We consider optimization problems whose objective functions have uncertain coefficients. We assumed that, initially, the uncertain data are given as ranges, and probing of the true values of data is possible. The complete probing of all uncertain data will yield the true optimal solution. However, probing all uncertain data is undesirable because each probing may require cost or time depending on the methods of probing. We are interested in finding a solution, which we call $\Gamma$-optimal, that is guaranteed to remain the best solution even after additional $\Gamma$ probings of uncertain data. An iterative algorithm to find the $\Gamma$-optimal solution is developed with theoretical probability bounds of the $\Gamma$-optimal solution being true optimal. Special algorithms are also developed for the problems on networks. The extensive computational study shows that the proposed approach could find the true optimal solutions at very high percentages, even with small numbers of probings.

我们考虑目标函数具有不确定系数的优化问题。我们假设，最初，不确定数据是作为范围给出的，并且可以探查数据的真实值。对所有不确定数据的完整探测将产生真正的最优解。然而，探查所有不确定的数据是不可取的，因为根据探查方法的不同，每次探查都可能需要成本或时间。我们有兴趣找到一个解决方案，我们称之为$\Gamma$- 最优的，即使在额外的 $\Gamma$不确定数据的探索。一种迭代算法来寻找$\Gamma$- 最优解是用理论概率界限开发的 $\Gamma$- 最优解是真正最优的。还针对网络问题开发了特殊算法。广泛的计算研究表明，即使使用少量探测，所提出的方法也可以以非常高的百分比找到真正的最佳解决方案。