Originally posted by: arccos0

Suppose Cplex is solving a MILP (Minimization) model by using traditional branch and cut and the node selection strategy is the default one (Best Bound Search). At this moment, if an arbitrary node splits into two children, say node 1 is non-integer with lower objective value and node 2 is integer with higher objective value. According to the best bound search, will Cplex choose node 1 prior to node 2?

I am wondering because node 2 is a feasible solution, choosing node 2 first will probably upgrade the upper bound and have potential to prune more nodes in the following search.

Whether a node is integer feasible or not can in general only be decided when the node is actually processed. Same goes for the exact objective value of the node since finding that requires solving the LP relaxation of the node.

Hence neither the "integrality" of a node nor its exact objective function value can be used for node selection.

(the objective function value CPLEX assigns to nodes when creating them is the objective function value of the LP relaxation of the parent node)

Originally posted by: arccos0

Daniel.

Thanks for your time. That makes sense.