I recently started with Pyomo and I have the following Problem:

I want to construct a ConstraintList with an if statement. I already learned, that it's not possible. But the problem still exists... My first code (with the if statement) was the following one:

for i in m.Stunde:
  for j in m.Kraftwerk:
     if pyo.value(m.Kraftwerkseinsatz[i,j]) != 0:

m.Stunde and m. Kraftwerk are indices.

m.Kraftwerkseinsatz is a variable!

m.MinOutput is a parameter.

In other words, my variable must be greater than the MinOutput parameter or zero (for every hour and every power plant).

I already thought of reframing the constraint like this: m.Kraftwerkseinsatz[i,j] must not be between 0.1 and m.MinOutput.

But I don't know how to code this either. Can anyone help me?


1 Answer 1


A variable that can assume values of zero or between some lower and upper bound is called a semi-continuous variable. Most high-end solvers have direct support for this type of variable. If not supported, you can model this with an additional binary variable: $$\begin{align} & \color{darkblue}L\cdot \color{darkred}\delta \le \color{darkred}x \le \color{darkblue}U \cdot \color{darkred}\delta \\ & \color{darkred}\delta \in \{0,1\} \\ &\color{darkred}x\in [0,\color{darkblue}U]\end{align}$$

AFAIK, Pyomo has no direct support for semi-continuous variables. So the obvious approach is to use binary variables. An alternative would be to use Pyomo's Disjunctive Programming tools (GDP).

Note: in the bounds for $\color{darkred}x$, I assumed $\color{darkblue}L\gt 0$. We can make this more general by stating $\color{darkred}x \in [\min(0,\color{darkblue}L),\max(0,\color{darkblue}U)]. $


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