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Research Papers: Design Automation

Optimization on Metamodeling-Supported Iterative Decomposition

[+] Author and Article Information
Kambiz Haji Hajikolaei

Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: khajihaj@sfu.ca

George H. Cheng

Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: ghc2@sfu.ca

G. Gary Wang

Professor
Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: gary_wang@sfu.ca

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 2, 2014; final manuscript received October 19, 2015; published online December 8, 2015. Assoc. Editor: Christopher Mattson.

J. Mech. Des 138(2), 021401 (Dec 08, 2015) (11 pages) Paper No: MD-14-1767; doi: 10.1115/1.4031982 History: Received December 02, 2014; Revised October 19, 2015

The recently developed metamodel-based decomposition strategy relies on quantifying the variable correlations of black-box functions so that high-dimensional problems are decomposed to smaller subproblems, before performing optimization. Such a two-step method may miss the global optimum due to its rigidity or requires extra expensive sample points for ensuring adequate decomposition. This work develops a strategy to iteratively decompose high-dimensional problems within the optimization process. The sample points used during the optimization are reused to build a metamodel called principal component analysis-high dimensional model representation (PCA-HDMR) for quantifying the intensities of variable correlations by sensitivity analysis. At every iteration, the predicted intensities of the correlations are updated based on all the evaluated points, and a new decomposition scheme is suggested by omitting the weak correlations. Optimization is performed on the iteratively updated subproblems from decomposition. The proposed strategy is applied for optimization of different benchmarks and engineering problems, and results are compared to direct optimization of the undecomposed problems using trust region mode pursuing sampling method (TRMPS), genetic algorithm (GA), cooperative coevolutionary algorithm with correlation-based adaptive variable partitioning (CCEA-AVP), and divide rectangles (DIRECT). The results show that except for the category of undecomposable problems with all or many strong (i.e., important) correlations, the proposed strategy effectively improves the accuracy of the optimization results. The advantages of the new strategy in comparison with the previous methods are also discussed.

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Figures

Grahic Jump Location
Fig. 3

Decomposed subproblems during OMID procedure for problem #10

Grahic Jump Location
Fig. 2

Decomposed subproblems during OMID procedure for problem #1

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