Stagnation detection meets fast mutation

Two mechanisms have recently been proposed that can significantly speed up finding distant improving solutions via mutation, namely using a random mutation rate drawn from a heavy-tailed distribution (“fast mutation”, Doerr et al. (2017) [2]) and increasing the mutation strength based on a stagnation detection mechanism (Rajabi and Witt (2020) [3]). Whereas the latter can obtain the asymptotically best probability of finding a single desired solution in a given distance, the former is more robust and performs much better when many improving solutions in some distance exist. In this work, we propose a mutation strategy that combines ideas of both mechanisms. We show that it can also obtain the best possible probability of finding a single distant solution. However, when several improving solutions exist, it can outperform both the stagnation-detection approach and fast mutation. The new operator is more than an interleaving of the two previous mechanisms and it outperforms any such interleaving.