  Stagnation detection has been proposed as a mechanism for randomized search
heuristics to escape from local optima by automatically increasing the size of
the neighborhood to find the so-called gap size, i.e., the distance to the next
improvement. Its usefulness has mostly been considered in simple multimodal
landscapes with few local optima that could be crossed one after another. In
multimodal landscapes with a more complex location of optima of similar gap
size, stagnation detection suffers from the fact that the neighborhood size is
frequently reset to $1$ without using gap sizes that were promising in the
past.
  In this paper, we investigate a new mechanism called radius memory which can
be added to stagnation detection to control the search radius more carefully by
giving preference to values that were successful in the past. We implement this
idea in an algorithm called SD-RLS$^{\text{m}}$ and show compared to previous
variants of stagnation detection that it yields speed-ups for linear functions
under uniform constraints and the minimum spanning tree problem. Moreover, its
running time does not significantly deteriorate on unimodal functions and a
generalization of the Jump benchmark. Finally, we present experimental results
carried out to study SD-RLS$^{\text{m}}$ and compare it with other algorithms.
