A Metaheuristic Adaptive Cubature Based Algorithm to Find Bayesian Optimal Designs for Nonlinear Models

Masoudi, Ehsan; Holling, Heinz; Duarte, Belmiro P.M.; Wong, Weng Kee

doi:10.1080/10618600.2019.1601097

Cited by 16 publications

(11 citation statements)

References 51 publications

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“…Their meteoric rise in popularity is well documented in Whitacre (2011a, b) with reasons. Recently, Chen et al (2018), Phoa et al (2016, Kim and Wong (2018), Masoudi et al (2019), and Storn and Price (1997) used meta-heuristic algorithms to tackle different types of optimal design problems. For example, Chen et al (2018) applied a version of PSO to find standardized maximin optimal designs for several enzyme-kinetic inhibition models by solving multilevel nested optimization problems over different types of search spaces, and Kim and Wong (2018) likewise applied PSO and solved an adaptive clinical trial design problem by solving a complex discrete optimization problem by determining the optimal choice of ten integers with multiple constraints.…”

Section: Competitive Swarm Optimizermentioning

confidence: 99%

G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm

et al. 2021

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Hierarchical linear models are widely used in many research disciplines and estimation issues for such models are generally well addressed. Design issues are relatively much less discussed for hierarchical linear models but there is an increasing interest as these models grow in popularity. This paper discusses the G-optimality for predicting individual parameters in such models and establishes an equivalence theorem for confirming the G-optimality of an approximate design. Because the criterion is non-differentiable and requires solving multiple nested optimization problems, it is much harder to find and study G-optimal designs analytically. We propose a nature-inspired meta-heuristic algorithm called competitive swarm optimizer (CSO) to generate G-optimal designs for linear mixed models with different means and covariance structures. We further demonstrate that CSO is flexible and generally effective for finding the widely used locally D-optimal designs for nonlinear models with multiple interacting factors and some of the random effects are correlated. Our numerical results for a few examples suggest that G and D-optimal designs may be equivalent and we establish that D and G-optimal designs for hierarchical linear models are equivalent when the models have only a random intercept only. The challenging mathematical question of whether their equivalence applies more generally to other hierarchical models remains elusive.

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Section: Competitive Swarm Optimizermentioning

confidence: 99%

G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm

et al. 2021

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“…In the absence of any knowledge about the confidence in the computer model, we recommend choosing c ¼ 2q=N: This recommendation is based on the fact that at least q runs are needed to estimate q parameters in the nonlinear model (e.g. Masoudi et al 2019). Thus using twice the minimum number of runs, we are likely to have two replicates for each run, which can be used for estimating the unknown error variance, r 2 :…”

Section: Model-form Uncertaintiesmentioning

confidence: 99%

“…In general, this is a very difficult optimization problem. Here we will use the metaheuristic algorithm proposed in Masoudi et al (2019), which is implemented in the R package ICAOD (Masoudi et al 2020).…”

Section: Model-form Uncertaintiesmentioning

confidence: 99%

Robust experimental designs for model calibration

Krishna

Joseph

et al. 2021

Journal of Quality Technology

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A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting physical experiments. This paper presents an approach to optimally design such a physical experiment. The problem of optimally designing a physical experiment, using a computer model, is similar to the problem of finding an optimal design for fitting nonlinear models. However, the problem is more challenging than the existing work on nonlinear optimal design because of the possibility of model discrepancy, that is, the computer model may not be an accurate representation of the true underlying model. Therefore, we propose an optimal design approach that is robust to potential model discrepancies. We show that our designs are better than the commonly used physical experimental designs that do not make use of the information contained in the computer model and other nonlinear optimal designs that ignore potential model discrepancies. We illustrate our approach using a toy example and a real example from industry.

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“…Nevertheless, it is widely reported that they frequently produce the optimum or solutions close to the optimum, which explains their popularity [ 38 , 39 ]. The researchers experience is similar; GA, PSO and modern nature-inspired metaheuristic algorithms, such as swarm-based techniques [ 40 , 41 ] Imperialist Competitive Algorithm [ 42 ], Differential Evolutionary [ 43 , 44 ] and Competitive Swarm Optimizer [ 45 ] can also produce highly efficient designs for complicated nonlinear models with or without random effects. They include finding high-dimensional optimal supersaturated designs, more flexible adaptive two-stage Phase II designs [ 41 ] and Bayesian optimal designs [ 42 ] using adaptive cubature for models with possibly multiple interacting factors and some factors are discrete [ 43 ] or continuous [ 46 ] or random [ 45 ].…”

Section: Introductionmentioning

confidence: 99%

Constructing robust and efficient experimental designs in groundwater modeling using a Galerkin method, proper orthogonal decomposition, and metaheuristic algorithms

2021

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Estimating parameters accurately in groundwater models for aquifers is challenging because the models are non-explicit solutions of complex partial differential equations. Modern research methods, such as Monte Carlo methods and metaheuristic algorithms, for searching an efficient design to estimate model parameters require hundreds, if not thousands of model calls, making the computational cost prohibitive. One method to circumvent the problem and gain valuable insight on the behavior of groundwater is to first apply a Galerkin method and convert the system of partial differential equations governing the flow to a discrete problem and then use a Proper Orthogonal Decomposition to project the high-dimensional model space of the original groundwater model to create a reduced groundwater model with much lower dimensions. The reduced model can be solved several orders of magnitude faster than the full model and able to provide an accurate estimate of the full model. The task is still challenging because the optimization problem is non-convex, non-differentiable and there are continuous variables and integer-valued variables to optimize. Following convention, heuristic algorithms and a combination is used search to find efficient designs for the reduced groundwater model using various optimality criteria. The main goals are to introduce new design criteria and the concept of design efficiency for experimental design research in hydrology. The two criteria have good utility but interestingly, do not seem to have been implemented in hydrology. In addition, design efficiency is introduced. Design efficiency is a method to assess how robust a design is under a change of criteria. The latter is an important issue because the design criterion may be subjectively selected and it is well known that an optimal design can perform poorly under another criterion. It is thus desirable that the implemented design has relatively high efficiencies under a few criteria. As applications, two heuristic algorithms are used to find optimal designs for a small synthetic aquifer design problem and a design problem for a large-scale groundwater model and assess their robustness properties to other optimality criteria. The results show the proof of concept is workable for finding a more informed and efficient model-based design for a water resource study.

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A Metaheuristic Adaptive Cubature Based Algorithm to Find Bayesian Optimal Designs for Nonlinear Models

Cited by 16 publications

References 51 publications

G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm

G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm

Robust experimental designs for model calibration

Constructing robust and efficient experimental designs in groundwater modeling using a Galerkin method, proper orthogonal decomposition, and metaheuristic algorithms

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