# On the representativeness of approximate solutions of discrete optimization problems with interval cost function

We consider discrete optimization problems with interval uncertainty of cost function coefficients. The interval uncertainty models the measurements errors. A possible optimal solution is a solution that is optimal for some possible values of the coefficients. The probability of a possible solution is a probability of obtaining such coefficients that the solution is optimal. Similarly we define the notion of a possible approximate solution and its probability. We consider a possible solution unrepresentative if its probability less than some boundary value. The mean (optimal or approximate) solution is a solution that we obtain for mean values of interval coefficients. We show that the share of instances of a discrete optimization problem with unrepresentative mean approximate solution may be large enough for rather small values of errors.

READ FULL TEXT