Hessian approximation algorithms for hybrid optimization methods

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This article introduces Hessian approximation algorithms to estimate the search direction of the quasi-Newton methods for solving optimization problems of continuous parameters. The proposed algorithms are quite different from other well-known quasi-Newton methods, such as symmetric rank-one, Davidon-Fletcher-Powell, and Broyden-Fletcher-Goldfarb-Shanno, in that the Hessian matrix is not calculated from the gradient information, rather directly from the function values. The proposed algorithms are designed for a class of hybrid algorithms that combine evolutionary search with the gradient-based methods of quasi-Newton type. The function values calculated for the evolutionary search are used for estimation of the Hessian matrix (or its inverse) as well as the gradient vector. Since the estimation process of the Hessian matrix is independent of that of the gradient vector, more reliable Hessian estimation with a small population is possible compared with the previous methods based upon the classical quasi-Newton methods. Numerical experiments show that the proposed algorithms are very competitive with state-of-the-art evolutionary algorithms for continuous optimization problems.
Publisher
TAYLOR FRANCIS LTD
Issue Date
2009-07
Language
English
Article Type
Article
Keywords

CODED GENETIC ALGORITHMS; MEMETIC ALGORITHMS; DATA ASSIMILATION; CONSTRAINED OPTIMIZATION; DIFFERENTIAL EVOLUTION; GLOBAL OPTIMIZATION; LOCAL SEARCH; STRATEGIES; TAXONOMY; DESIGN

Citation

ENGINEERING OPTIMIZATION, v.41, no.7, pp.609 - 633

ISSN
0305-215X
DOI
10.1080/03052150902736879
URI
http://hdl.handle.net/10203/99657
Appears in Collection
AE-Journal Papers(저널논문)
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