CPXMIP_OPTIMAL

An optimal integer solution has been found.

CPLEX returns CPXMIP_OPTIMAL when CPLEX has proven optimality. Indeed, CPLEX can return CPXMIP_OPTIMAL even when the MIP gap tolerances are strictly greater than 0 (zero). Examples where CPLEX can prove optimality of a solution include finding a solution of a feasibility problem where no objective function is defined, or finding a solution that has a value equal to the current dual bound. (In that case, the gap is exactly 0 (zero).)

In contrast, CPLEX returns CPXMIP_OPTIMAL_TOL when the current solution has not been proven optimal but appears optimal within the tolerance of the relative or absolute MIP gap, as set by the parameters relative MIP gap tolerance or absolute MIP gap tolerance.