The (1+λ) Evolutionary Algorithm with Self-Adjusting Mutation Rate

We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current mutation rate and the other half with half the current rate. The mu...

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Vydáno v:Algorithmica Ročník 81; číslo 2; s. 593 - 631
Hlavní autoři: Doerr, Benjamin, Gießen, Christian, Witt, Carsten, Yang, Jing
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 15.02.2019
Springer Nature B.V
Springer Verlag
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Evolutionary algorithms
Fitness
Genetic algorithms
Mathematics of Computing
Mutation
Optimization
Parameters
Special Issue on Theory of Genetic and Evolutionary Computation
Theory of Computation
Yeast
Mutation
Runtime analysis
Self-adaptation
Evolutionary computation
ISSN:0178-4617, 1432-0541
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Shrnutí:We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current mutation rate and the other half with half the current rate. The mutation rate is then updated to the rate used in that subpopulation which contains the best offspring. We analyze how the ( 1 + λ ) evolutionary algorithm with this self-adjusting mutation rate optimizes the OneMax test function. We prove that this dynamic version of the ( 1 + λ )  EA finds the optimum in an expected optimization time (number of fitness evaluations) of O ( n λ / log λ + n log n ) . This time is asymptotically smaller than the optimization time of the classic ( 1 + λ ) EA. Previous work shows that this performance is best-possible among all λ -parallel mutation-based unbiased black-box algorithms. This result shows that the new way of adjusting the mutation rate can find optimal dynamic parameter values on the fly. Since our adjustment mechanism is simpler than the ones previously used for adjusting the mutation rate and does not have parameters itself, we are optimistic that it will find other applications.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-018-0502-x