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On the representativeness of approximate solutions of discrete optimization problems with interval cost function | | Alexander Prolubnikov
; | | Date: |
1 Jan 2022 | | Abstract: | 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. | | Source: | arXiv, 2201.00182 | | Services: | Forum | Review | PDF | Favorites | |
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