Important Markov-Chain Properties of (1,lambda)-ES Linear Optimization Models

0432405 - ÚI 2015 RIV CZ eng C - Conference Paper (international conference)
Chotard, A. - Holeňa, Martin
Important Markov-Chain Properties of (1,lambda)-ES Linear Optimization Models.
ITAT 2014. Information Technologies - Applications and Theory. Part II. Prague: Institute of Computer Science AS CR, 2014 - (Kůrková, V.; Bajer, L.; Peška, L.; Vojtáš, R.; Holeňa, M.; Nehéz, M.), s. 44-52. ISBN 978-80-87136-19-5.
[ITAT 2014. European Conference on Information Technologies - Applications and Theory /14./. Demänovská dolina (SK), 25.09.2014-29.09.2014]
R&D Projects: GA ČR GA13-17187S
Institutional support: RVO:67985807
Keywords : evolution strategies * random steps * linear optimization * Markov chain models * Archimedean copulas
Subject RIV: IN - Informatics, Computer Science

Several recent publications investigated Markov-chain modelling of linear optimization by a (1,lambda)-ES, considering both unconstrained and linearly constrained optimization, and both constant and varying step size. All of them assume normality of the involved random steps. This is a very strong and specific assumption. The objective of our contribution is to show that in the constant step size case, valuable properties of the Markov chain can be obtained even for steps with substantially more general distributions. Several results that have been previously proved using the normality assumption are proved here in a more general way without that assumption. Finally, the decomposition of a multidimensional distribution into its marginals and the copula combining them is applied to the new distributional assumptions, particular attention being paid to distributions with Archimedean copulas.
Permanent Link: http://hdl.handle.net/11104/0236769