Dear all,
I wonder how the CP Optimizer updates the lower bounds in minimization problem. Does it transfer the CP problem into MIP and get the relaxation? If not, then what techniques are used instead?

The problem solved is a scheduling problem and is this case CP Optimizer uses linear programming relaxations of a part or the totality of the model. This relaxation is solved regularly by CPLEX  and provides lower bounds. This is not always the case and other techniques like probing on objective bounds can be used for that purpose.