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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February 2016
Research-Article
Optimization on Metamodeling-Supported Iterative Decomposition
Kambiz Haji Hajikolaei,
Kambiz Haji Hajikolaei
Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: khajihaj@sfu.ca
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: khajihaj@sfu.ca
Search for other works by this author on:
George H. Cheng,
George H. Cheng
Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: ghc2@sfu.ca
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: ghc2@sfu.ca
Search for other works by this author on:
G. Gary Wang
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
Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: gary_wang@sfu.ca
Search for other works by this author on:
Kambiz Haji Hajikolaei
Product Design and
Optimization Laboratory (PDOL),
School of Mechatronic Systems Engineering,
Simon Fraser University,
BC, Canada
e-mail: khajihaj@sfu.ca
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
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
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. Feb 2016, 138(2): 021401 (11 pages)
Published Online: December 8, 2015
Article history
Received:
December 2, 2014
Revised:
October 19, 2015
Citation
Haji Hajikolaei, K., Cheng, G. H., and Wang, G. G. (December 8, 2015). "Optimization on Metamodeling-Supported Iterative Decomposition." ASME. J. Mech. Des. February 2016; 138(2): 021401. https://doi.org/10.1115/1.4031982
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