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Research Papers

Value-Based Global Optimization

[+] Author and Article Information
Roxanne A. Moore

The G.W. Woodruff School
of Mechanical Engineering,
Center for Education Integrating Science,
Mathematics, and Computing (CEISMC),
Georgia Institute of Technology,
760 Spring Street, Suite 102,
Atlanta, GA 30308
e-mail: roxanne.moore@ceismc.gatech.edu

David A. Romero

Research Associate
Mem. ASME
Mechanical and Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: d.romero@utoronto.ca

Christiaan J. J. Paredis

Professor of Mechanical Engineering,
Woodruff Faculty Fellow
Mem. ASME
The G.W. Woodruff School
of Mechanical Engineering,
The Model-Based Systems Engineering Center,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: chris.paredis@me.gatech.edu

Note that, in general, each roughness parameter has units of one over the units of the corresponding optimization variable. The units of the objective function are always expressed in dollars, so that improvements of the objective can be meaningfully compared with the cost of further analysis, expressed in dollars per analysis.

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 26, 2012; final manuscript received November 22, 2013; published online January 31, 2014. Assoc. Editor: Michael Kokkolaras.

J. Mech. Des 136(4), 041003 (Jan 31, 2014) (14 pages) Paper No: MD-12-1326; doi: 10.1115/1.4026281 History: Received June 26, 2012; Revised November 22, 2013

In this paper, a value-based global optimization (VGO) algorithm is introduced. The algorithm uses kriging-like surrogate models and a sequential sampling strategy based on value of information (VoI) to optimize an objective characterized by multiple analysis models with different accuracies. VGO builds on two main contributions. The first contribution is a novel surrogate modeling method that accommodates data from any number of different analysis models with varying accuracy and cost. Rather than interpolating, it fits a model to the data, giving more weight to more accurate data. The second contribution is the use of VoI as a new metric for guiding the sequential sampling process for global optimization. Based on information about the cost and accuracy of each available model, predictions from the current surrogate model are used to determine where to sample next and with what level of accuracy. The cost of further analysis is explicitly taken into account during the optimization process, and no further analysis occurs if the expected value of the new information is negative. In this paper, we present the details of the VGO algorithm and, using a suite of randomly generated test cases, compare its performance with the performance of the efficient global optimization (EGO) algorithm (Jones, D. R., Matthias, S., and Welch, W. J., 1998, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492). Results indicate that the VGO algorithm performs better than EGO in terms of overall expected utility—on average, the same quality solution is achieved at a lower cost, or a better solution is achieved at the same cost.

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Figures

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Fig. 1

VGO approach for cost-effective optimization using models of differing accuracies

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Fig. 2

Posterior mean and variance with respect to Model 1

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Fig. 3

An example of the status of the VGO algorithm at the end of the first iteration. Left top: the truth model. Right top: the current best estimate of the truth (based on the currently available samples). Bottom: the computed VoI for model 1 (low fidelity) and model 2 (high fidelity), respectively.

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Fig. 4

The status of the VGO algorithm after the 20th iteration (same example as in Fig. 3)

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Fig. 5

The status of the VGO algorithm after the final (37th) iteration (same example as in Fig. 3)

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Fig. 6

Box plots representing the difference in utilities using VGO versus EGO with different values for the EGO stopping criterion, εa

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Fig. 7

Box plots representing the difference in analysis costs using VGO versus EGO with different values of the EGO stopping criterion, εa

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Fig. 8

Box plots representing the difference in analysis costs using VGO versus EGO with a low-fidelity model for different values of the EGO stopping criterion, εa

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Fig. 9

Drivetrain architecture for the hydraulic hybrid car

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Fig. 10

Influence diagram for the hydraulic hybrid car

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