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Research Papers: Design Automation

Learning an Optimization Algorithm Through Human Design Iterations

[+] Author and Article Information
Thurston Sexton

National Institute of Standards and Technology,
Gaithersburg, MD 20899
e-mail: thurston.sexton@nist.gov

Max Yi Ren

Department of Mechanical Engineering,
Arizona State University,
Tempe, AZ 85287
e-mail: yiren@asu.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 1, 2016; final manuscript received July 19, 2017; published online August 30, 2017. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 139(10), 101404 (Aug 30, 2017) (10 pages) Paper No: MD-16-1804; doi: 10.1115/1.4037344 History: Received December 01, 2016; Revised July 19, 2017

Solving optimal design problems through crowdsourcing faces a dilemma: On the one hand, human beings have been shown to be more effective than algorithms at searching for good solutions of certain real-world problems with high-dimensional or discrete solution spaces; on the other hand, the cost of setting up crowdsourcing environments, the uncertainty in the crowd's domain-specific competence, and the lack of commitment of the crowd contribute to the lack of real-world application of design crowdsourcing. We are thus motivated to investigate a solution-searching mechanism where an optimization algorithm is tuned based on human demonstrations on solution searching, so that the search can be continued after human participants abandon the problem. To do so, we model the iterative search process as a Bayesian optimization (BO) algorithm and propose an inverse BO (IBO) algorithm to find the maximum likelihood estimators (MLEs) of the BO parameters based on human solutions. We show through a vehicle design and control problem that the search performance of BO can be improved by recovering its parameters based on an effective human search. Thus, IBO has the potential to improve the success rate of design crowdsourcing activities, by requiring only good search strategies instead of good solutions from the crowd.

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Figures

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Fig. 1

(a) Summary of player participation and performance and (b) results from the game showed while most players failed to outperform the Bayesian optimization algorithm, some of them can identify good solutions early on. (Reproduced with permission from Ren et al. [8,11]. Copyright 2016 and 2015 by ASME.)

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Fig. 2

Four iterations of BO on a 1D function. Obj: The objective function. GP: Gaussian process model. EI: Expected improvement function. Image is modified from Ref. [11].

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Fig. 3

The minimal cost L for search trajectory lengths N=5,...,20 with respect to GαBO and GK0. αINI is fixed to 1.0 and 10.0.

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Fig. 4

(a) Comparison on BO convergence using four algorithmic settings: (orange) Λ=10.0I, (green) Λ=0.01I, (gray) the MLE of Λ is used for each new sample, and (red) the initial setting Λ=10.0I is updated by IBO using the trajectory from Λ=0.01I. (b) The percentages of estimated Λ̂MLE along the number of iterations, averaged over the cases with Λ={0.01I,0.1I,1.0I,10.0I} and 30 trials for each case.

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Fig. 5

Independent component analysis (ICA) bases learned from all human plays and the ecoRacer track. Vertical lines on the track correspond to the peak locations of the bases.

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Fig. 6

The residual of current best score versus the known best score, with settings λ̂ (IBO, red), λ̂GP (MLE, blue), and the default λ=I (green). Results are shown as averages over 30 trials. One-sigma confidence intervals are calculated via 5000 bootstrap samples. Red and black dots are scores from P2 and P3, respectively.

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Fig. 7

Qualitative comparison on control strategies from the theoretical optimal solution (top), one of the BO solutions (middle), and the best player solution (bottom)

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