Currently, I am reading the paper "Exploring relaxation induced neighborhood to improve MIP solutions" by Danna et.al. from 2004 and they are talking about a symmetric role of incumbent and the relaxed solution. Which I understood as following:
An incumbent of poor quality can be improved because the respective relaxation is leading into a good direction. And vice versa, a loose relaxation can be compensated by an incumbent of good quality.
How does it work? Can it not happen that it still continues into a completely bad direction?