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
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
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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Von Neumann, J., and Morgenstern, O., 1980, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ.
Lewis, K. E., Chen, W., and Schmidt, L. C., 2006, Decision Making in Engineering Design, American Society of Mechanical Engineers, New York.
Thompson, S. C., and Paredis, C. J. J., 2010, “An Investigation into the Decision Analysis of Design Process Decisions,” ASME J. Mech. Des., 132(12), p. 121009. [CrossRef]
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. [CrossRef]
Moore, R. A., Kerzhner, A. A., and Paredis, C. J. J., 2009, “Model-Based Optimization of a Hydraulic Backhoe Using Multi-Attribute Utility Theory,” SAE Int. J. Mater. Manuf., 2(1), pp. 298–309.
Jones, D. R., 2001, “A Taxonomy of Global Optimization Methods Based on Response Surfaces,” J. Global Optim., 21(4), pp. 345–383. [CrossRef]
Eldred, M. S., Giunta, A. A., Wojtkiewicz, S. F., and Trucano, T. G., 2002, “Formulations for Surrogate-Based Optimization Under Uncertainty,” AIAA Paper No. 2002–5585, Atlanta, GA, 189(194).
Ong, Y. S., Nair, P. B., Keane, A. J., and Wong, K. W., 2004, “Surrogate-Assisted Evolutionary Optimization Frameworks for High-Fidelity Engineering Design Problems,” Knowledge Incorporation in Evolutionary Compuation, Springer Verlag, Springer-Verlag Berlin Heidelberg 2005.
Sacks, J. S., Susannah, B., and Welch, W. J., 1989, “Designs for Computer Experiments,” Technometrics, 31(1), pp. 41–47. [CrossRef]
Sacks, J., Welch, W. J., Mictchell, T. J., and Wynn, H. P., 1989, “Design and Analysis of Computer Experiments,” Statist. Sci., 4(4), pp. 409–435. [CrossRef]
Shan, S. W., and Gary, G., 2010, “Metamodeling for High Dimensional Simulation-Based Design Problems,” ASME J. Mech. Des., 132(5), p. 051009. [CrossRef]
Simpson, T. W., Poplinski, J. D., Koch, P. N., and Allen, J. K., 2001, “Metamodels for Computer-Based Engineering Design: Survey and Recommendations,” Eng. Comput., 17(2), pp. 129–150. [CrossRef]
Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T. J., and Morris, M. D., 1992, “Screening, Predicting, and Computer Experiments,” Technometrics, 34(1), pp. 15–25. [CrossRef]
Mckay, M. D., Beckman, R. J., and Conover, W. J., 1979, “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” Technometrics, 22(2), pp. 239–245.
Xiong, F., Xiong, Y., Chen, W., and Yang, S., 2009, “Optimizing Latin Hypercube Design for Sequential Sampling of Computer Experiments,” Eng. Optim., 41(8), pp. 793–810. [CrossRef]
Handcock, M. S., 1991, “On Cascading Latin Hypercube Designs and Additive Models for Experiments,” Commun. Stat. Theory Methods, 20(2), pp. 417–439. [CrossRef]
Tang, B., 1993, “Orthogonal Array-Based Latin Hypercubes,” J. Am. Stat. Assoc., 88(424), pp. 1392–1397. [CrossRef]
Joseph, V. R., and Hung, Y., 2008, “Orthogonal-Maximin Latin Hypercube Designs,” Statistica Sinica, 18(1), pp. 171–186.
Huang, D., Allen, T. T., Notz, W. I., and Miller, R. A., 2006, “Sequential Kriging Optimization Using Multiple-Fidelity Evaluations,” Struct. Multidiscip. Optim., 32(5), pp. 369–382. [CrossRef]
Ginsbourger, D., Le Riche, R., and Carraro, L., 2008, “A Multi-Points Criterion for Deterministic Parallel Global Optimization Based on Gaussian Processes.” Available at: http://hal.archives-ouvertes.fr/hal-00260579
Jones, D. R., Schonlau, M., and Welch, W. J., 1998, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492. [CrossRef]
Paredis, C. J. J., 1996, “An Agent-Based Approach to the Design of Rapidly Deployable Fault Tolerant Manipulators,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
Alexandrov, N. M., Lewis, R. M., Gumbert, C. R., Green, L. L., and Newman, P. A., 1999, “Optimization With Variable-Fidelity Models Applied to Wing Design,” Institute for Computer Applications in Science and Engineering, Hampton, VA, Report No. NASA/CR-1999-209826.
Schmit, L. A., and Farshi, B., 1974, “Some Approximation Concepts for Structural Synthesis,” AIAA J., 12(5), pp. 692–699. [CrossRef]
Gano, S. E., Perez, V. M., Renaud, J. E., and Batill, S. M., 2004, “Multilevel Variable Fidelity Optimization of a Morphing Unmanned Aerial Vehicle,” AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, CA.
Le Moigne, A., and Qin, N., 2004, “Variable-Fidelity Aerodynamic Optimization for Turbulent Flows Using a Discrete Adjoint Formulation,” AIAA J., 42(7), pp. 1281–1292. [CrossRef]
Hays, R., and Singer, M., 1989, Simulation Fidelity in Training System Design: Bridging the Gap between Reality and Training, Springer-Verlag, New York.
Cellier, F. E., 1991, Continuous System Modeling, Springer-Verlag, New York.
Gurnani, A., Ferguson, S., Lewis, K., and Donndelinger, J., 2006, “A Constraint-Based Approach to Feasibility Assessment in Preliminary Design,” Artif. Intell. Eng. Des., Anal. Manuf., 20(4), pp. 351–367. [CrossRef]
Paredis, C. J. J., and Khosla, P. K., 1997, “Agent-Based Design of Fault Tolerant Manipulators for Satellite Docking,” Proceedings of the 1997 IEEE Conference on Robotics and Automation, Albuquerque, NM, Vol. 4, pp. 3473–3480.
Bakr, M. H., and Bandler, J. W., 2000, “Review of the Space Mapping Approach to Engineering Optimization and Modeling,” Optim. Eng., 1(3), pp. 241–276. [CrossRef]
Alexandrov, N. M., and Lewis, R. M., 2001, “An Overview of First-Order Model Management for Engineering Optimization,” Optim. Eng., 2(4), pp. 413–430. [CrossRef]
Alexandrov, N. M., Lewis, R. M., Gumbert, C. R., Green, L. L., and Newman, P. A., 2001, “Approximation and Model Management in Aerodynamic Optimization With Variable-Fidelity Models,” J. Aircraft, 38(6), pp. 1093–1101. [CrossRef]
Moore, R. A., 2009, “Variable Fidelity Modeling as Applied to Trajectory Optimization for a Hydraulic Backhoe,” Masters thesis, Georgia Institute of Technology, Atlanta, GA.
Rodriguez, J. F., and Renaud, J. E., 1998, “Convergence of Trust Region Augmented Lagrangian Methods Using Variable Fidelity Approximation Data,” Struct. Optim., 15(3), pp. 141–156. [CrossRef]
Rodriguez, J. F., Perez, V. M., Padmanabhan, D., and Renaud, J. E., 2001, “Sequential Approximate Optimization Using Variable Fidelity Response Surface Approximations,” Struct. Multidiscip. Optim., 22(1), pp. 23–34. [CrossRef]
Xia, L., and Gao, Z.-H., 2006, “Application of Variable-Fidelity Models to Aerodynamic Optimization,” Appl. Math. Mech., 27(8), pp. 1089–1095. [CrossRef]
Lawrence, D. B., 1999, The Economic Value of Information, Springer Science+Business Media, New York.
Howard, R., 1966, “Information Value Theory,” IEEE Trans. Syst. Sci. Cybernet., SSC-2(1), pp. 779–783.
Brathwaite, J., and Saleh, J. H., 2009, “Value-Centric Framework and Pareto Optimality for Design and Acquisition of Communication Satellites,” Int. J. Satellite Commun., 27(6), pp. 330–348. [CrossRef]
Cheung, J., Scanlan, J., Wong, J., Forrester, J., Eres, H., Collopy, P., Hollingsworth, P., Wiseall, S., and Briceno, S., 2010, “Application of Value-Driven Design to Commercial Aero-Engine System,” 10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Fort Worth, TX.
Collopy, P., and Hollingsworth, P., 2009, Value-Driven Design, American Institute of Aeronautics and Astronautics, Reston, VA, pp. 2009–7099.
Hazelrigg, G. A., 2012, Fundamentals of Decision Making for Engineering Design and Systems Engineering. Available at: http://www.engineeringdecisionmaking.com/
Cressie, N. A. C., 1993, Statistics for Spatial Data, John Wiley & Sons, Inc., New York.
Gano, S. E., Renaud, J. E., Martin, J. D., Simpson, T. W., 2005, “Update Strategies for Kriging Models for Use in Variable Fidelity Optimization,” 1st AIAA Multidisciplinary Design Optimization Specialist Conference, Austin, TX.
Handcock, M. S. S., and Michael, L., 1993, “A Bayesian Analysis of Kriging,” Technometrics, 35(4), pp. 403–410. [CrossRef]
Lophaven, S. N., Nielsen, H. B., and Sondergaard, J., 2002, “Dace: A Matlab Kriging Toolbox,” Technical University of Denmark, Report No. IMM-TR-2002-12.
Ankenman, B., Nelson, B. L., and Staum, J., 2008, “Stochastic Kriging for Simulation Metamodeling,” Proceedings of the 40th Conference on Winter Simulation, Miami, FL, pp. 362–370.
Kennedy, M., and O'Hagan, A., 2001, “Bayesian Calibration of Computer Models,” J. R. Stat. Soc., Ser. B (Statistical Methodology), 63(3), pp. 425–464. [CrossRef]
Huang, D., Allen, T. T., Notz, W. I., and Zeng, N., 2006, “Global Optimization of Stochastic Black-Box Systems Via Sequential Kriging Meta-Models,” J. Global Optim., 34(3), pp. 441–466. [CrossRef]
Kennedy, M. C., and O'Hagan, A., 2000, “Predicting the Output From a Complex Computer Code When Fast Approximations are Available,” Biometrika, 87(1), pp. 1–13. [CrossRef]
Bernardo, J. M., and Smith, A. F. M., 1994, Bayesian Theory, John Wiley & Sons, Inc., New York.
Moore, R. A., 2012, “Value-Based Global Optimization,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
Kahn, H., and Marshall, A. W., 1953, “Methods of Reducing Sample Size in Monte Carlo Computations,” J. Oper. Res. Soc. Am., 1(5), pp. 263–271.
Li, P. Y., and Mensing, F., 2010, “Optimization and Control of a Hydro-Mechanical Transmission Based Hybrid Hydraulic Passenger Vehicle,” 7th International Fluid Power Conference, Aachen, Germany.


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Posterior mean and variance with respect to Model 1

Grahic Jump Location
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.

Grahic Jump Location
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. 10

Influence diagram for the hydraulic hybrid car

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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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