Browsing by Author "Asaki, Thomas J."

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    An Efficient Class of Direct Search Surrogate Methods for Solving Expensive Optimization Problems with CPU-Time-Related Functions
    (2008-06) Abramson, Mark A.; Asaki, Thomas J.; Dennis, J.E. Jr.; Magallanez, Raymond; Sottile, Matthew J.
    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.
  • Thumbnail Image
    Item
    Characteristic Shape Sequences for Measures on Images
    (2006-11) Pingel, Rachael L.; Abramson, Mark A.; Asaki, Thomas J.; Dennis, J.E. Jr.
    Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ellipses from two-dimensional image data. To solve the problem numerically, we augment the class of mesh adaptive direct search (MADS) algorithms with a filter, so as to allow infeasible starting points and to achieve better local solutions. Results here show that the MADS filter algorithm is successful in the test problem of finding good characteristic ellipse solutions from simple but noisy images.
  • Thumbnail Image
    Item
    Quantitative Object Reconstruction using Abel Transform X-Ray Tomography and Mixed Variable Optimization
    (2007-02) Abramson, Mark A.; Asaki, Thomas J.; Dennis, J.E. Jr.; O'Reilly, Kevin R.; Pingel, Rachael L.
    This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric objects from radiograph data obtained via x-ray tomography. Specifically, a mixed variable programming (MVP) problem is formulated, in which the variables of interest are the number and types of materials and the thickness of each concentric layer. The objective function is a measure of distance between one-dimensional radiograph data and a material property vector operated on by a forward projection based on the Abel transform. The mixed variable pattern search (MVPS) algorithm for linearly constrained MVP problems is applied to the problem by means of the NOMADm MATLAB® software package. Numerical results are presented for several test configurations and show that, while there are difficulties yet to be overcome, the method appears to be very promising for solving this class of problems in practice.