Evolution-based hessian approximation for hybrid numerical optimization methods = 하이브리드 수치최적화 기법을 위한 진화기반 헤시안 추정

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In this dissertation, Hessian approximation algorithms are proposed 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(SRO), Davidon-Fletcher-Powell(DFP) and Broyden-Fletcher-Goldfarb-Shanno(BFGS) in that the Hessian matrix is not calculated from the gradient information but from the function values directly. The proposed algorithms are designed for a class of hybrid methods 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. The Hessian matrix is recursively corrected so that its curvature matches the curvature information found from the fitness values. For this purpose, two different update methods, one called batch update and the other sequential update, are proposed. Furthermore, convergence properties of repetitive application of the proposed update schemes are investigated, both analytically and numerically. Since the estimation process of the Hessian matrix is independent of that of the gradient vector, more reliable Hessian estimation with a sparse 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 regards to state-of-the-art evolutionary algorithms for continuous optimization problems.
Advisors
Tahk, Min-Jearesearcher탁민제researcher
Description
한국과학기술원 : 항공우주공학전공,
Publisher
한국과학기술원
Issue Date
2009
Identifier
327802/325007  / 020045092
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 항공우주공학전공, 2009. 8., [ vii, 136 p. ]

Keywords

Numerical Optimization Method; Hybrid Algorithm; Evolutionary Computation; Hessian Approximation; Quasi-Newton Method; 수치최적화 기법; 하이브리드 알고리즘; 진화 연산; 헤시안 근사; 의사-뉴튼 방법; Numerical Optimization Method; Hybrid Algorithm; Evolutionary Computation; Hessian Approximation; Quasi-Newton Method; 수치최적화 기법; 하이브리드 알고리즘; 진화 연산; 헤시안 근사; 의사-뉴튼 방법

URI
http://hdl.handle.net/10203/26386
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=327802&flag=dissertation
Appears in Collection
AE-Theses_Ph.D.(박사논문)
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