Stagnation Detection Meets Fast Mutation

TL;DR

This paper introduces a novel mutation strategy combining fast mutation and stagnation detection, achieving superior performance in finding distant solutions, especially when multiple improving solutions are present.

Contribution

It proposes a new mutation operator that unites two recent mechanisms, outperforming both individually and any simple combination in evolutionary algorithms.

Findings

Achieves the best probability of finding distant solutions.

Outperforms individual mechanisms in multi-solution scenarios.

Surpasses simple interleavings of previous methods.

Abstract

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)) and increasing the mutation strength based on stagnation detection (Rajabi and Witt (2020)). 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 also outperforms any such interleaving.