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Research Papers: Design Automation

Expensive Black-Box Model Optimization Via a Gold Rush Policy

[+] Author and Article Information
Benson Isaac

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: isaacbn@tamu.edu

Douglas Allaire

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: dallaire@tamu.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 18, 2018; final manuscript received November 16, 2018; published online January 10, 2019. Assoc. Editor: Gary Wang.

J. Mech. Des 141(3), 031401 (Jan 10, 2019) (9 pages) Paper No: MD-18-1458; doi: 10.1115/1.4042113 History: Received June 18, 2018; Revised November 16, 2018

The optimization of black-box models is a challenging task owing to the lack of analytic gradient information and structural information about the underlying function, and also due often to significant run times. A common approach to tackling such problems is the implementation of Bayesian global optimization techniques. However, these techniques often rely on surrogate modeling strategies that endow the approximation of the underlying expensive function with nonexistent features. Further, these techniques tend to push new queries away from previously queried design points, making it difficult to locate an optimum point that rests near a previous model evaluation. To overcome these issues, we propose a gold rush (GR) policy that relies on purely local information to identify the next best design alternative to query. The method employs a surrogate constructed pointwise, that adds no additional features to the approximation. The result is a policy that performs well in comparison to state of the art Bayesian global optimization methods on several benchmark problems. The policy is also demonstrated on a constrained optimization problem using a penalty method.

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Figures

Grahic Jump Location
Fig. 1

A graphical depiction of the computation of the weights required for the pointwise construction of a surrogate model of the expensive black-box function to be optimized

Grahic Jump Location
Fig. 2

Depiction of the LI for a one-dimensional function with three evaluations of the expensive black-box function

Grahic Jump Location
Fig. 3

A depiction of a few queries from an expensive black-box one-dimensional function being used to make pointwise surrogate approximations (top plot) and estimate the GR index (bottom plot)

Grahic Jump Location
Fig. 4

Graphs of the true Michalewicz function (left), a Gaussian process regression surrogate (middle), and a pointwise surrogate (right). The surrogate models were constructed using the same 5 × 5 grid of data.

Grahic Jump Location
Fig. 7

Golinski's speed reducer [46]

Grahic Jump Location
Fig. 8

Convergence results for the GR policy for a three-dimensional version of Golinski's speed reducer

Grahic Jump Location
Fig. 5

Convergence results for the CKG and GR policies for the Michalewicz, six-hump camel back, and Tilted Branin functions with an initial 3 × 3 grid

Grahic Jump Location
Fig. 6

Querying paths for the GR and CKG policies on the Tilted Branin function

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