[Scip] dependent variables and if-then-else constraints

[Wei Wang]

Hi,

I have a question about if-then-else constraints, and dependent 
variables. In my MILP problem I have a large number of dependent 
variables and if-then-else constraints. The constraints look like this,

if x_i>100 then y_i = 1 else y_i=0

That is, y is a dependent variable of x, and y is also a binary integer 
variable. I converted this if-then-else constraint to linear equations 
using the method described here,
http://www.yzuda.org/Useful_Links/optimization/if-then-else-02.html.

This converting method adds another 4 binary integer variables for each 
if-then-else constraint.

The problem is that I have about 10000 if-then-else constraints, which 
means, I have to add 40000 binary integer variables. And adding these 
many variables considerably increases the time to solve my problem.

Because the added variables and the y variables are all dependent 
variables, and I only have about 400 independent variables, I think 
there should be a way to reduce the solving time. Can somebody give me 
some suggestions on how to optimize it?

thanks,
Wei