1,...,N} v[n] * x[n]

where v[n] is the nth possible value. Finally, add a constraint that says:

sum {n=1,...,N} x[n] == 1 

I'm not writing these in Pyomo syntax, but this is a general modeling approach that is the same no matter what modeling language/package you use.