If this adjustment is insufficient to give satisfactory results, you can also try setting EpInt all the way to zero, preferably in conjunction with a tightened EpRHS setting. This very tight integrality tolerance directs ILOG CPLEX to attempt to branch on any integer infeasibility, no matter how small. Numeric roundoff due to floating-point arithmetic on any computer may make it impossible to achieve this tolerance, but in practice, the setting achieves its aim in many models and reduces the integrality violations in many others. In cases where the integrality violation even after branching remains above EpInt or is above 1e-10 when EpInt has been set to a value smaller than that, a solution status returned will be CPX_STAT_OPTIMAL_INFEAS instead of the usual CPX_STAT_OPTIMAL. In most cases a solution with status CPX_STAT_OPTIMAL_INFEAS will be satisfactory, and reflects only roundoff error after presolve uncrush, but extra care in using the solution may be advisable in numerically sensitive formulations.