Smoothed Analysis: If a Problem has Pseudopolynomial Complexity, is it in Smooth P?
Integer programming is strongly NP-hard, thus integer programs can in general not be solved in pseudo-polynomial time. The result of Röglin and Vöcking is that, provided that the range of integers that the variables can assume is polynomially bounded, (randomized) pseudo-polynomial solvability is equivalent to polynomial smoothed complexity. Thus, general integer programs do not have polynomial smoothed complexity.

The statement "randomized pseudo-polynomial complexity = polynomial smoothed complexity" is not known to be true in general. For instance, the flip heuristic for Max-Cut runs in pseudo-polynomial time, but it is unknown if a local optimum w.r.t. the flip heuristic can be found with polynomial smoothed complexity (cf. Etscheid and Röglin, SODA 2014).