Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization

Geometric and information frameworks for constructing global optimization algorithms are considered, and several new ideas to speed up the search are proposed. The accelerated global optimization methods automatically realize a local behavior in the promising subregions without the necessity to stop...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2016-10, Vol.171 (1), p.186-208
Main Authors: Sergeyev, Yaroslav D., Mukhametzhanov, Marat S., Kvasov, Dmitri E., Lera, Daniela
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Benchmarking
Calculus of Variations and Optimal Control
Optimization
Engineering
Estimates
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Optimization algorithms
Phases
Studies
Test sets
Theory of Computation
Tuning
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Summary:Geometric and information frameworks for constructing global optimization algorithms are considered, and several new ideas to speed up the search are proposed. The accelerated global optimization methods automatically realize a local behavior in the promising subregions without the necessity to stop the global optimization procedure. Moreover, all the trials executed during the local phases are used also in the course of the global ones. The resulting geometric and information global optimization methods have a similar structure, and a smart mixture of new and traditional computational steps leads to 22 different global optimization algorithms. All of them are studied and numerically compared on three test sets including 120 benchmark functions and 4 applied problems.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-016-0947-5