Markov chain analysis of evolutionary algorithms for monotonic functions

The theoretical investigation of evolutionary algorithms (EAs) has increased our knowledge of the computational mechanism of algorithms. In this paper, we report the convergence properties of an algorithm that is a variant of (1+1) EA, partially ordered evolutionary algorithm (PO-EA), which was init...

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Published inArtificial life and robotics Vol. 24; no. 1; pp. 82 - 87
Main Authors Ma, QinLian, Zhang, Yu-an, Yamamori, Kunihito, Furutani, Hiroshi, Hiwa, Satoru, Hiroyasu, Tomoyuki
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 15.03.2019
Springer Nature B.V
Subjects
Artificial Intelligence
Boolean algebra
Boolean functions
Computation by Abstract Devices
Computer Science
Control
Economic models
Evolutionary algorithms
Genetic algorithms
Linear functions
Markov analysis
Markov chains
Mechatronics
Original Article
Robotics
Upper bounds
Monotonic function
Markov chain
PO-EA
Evolutionary algorithm
OneMax function
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Summary:The theoretical investigation of evolutionary algorithms (EAs) has increased our knowledge of the computational mechanism of algorithms. In this paper, we report the convergence properties of an algorithm that is a variant of (1+1) EA, partially ordered evolutionary algorithm (PO-EA), which was initially designed for representing the evolutionary behaviors of all linear functions. Recently, PO-EA has been expected to give a model for deriving an upper bound on the expected hitting time of EA for monotonic functions. A monotonic function is a pseudo-boolean function whose value increases by flipping positive number of zeros to one. This study makes use of Markov chain model to analyze the movement of PO-EA. We divide PO-EA into two parts, PO-mutation and ZeroMax models, and study their mutation rate dependences of the expected hitting times.
ISSN:1433-5298
1614-7456
DOI:10.1007/s10015-018-0463-9