Runtime Analysis for Self-adaptive Mutation Rates

We propose and analyze a self-adaptive version of the ( 1 , λ ) evolutionary algorithm in which the current mutation rate is encoded within the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark function reveals that a simple local mutation scheme for t...

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Veröffentlicht in:Algorithmica Jg. 83; H. 4; S. 1012 - 1053
Hauptverfasser: Doerr, Benjamin, Witt, Carsten, Yang, Jing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2021
Springer Nature B.V
Schlagworte:
2018
Algorithm Analysis and Problem Complexity
Algorithms
Asymptotic properties
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Drift
Evolutionary algorithms
Evolutionary computation
Mathematics of Computing
Mutation
Optimization
Parameters
Run time (computers)
Special Issue on Genetic and Evolutionary Computation
Theory of Computation
Two dimensional analysis
Runtime analysis
Self-adaptive
Evolutionary algorithms
ISSN:0178-4617, 1432-0541
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Zusammenfassung:We propose and analyze a self-adaptive version of the ( 1 , λ ) evolutionary algorithm in which the current mutation rate is encoded within the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark function reveals that a simple local mutation scheme for the rate leads to an expected optimization time (number of fitness evaluations) of O ( n λ / log λ + n log n ) when λ is at least C ln n for some constant C > 0 . For all values of λ ≥ C ln n , this performance is asymptotically best possible among all λ -parallel mutation-based unbiased black-box algorithms. Our result rigorously proves for the first time that self-adaptation in evolutionary computation can find complex optimal parameter settings on the fly. In particular, it gives asymptotically the same performance as the relatively complicated self-adjusting scheme for the mutation rate proposed by Doerr, Gießen, Witt, and Yang (Algorithmica 2019). On the technical side, the paper contributes new tools for the analysis of two-dimensional drift processes arising in the analysis of dynamic parameter choices in EAs, including bounds on occupation probabilities in processes with non-constant drift.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00726-2