One-dimensional Global Optimization Based on Statistical Models

Calvin, James M.; Žilinskas, Antanas

doi:10.1007/0-306-47648-7_4

Cited by 3 publications

(2 citation statements)

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“…The majority of work on the P-algorithm [62,122,123,124,22] has been for onedimensional multimodal optimization and extending the axiomatic P-algorithm to the n-dimensional case has proved difficult [22,125,114,113,81,82,69,124]. In this research, the heuristic motivation for the P-algorithm is extended to the multidimensional case using GPs [54].…”

Section: Probability Of Improvementmentioning

confidence: 99%

Methodology for Global Optimization of Computationally Expensive Design Problems

Koullias

Mavris

2014

Journal of Mechanical Design

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The design of unconventional systems requires early use of high-fidelity physics-based tools to search the design space for improved and potentially optimum designs. Current methods for incorporating these computationally expensive tools into early design for the purpose of reducing uncertainty are inadequate due to the limited computational resources that are available in early design. Furthermore, the lack of finite difference derivatives, unknown design space properties, and the possibility of code failures motivates the need for a robust and efficient global optimization (EGO) algorithm. A novel surrogate model-based global optimization algorithm capable of efficiently searching challenging design spaces for improved designs is presented. The algorithm, called fBcEGO for fully Bayesian constrained EGO, constructs a fully Bayesian Gaussian process (GP) model through a set of observations and then uses the model to make new observations in promising areas where improvements are likely to occur. This model remedies the inadequacies of likelihood-based approaches, which may provide an incomplete inference of the underlying function when function evaluations are expensive and therefore scarce. A challenge in the construction of the fully Bayesian GP model is the selection of the prior distribution placed on the model hyperparameters. Previous work employs static priors, which may not capture a sufficient number of interpretations of the data to make any useful inferences about the underlying function. An iterative method that dynamically assigns hyperparameter priors by exploiting the mechanics of Bayesian penalization is presented. fBcEGO is incorporated into a methodology that generates relatively few infeasible designs and provides large reductions in the objective function values of design problems. This new algorithm, upon implementation, was found to solve more nonlinearly constrained algebraic test problems to higher accuracies relative to the global minimum than other popular surrogate model-based global optimization algorithms and obtained the largest reduction in the takeoff gross weight objective function for the case study of a notional 70-passenger regional jet when compared with competing design methods.

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Section: Probability Of Improvementmentioning

confidence: 99%

Methodology for Global Optimization of Computationally Expensive Design Problems

Koullias

Mavris

2014

Journal of Mechanical Design

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“…Bayesian Global Optimization (BGO) methods are one class of methods for solving such problems. They were initially proposed by Kushner (1964), with early work pursued in Mockus et al (1978) and Mockus (1989), and more recent work including improved algorithms (Boender and Kan 1987, Jones et al 1998, Huang et al 2006, convergence analysis (Calvin 1997, Calvin and Žilinskas 2002, Vazquez and Bect 2010, and allowing noisy function evaluations (Calvin et al 2005, Villemonteix et al 2009, Frazier et al 2009, Huang et al 2006.…”

Section: Introductionmentioning

confidence: 99%

Parallel Bayesian Global Optimization of Expensive Functions

Wang¹,

Clark

Liu

et al. 2016

Preprint

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We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger et al. (2007). At the heart of this algorithm is maximizing the information criterion called the "multi-points expected improvement", or the q-EI.To accomplish this, we use infinitessimal perturbation analysis (IPA) to construct a stochastic gradient estimator and show that this estimator is unbiased. We also show that the stochastic gradient ascent algorithm using the constructed gradient estimator converges to a stationary point of the q-EI surface, and therefore, as the number of multiple starts of the gradient ascent algorithm and the number of steps for each start grow large, the one-step Bayes optimal set of points is recovered. We show in numerical experiments that our method for maximizing the q-EI is faster than methods based on closed-form evaluation using high-dimensional integration, when considering many parallel function evaluations, and is comparable in speed when considering few. We also show that the resulting one-step Bayes optimal algorithm for parallel global optimization finds high-quality solutions with fewer evaluations than a heuristic based on approximately maximizing the q-EI. A high-quality open source implementation of this algorithm is available in the open source Metrics Optimization Engine (MOE).

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