Markov chain analysis of Leading Ones problem

Evolutionary algorithms (EAs) are randomized optimization search techniques, and the theoretical study of the first hitting time is very important in the practical applications of EA. We investigate the first hitting time of Leading Ones (LO) problem theoretically on Random Local Search (RLS) algori...

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Bibliographic Details
Published inArtificial life and robotics Vol. 22; no. 4; pp. 443 - 448
Main Authors Du, Yifei, Aoki, Kenji, Sakamoto, Makoto, Furutani, Hiroshi, Yamamori, Kunihito
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.12.2017
Springer Nature B.V
Subjects
Artificial Intelligence
Computation by Abstract Devices
Computer Science
Control
Evolutionary algorithms
Markov analysis
Markov chains
Mathematical analysis
Mechatronics
Original Article
Quadratic equations
Random walk theory
Robotics
Run time (computers)
Markov chain
Leading Ones
Evolutionary algorithm
Hitting time
Random Local Search
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Summary:Evolutionary algorithms (EAs) are randomized optimization search techniques, and the theoretical study of the first hitting time is very important in the practical applications of EA. We investigate the first hitting time of Leading Ones (LO) problem theoretically on Random Local Search (RLS) algorithm and (1 + 1)EA by absorbing Markov chain. This paper reports the calculation method of the first hitting time on LO problem with (1 + 1)EA and RLS. We found that the results only depend on the length of string, and the hitting times can be given approximately by the quadratic function. In the numerical experiments, we showed the agreement between the results of the practical calculation and the theoretical results. Our results give the good example to predict the running time of the practical EA calculations by Markov chain method.
ISSN:1433-5298
1614-7456
DOI:10.1007/s10015-017-0381-2