The Relative Optimality Tolerance is a value r, ranging from 0 to 1, indicating to the branch-and-bound solver that it should only search for integer solutions with objective values at least 100*r% better than the best integer solution found so far.

The end results of modifying the search procedure in this way are twofold. First, on the positive side, solution times can be improved tremendously. Second, on the negative side, the final solution obtained by LINGO may not be the true optimal solution. You will, however, be guaranteed the solution is within 100*r% of the true optimum.

Typical values for the relative optimality tolerance would be in the range .01 to .05. In other words, you would be happy to get a solution within 1% to 5% of the true optimal value. On large integer models, the alternative of getting a solution within a few percentage points of the true optimum after several minutes of runtime, as opposed to the true optimum after several days, makes the use of an optimality tolerance quite attractive.

Note:Generally speaking, the relative optimality tolerance is the tolerance that will most likely improve runtimes on integer models. You should be sure to set this tolerance whenever near optimal solutions are acceptable.  Do keep in mind that when you set this option, LINGO may not return the true global optimum.  However, you will be guaranteed the solution is within 100*r% of the true optimum.

The default for the relative optimality tolerance is 5e-8.