Sometimes ILOG CPLEX finds a good integer solution early, but must examine many additional nodes to prove the solution is optimal. You can speed up the process in such a case if you are willing to change the optimality tolerance. ILOG CPLEX supports two kinds of tolerance:

The default relative optimality tolerance is 0.0001. At this tolerance, the final integer solution is guaranteed to be within 0.01% of the optimal value. Of course, many formulations of integer or mixed integer programs do not require such tight tolerance, so requiring ILOG CPLEX to seek integer solutions that meet this tolerance in those cases is wasted computation. If you can accept greater optimality tolerance in your model, then you should change the parameter EpGap.

If, however, you know that the objective values of your problem are near zero, then you should change the absolute gap because percentages of very small numbers are less useful as optimality tolerance. Change the parameter EpAGap in this case.

Cutoff parameters can also be helpful in restricting the search for optimality. If you know that there are solutions within a certain distance of the initial relaxation of your problem, then you can readily set the upper cutoff parameter for minimization problems and the lower cutoff parameter for maximization problems. Set the parameters CutUp and CutLo, respectively, to establish a cutoff value.

When you set a MIP cutoff value, ILOG CPLEX searches with the same solution strategy as though it had already found an integer solution, using a node selection strategy that differs from the one it uses before a first solution has been found.