Stagnation Detection with Randomized Local Search

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.

24 pages. Full version of a paper appearing at EvoCOP 2021

References in corpus (6)

• Probabilistic Tools for the Analysis of Randomized Optimization Heuristics
• Theory of Parameter Control for Discrete Black-Box Optimization: Provable Performance Gains Through Dynamic Parameter Choices
• The (1+$\lambda$) Evolutionary Algorithm with Self-Adjusting Mutation Rate
• Self-Adjusting Evolutionary Algorithms for Multimodal Optimization
• Stagnation Detection with Randomized Local Search
• The 1/5-th Rule with Rollbacks: On Self-Adjustment of the Population Size in the $(1+(\lambda ,\lambda ))$ GA

Cited by in corpus (6)

• A First Runtime Analysis of the NSGA-II on a Multimodal Problem
• Stagnation Detection with Randomized Local Search
• Lower Bounds from Fitness Levels Made Easy
• A Rigorous Runtime Analysis of the $(1+(\lambda ,\lambda ))$ GA on Jump Functions
• Lazy Parameter Tuning and Control: Choosing All Parameters Randomly From a Power-Law Distribution
• An Extended Jump Functions Benchmark for the Analysis of Randomized Search Heuristics