Stagnation Detection with Randomized Local Search

TL;DR

This paper extends stagnation detection mechanisms to randomized local search with k-bit flips, achieving faster optimization and proposing schemes to avoid infinite runtimes, while also comparing with standard bit mutation.

Contribution

It introduces stagnation detection for k-bit flip operators, providing improved runtime bounds and schemes to prevent infinite optimization times.

Findings

Achieves up to e=2.71 speed-up over previous methods.

Proposes schemes to prevent infinite optimization times.

Standard bit mutation can outperform local k-bit flip in some cases.

Abstract

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.