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Finite element approximation of complex functions for spatial optimization and search. (English) Zbl 1109.65055
Summary: A simple finite-element-based procedure is developed for the approximation and optimization of complex spatial functions with multiple, close maxima. Starting from an initial coarse triangulation, a new point is introduced at the edge of ‘highest error of interest’. This error combines an interpolation estimate of the error, and is also weighted by the edge size (in order to account for size disparity) and the function itself (in order to accentuate the maxima). The results indicate that the finite-element-based search procedure outperforms the standard genetic optimization technique by a considerable margin, enabling an accurate search for locations of maxima with far fewer cost function evaluations.
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C15 Stochastic programming
Full Text: DOI
[1] Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (1989) · Zbl 0721.68056
[2] Genetic Algorithms in Engineering and Computer Science (1995)
[3] Genetic Algorithms in Engineering and Computer Science (1998)
[4] Deb, Multi-Objective Optimization Using Evolutionary Algorithms (2001) · Zbl 0970.90091
[5] Löhner, Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations, ICASE Report 87-4. International Journal for Numerical Methods in Fluids 7 pp 1093– (1987)
[6] Baum JD Löhner R Numerical simulation of shock interaction with a modern main battlefield tank 1991
[7] Baum JD Luo H Löhner R Numerical simulation of blast in the world trade center 1995
[8] Baum JD Luo H Mestreau E Löhner R Pelessone D Charman C A coupled CFD/CSD methodology for modeling weapon detonation and fragmentation 1999
[9] Baum JD Mestreau E Luo H Löhner R Pelessone D Charman Ch Modeling structural response to blast loading using a coupled CFD/CSD methodology 2003
[10] Löhner R Baum JD Rice D Comparison of coarse and fine mesh 3-D Euler predictions for blast loads on generic building configurations 2004
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