If an integer programming model is relatively easy to solve, then we would like to have the solver press on to the true optimal solution without immediately resorting to a relative optimality tolerance. On the other hand, if, after running for a while, it becomes apparent that the optimal solution won’t be immediately forthcoming, then you might want the solver to switch to using a relative optimality tolerance. TIM2RL, the time to relative tolerance, can be used in this manner. This tolerance is the number of seconds before the branch-and-bound solver begins using the relative optimality tolerance. For the first n seconds, where n is the value of the time to relative tolerance, the branch-and-bound solver will not use the relative optimality tolerance and will attempt to find the true optimal solution to the model. Thereafter, the solver will use the relative optimality tolerance in its search.

The default value for the time to relative tolerance is 100 seconds.