Stagnation Detection with Randomized Local Search
This work addresses stagnation issues in evolutionary algorithms for optimization, but it is incremental as it builds on existing stagnation detection mechanisms.
The paper tackles the problem of stagnation in evolutionary algorithms by applying stagnation detection to the k-bit flip operator in randomized local search, resulting in a speed-up of up to e=2.71 compared to previous methods and proposing schemes to prevent infinite optimization times.
Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called $SD-(1+1)EA$ introduced by Rajabi and Witt (GECCO 2020) adds stagnation detection to the classical $(1+1)EA$ with standard bit mutation, which flips each bit independently with some mutation rate, and raises the mutation rate when the algorithm is likely to have encountered local optima. In this paper, we investigate stagnation detection in the context of the $k$-bit flip operator of randomized local search that flips $k$ bits chosen uniformly at random and let stagnation detection adjust the parameter $k$. We obtain improved runtime results compared to the $SD-(1+1)EA$ amounting to a speed-up of up to $e=2.71\dots$ Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of $k$ due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the local $k$-bit flip with stagnation detection.