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Research Papers: Design Automation

Mode Pursuing Sampling Method for Discrete Variable Optimization on Expensive Black-Box Functions

[+] Author and Article Information
Behnam Sharif, Tarek Y. ElMekkawy

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada

G. Gary Wang

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canadagary̱wang@umanitoba.ca

J. Mech. Des 130(2), 021402 (Jan 03, 2008) (11 pages) doi:10.1115/1.2803251 History: Received December 01, 2006; Revised March 16, 2007; Published January 03, 2008

Based on previously developed Mode Pursuing Sampling (MPS) approach for continuous variables, a variation of MPS for discrete variable global optimization problems on expensive black-box functions is developed in this paper. The proposed method, namely, the discrete variable MPS (D-MPS) method, differs from its continuous variable version not only on sampling in a discrete space, but moreover, on a novel double-sphere strategy. The double-sphere strategy features two hyperspheres whose radii are dynamically enlarged or shrunk in control of, respectively, the degree of “exploration” and “exploitation” in the search of the optimum. Through testing and application to design problems, the proposed D-MPS method demonstrates excellent efficiency and accuracy as compared to the best results in literature on the test problems. The proposed method is believed a promising global optimization strategy for expensive black-box functions with discrete variables. The double-sphere strategy provides an original search control mechanism and has potential to be used in other search algorithms.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Contour plot of the SC function

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Figure 2

Plot of the ranked point distributions of (a) g[k] and (b) G[k]

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Figure 3

Flowchart of the proposed complete DMPS algorithm

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Figure 4

Hypersphere radii over iterations

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Figure 5

Example for D-MPS with the double-sphere strategy for SC function

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Figure 6

Result comparison between (a) the basic D-MPS and (b) complete D-MPS

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Figure 7

Parameter interaction plot (mean versus nEval)

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