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Stagnation Detection with Randomized Local Search.

Amirhossein Rajabi¹, Carsten Witt²

¹DTU Compute, Technical University of Denmark, Kgs. Lyngby, Denmark amraj@dtu.dk.

Evolutionary Computation

|July 20, 2022

Summary

This summary is machine-generated.

Stagnation detection enhances evolutionary algorithms by adjusting mutation rates. This study improves upon existing methods using k-bit flips, achieving significant speedups in optimization tasks.

Keywords:

Randomized search heuristics local search multimodal functions runtime analysis self-adjusting algorithms

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Area of Science:

Computer Science
Artificial Intelligence
Optimization Algorithms

Background:

Evolutionary algorithms can get stuck in local optima.
Stagnation detection was recently proposed to automatically adjust mutation rates.
The SD-(1+1) EA uses stagnation detection with standard bit mutation.

Purpose of the Study:

Investigate stagnation detection with the k-bit flip operator in randomized local search.
Improve runtime performance compared to existing stagnation detection methods.
Develop schemes to prevent infinite optimization times.

Main Methods:

Applied stagnation detection to adjust the k-bit flip parameter.
Analyzed runtime improvements against the SD-(1+1) EA.
Introduced new schemes to ensure algorithm termination.

Main Results:

Achieved runtime speedups of at least (1-o(1))2πm over the SD-(1+1) EA, where m is the gap size.
Developed methods to prevent infinite optimization times.
Identified a specific case where standard bit mutation outperformed the k-bit flip operator with stagnation detection.

Conclusions:

Stagnation detection with k-bit flips offers significant performance improvements for evolutionary algorithms.
The proposed schemes ensure algorithm robustness and prevent non-termination.
While generally effective, standard bit mutation can still be superior in certain scenarios.