An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions |
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Authors: | Mark A Abramson Thomas J Asaki John E Dennis Jr Raymond Magallanez Jr Matthew J Sottile |
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Affiliation: | (1) The Boeing Company, PO Box 3707, MC 7L-21, Seattle, WA 98124-2207, USA;(2) Department of Mathematics, Washington State University, PO Box 643113, Neill Hall 103, Pullman, WA 99164-3113, USA;(3) Department of Computational and Applied Mathematics, Rice University, 8419 42nd Avenue SW, Seattle, WA 98136-2360, USA;(4) Department of Mathematical Sciences, United States Air Force Academy, Colorado Springs, CO, USA;(5) Galois, Inc., 421 SW 6th Ave. Suite 300, Portland, OR 97204, USA |
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Abstract: | In this paper, we characterize a new class of computationally expensive optimization problems and introduce an approach for
solving them. In this class of problems, objective function values may be directly related to the computational time required
to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate the objective
is significantly less than at points farther away from the solution. This is motivated by an application in which each objective
function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is
to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation
and the reference image through the image comparison process. In designing an approach to numerically solve the more general
class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather
than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the
expected positive correlation between function values and their CPU times, a time cutoff parameter is added to the objective
function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold.
The approach was tested using the NOMADm and DACE MATLAB? software packages, and results are presented. |
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