Self-Adjusting Evolutionary Algorithms for Multimodal Optimization

Recent theoretical research has shown that self-adjusting and self-adaptive mechanisms can provably outperform static settings in evolutionary algorithms for binary search spaces. However, the vast majority of these studies focuses on unimodal functions which do not require the algorithm to flip sev...

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Veröffentlicht in:Algorithmica Jg. 84; H. 6; S. 1694 - 1723
Hauptverfasser: Rajabi, Amirhossein, Witt, Carsten
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2022
Springer Nature B.V
Schlagworte:
2020
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Evolutionary algorithms
Genetic algorithms
Mathematics of Computing
Modules
Optimization
Special Issue on Genetic and Evolutionary Computation
Stagnation
Theory of Computation
Randomized search heuristics
Self-adjusting algorithms
Runtime analysis
Multimodal functions
ISSN:0178-4617, 1432-0541
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Zusammenfassung:Recent theoretical research has shown that self-adjusting and self-adaptive mechanisms can provably outperform static settings in evolutionary algorithms for binary search spaces. However, the vast majority of these studies focuses on unimodal functions which do not require the algorithm to flip several bits simultaneously to make progress. In fact, existing self-adjusting algorithms are not designed to detect local optima and do not have any obvious benefit to cross large Hamming gaps. We suggest a mechanism called stagnation detection that can be added as a module to existing evolutionary algorithms (both with and without prior self-adjusting schemes). Added to a simple (1+1) EA, we prove an expected runtime on the well-known Jump benchmark that corresponds to an asymptotically optimal parameter setting and outperforms other mechanisms for multimodal optimization like heavy-tailed mutation. We also investigate the module in the context of a self-adjusting (1+ λ ) EA. To explore the limitations of the approach, we additionally present an example where both self-adjusting mechanisms, including stagnation detection, do not help to find a beneficial setting of the mutation rate. Finally, we investigate our module for stagnation detection experimentally.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00933-z