I am solving big optimization models (more than 100k variables) with the academic version of CPLEX but I'd like to see if I can find an open source alternative, I solve mixed integ …

What are some guidelines for deciding whether a MIP or CP approach is more appropriate for modeling an optimization problem? Or in what cases should CP be used instead of MIP?

I would like to know some common approaches to work around the big integrality gap caused by big M formulations in MIP proplems.