A Generalized Markov-Chain Modelling Approach to (1,lambda)-ES Linear Optimization

0441534 - ÚI 2015 RIV CH eng C - Conference Paper (international conference)
Chotard, A. - Holeňa, Martin
A Generalized Markov-Chain Modelling Approach to (1,lambda)-ES Linear Optimization.
Parallel Problem Solving from Nature - PPSN XIII. Cham: Springer, 2014 - (Bartz-Beielstein, T.; Branke, J.; Filipič, B.; Smith, J.), s. 902-911. Lecture Notes in Computer Science, 8672. ISBN 978-3-319-10761-5. ISSN 0302-9743.
[PPSN 2014. International Conference on Parallel Problem Solving from Nature /13./. Ljubljana (SI), 13.09.2014-17.09.2014]
R&D Projects: GA ČR GA13-17187S
Institutional support: RVO:67985807
Keywords : evolution strategies * continuous optimization * linear optimization * linear constraint * linear function * 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, and while this is consistent with a black-box scenario, information on the function to be optimized (e.g. separability) may be exploited by the use of another distribution. The objective of our contribution is to complement previous studies realized with normal steps, and to give sufficient conditions on the distribution of the random steps for the success of a constant step-size (1, lambda)-ES on the simple problem of a linear function with a linear constraint. 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/11104/0244526