Tail Bounds on the Runtime of Categorical Compact Genetic Algorithm.
| Autor: | Hamano R; CyberAgent, Inc., Tokyo, Japan hamano_ryoki_xa@cyberagent.co.jp., Uchida K; Yokohama National University, Kanagawa, Japan uchida-kento-fz@ynu.ac.jp., Shirakawa S; Yokohama National University, Kanagawa, Japan shirakawa-shinichi-bg@ynu.ac.jp., Morinaga D; University of Tsukuba, Ibaraki, Japan.; RIKEN Center for Advanced Intelligence Project, Tokyo, Japan morinaga@bbo.cs.tsukuba.ac.jp., Akimoto Y; University of Tsukuba, Ibaraki, Japan.; RIKEN Center for Advanced Intelligence Project, Tokyo, Japan akimoto@cs.tsukuba.ac.jp. |
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| Jazyk: | angličtina |
| Zdroj: | Evolutionary computation [Evol Comput] 2024 Oct 01, pp. 1-52. Date of Electronic Publication: 2024 Oct 01. |
| DOI: | 10.1162/evco_a_00361 |
| Abstrakt: | The majority of theoretical analyses of evolutionary algorithms in the discrete domain focus on binary optimization algorithms, even though black-box optimization on the categorical domain has a lot of practical applications. In this paper, we consider a probabilistic model-based algorithm using the family of categorical distributions as its underlying distribution and set the sample size as two. We term this specific algorithm the categorical compact genetic algorithm (ccGA). The ccGA can be considered as an extension of the compact genetic algorithm (cGA), which is an efficient binary optimization algorithm. We theoretically analyze the dependency of the number of possible categories K, the number of dimensions D, and the learning rate η on the runtime. We investigate the tail bound of the runtime on two typical linear functions on the categorical domain: categorical OneMax (COM) and KVAL. We derive that the runtimes on COM and KVAL are O(Dln(DK)/η) and Θ(DlnK/η) with high probability, respectively. Our analysis is a generalization for that of the cGA on the binary domain. (© 2024 Massachusetts Institute of Technology.) |
| Databáze: | MEDLINE |
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