Global Line Search Algorithm Hybridized with Quadratic Interpolation and Its Extension to Separable Functions
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Book chapterAutor
Baudiš, Petr
Pošík, Petr
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We propose a novel hybrid algorithm“Brent-STEP” for uni-
variate global function minimization, based on the global
line search method STEP and accelerated by Brent’s method,
a local optimizer that combines quadratic interpolation and
golden section steps. We analyze the performance of the hy-
brid algorithm on various one-dimensional functions and ex-
perimentally demonstrate a significant improvement relative
to its constituent algorithms in most cases. We then gener-
alize the algorithm to multivariate functions, adopting the
recently proposed [8] scheme to interleave evaluations across
dimensions to achieve smoother and more efficient conver-
gence. We experimentally demonstrate the highly competi-
tive performance of the proposed multivariate algorithm on
separable functions of the BBOB benchmark. The combina-
tion of good performance and smooth convergence on sepa-
rable functions makes the algorithm an interesting candidate
for inclusion in algorithmic portfolios or hybrid algorithms
that aim to provide good performance on a wide range of
problems.
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