Surrogate Models for Mixed Discrete-Continuous Variables

Swiler, Laura Painton; Hough, Patricia Diane; Qian, Peter Z. G.; Xu, Xu; Storlie, Curtis B.; Lee, Herbert K. H.

doi:10.1007/978-3-319-04280-0_21

Cited by 33 publications

(10 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first mathematical test function adapted from Swiler et al (2014) has one qualitative variable with five levels, and two continuous variables 1 , 2 ∈ [0,1]. This function has regions where the response behaviors at different qualitative levels are very similar.…”

Section: Math Functionmentioning

confidence: 99%

See 1 more Smart Citation

A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors

Zhang¹,

Tao²,

Chen

et al. 2019

Technometrics

View full text Add to dashboard Cite

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and relate them via a multiresponse cross-covariance matrix. We introduce a substantially different approach that maps each qualitative factor to an underlying numerical latent variable (LV), with the mapped value for each level estimated similarly to the correlation parameters. This provides a parsimonious GP parameterization that treats qualitative factors the same as numerical variables and views them as effecting the response via similar physical mechanisms. This has strong physical justification, as the effects of a qualitative factor in any physics-based simulation model must always be due to some underlying numerical variables. Even when the underlying variables are many, sufficient dimension reduction arguments imply that their effects can be represented by a low-dimensional LV. This conjecture is supported by the superior predictive performance observed across a variety of examples. Moreover, the mapped LVs provide substantial insight into the nature and effects of the qualitative factors.

show abstract

Section: Math Functionmentioning

confidence: 99%

“…We first test the four methods on two mathematical functions that have been used in the literature as benchmark problems involving qualitative factors (Deng et al 2017;Swiler et al 2014). We also include four engineering examples that are popular choices for assessing surrogate models with numerical inputs.…”

Section: Mathematical Examplesmentioning

confidence: 99%

A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors

Zhang¹,

Tao²,

Chen

et al. 2019

Technometrics

View full text Add to dashboard Cite

show abstract

“…[37] propose a mixed-variable BO approach named MiVaBO, using a linear surrogate model and Thompson sampling. Likewise, [38] propose several surrogate models for mixed discrete-continuous variables. [39] observe that optimization of the acquisition function is more challenging for discrete search spaces, as gradient-based optimization can not be applied.…”

Section: General Structurementioning

confidence: 99%

Bayesian Optimization for auto-tuning GPU kernels

Willemsen¹,

Nieuwpoort²,

Werkhoven³

2021

Preprint

View full text Add to dashboard Cite

Finding optimal parameter configurations for tunable GPU kernels is a non-trivial exercise for large search spaces, even when automated. This poses an optimization task on a nonconvex search space, using an expensive to evaluate function with unknown derivative. These characteristics make a good candidate for Bayesian Optimization, which has not been applied to this problem before.However, the application of Bayesian Optimization to this problem is challenging. We demonstrate how to deal with the rough, discrete, constrained search spaces, containing invalid configurations. We introduce a novel contextual variance exploration factor, as well as new acquisition functions with improved scalability, combined with an informed acquisition function selection mechanism.By comparing the performance of our Bayesian Optimization implementation on various test cases to the existing search strategies in Kernel Tuner, as well as other Bayesian Optimization implementations, we demonstrate that our search strategies generalize well and consistently outperform other search strategies by a wide margin.

show abstract

“…At present, most of SAEAs are presented to solve expensive continuous optimization problems, and few scholars also developed such models for expensive CMODOPs. For example, to mitigate the computational expense of models with both continuous and discrete parameters, Swiler et al [33] investigated and analyzed the performance of three types of response surfaces developed for mixed-variable models. Nguyen et al [34] proposed a new surrogate assisted genetic programming in terms of automated design problems of dispatching rules for production systems to improve the quality of the evolved rules without significant computational costs.…”

Section: Introductionmentioning

confidence: 99%

Surrogate-assisted evolutionary algorithm for expensive constrained multi-objective discrete optimization problems

Wang

Xiong

et al. 2021

Complex Intell. Syst.

View full text Add to dashboard Cite

Surrogate-assisted optimization has attracted much attention due to its superiority in solving expensive optimization problems. However, relatively little work has been dedicated to addressing expensive constrained multi-objective discrete optimization problems although there are many such problems in the real world. Hence, a surrogate-assisted evolutionary algorithm is proposed in this paper for this kind of problem. Specifically, random forest models are embedded in the framework of the evolutionary algorithm as surrogates to improve approximate accuracy for discrete optimization problems. To enhance the optimization efficiency, an improved stochastic ranking strategy based on the fitness mechanism and adaptive probability operator is presented, which also takes into account both convergence and diversity to advance the quality of candidate solutions. To validate the proposed algorithm, it is comprehensively compared with several well-known optimization algorithms on several benchmark problems. Numerical experiments are demonstrated that the proposed algorithm is very promising for the expensive constrained multi-objective discrete optimization problems.

show abstract

Surrogate Models for Mixed Discrete-Continuous Variables

Cited by 33 publications

References 30 publications

A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors

A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors

Bayesian Optimization for auto-tuning GPU kernels

Surrogate-assisted evolutionary algorithm for expensive constrained multi-objective discrete optimization problems

Contact Info

Product

Resources

About