When solving the LPs with a simplex algorithm, that is using all but the IloCplex::Barrier optimizer options, basis information is available as well. Basis information can be consulted using the method IloCplex::getStatuses() which returns basis status information for variables and constraints.

Such information is encoded by the nested enumeration type:

IloCplex::BasisStatus { Basic, AtLower, AtUpper, FreeOrSuperbasic };