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RESEARCH PAPERS

Objective Function Effect Based Pattern Search—Theoretical Framework Inspired by 3D Component Layout

[+] Author and Article Information
Chandankumar Aladahalli

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213chandan@alumni.cmu.edu

Jonathan Cagan1

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213cagan@cmu.edu

Kenji Shimada

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213shimada@cmu.edu

1

Corresponding author.

J. Mech. Des 129(3), 243-254 (Mar 16, 2006) (12 pages) doi:10.1115/1.2406095 History: Received November 11, 2005; Revised March 16, 2006

Though pattern search algorithms have been successfully applied to three-dimensional (3D) component layout problems, a number of unanswered questions remain regarding their parameter tuning. One such question is the scheduling of patterns in the search. Current pattern search methods treat all patterns similarly and all of them are active from the beginning to the end of the search. Observations from 3D component layout motivate the question whether patterns should be introduced in some different order during the search. This paper presents a novel method for scheduling patterns that is inspired by observations from 3D component layout problems. The new method introduces patterns into the search in the decreasing order of a priori expectation of the objective function change due to the patterns. Pattern search algorithms based on the new pattern schedule run 30% faster on average than conventional pattern search based algorithms on 3D component layout problems and general 2D multimodal surface minimization problems. However since determining the expected change in objective function value due to the patterns is expensive, we explore approximations using domain information.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Effect on objective function that is the sum of pairwise intersection volumes in 3D layout due to different patterns and step sizes

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Figure 2

The generalized pattern search algorithm

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Figure 3

GPS algorithm (left) and proposed class of OPS algorithms (right)

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Figure 4

Objective function variation with successive steps along a pattern (left) and the resultant expected change in objective function value as a function of the step size (solid lines) and fitted power law relation (dashed line) (right)

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Figure 5

The three examples used to compare the GPS and OPS algorithms

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Figure 6

Results comparing the GPS and OPS algorithms for the three packing problems. Each of the three columns represents two examples each for the three packing problems.

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Figure 7

Results comparing the GPS and OPS algorithms for the two fractal surfaces. The column on the left shows the actual surface.

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