Originally posted by: Lessi

https://www.ibm.com/support/knowledgecenter/es/SSSA5P_12.5.0/ilog.odms.cplex.help/refcppcplex/html/classes/IloCplex_BranchCallbackI.html#method_isIntegerFeasible

The method says that it returns true if the solution of the current node is integer feasible. So in the case of "true", it means that the incumbent callback will be activated after the call to branch callback? 

Thank you

Assuming an incumbent callback is present, it would have been called before reaching the branch callback.

Originally posted by: Lessi

Thank you, Paul.

It seems that if I do not reject a solution in the incumbent callback, it will be accepted and I cannot reject it later in branch callback? In other words, CPLEX will stop branching on a node where a feasible solution is found? 

Thank you,

Correct. If you don't reject a solution in the incumbent or lazy constraint callback then it is accepted. And if the solution comes from an integral node then of course no further branching from that node is required.