We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can be $\Sigma^{\text P}_2$-hard, even when the certain bilevel problem is NP-equivalent and the follower's problem is tractable. On the contrary, in the discrete uncertainty case, the robust bilevel problem is at most one level harder than the follower's problem.

翻译：我们用一种稳健的优化方法来调查双级组合优化的复杂性,并找出跟踪者目标的不确定性。 我们发现,在间隔期不确定性下的双级问题中,强势对应方可以是$\Sigma ⁇ text P ⁇ 2$-hard,即使某些双级问题相当于NP,而跟踪者的问题可以伸缩。 相反,在离散的不确定性案例中,稳健的双级问题最多比跟踪者的问题更难解决一个层次。