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An Analytical Framework for Runtime of a Class of Continuous Evolutionary Algorithms

Although there have been many studies on the runtime of evolutionary algorithms in discrete optimization, relatively few theoretical results have been proposed on continuous optimization, such as evolutionary programming (EP). This paper proposes an analysis of the runtime of two EP algorithms based...

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Detalles Bibliográficos
Autores principales: Zhang, Yushan, Hu, Guiwu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4556928/
https://www.ncbi.nlm.nih.gov/pubmed/26366166
http://dx.doi.org/10.1155/2015/485215
Descripción
Sumario:Although there have been many studies on the runtime of evolutionary algorithms in discrete optimization, relatively few theoretical results have been proposed on continuous optimization, such as evolutionary programming (EP). This paper proposes an analysis of the runtime of two EP algorithms based on Gaussian and Cauchy mutations, using an absorbing Markov chain. Given a constant variation, we calculate the runtime upper bound of special Gaussian mutation EP and Cauchy mutation EP. Our analysis reveals that the upper bounds are impacted by individual number, problem dimension number n, searching range, and the Lebesgue measure of the optimal neighborhood. Furthermore, we provide conditions whereby the average runtime of the considered EP can be no more than a polynomial of n. The condition is that the Lebesgue measure of the optimal neighborhood is larger than a combinatorial calculation of an exponential and the given polynomial of n.