Fast Mutation in Crossover-Based Algorithms

The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms. There, it can relieve the algorithm designer from finding the optimal mutation rate and n...

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Veröffentlicht in:Algorithmica Jg. 84; H. 6; S. 1724 - 1761
Hauptverfasser: Antipov, Denis, Buzdalov, Maxim, Doerr, Benjamin
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
Asymptotic properties
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Empirical analysis
Genetic algorithms
Mathematics of Computing
Mutation
Optimization
Special Issue on Genetic and Evolutionary Computation
Theory of Computation
ISSN:0178-4617, 1432-0541
Online-Zugang:Volltext
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Zusammenfassung:The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms. There, it can relieve the algorithm designer from finding the optimal mutation rate and nevertheless obtain a performance close to the one that the optimal mutation rate gives. In this first runtime analysis of a crossover-based algorithm using a heavy-tailed choice of the mutation rate, we show an even stronger impact. For the ( 1 + ( λ , λ ) ) genetic algorithm optimizing the OneMax benchmark function, we show that with a heavy-tailed mutation rate a linear runtime can be achieved. This is asymptotically faster than what can be obtained with any static mutation rate, and is asymptotically equivalent to the runtime of the self-adjusting version of the parameters choice of the ( 1 + ( λ , λ ) ) genetic algorithm. This result is complemented by an empirical study which shows the effectiveness of the fast mutation also on random satisfiable MAX-3SAT instances.
Bibliographie:ObjectType-Article-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00957-5