Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs

Masoudi, Ehsan; Holling, Heinz; Wong, Weng Kee

doi:10.1016/j.csda.2016.06.014

Cited by 21 publications

(21 citation statements)

References 39 publications

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“…The structure of BICA is similar to the minimax version introduced in Masoudi, Holling, and Wong (2017). The major difference lies in the evaluation of the cost function or, equivalently, the optimality criterion.…”

Section: Ica For Bayesian Optimal Design Problemsmentioning

confidence: 99%

“…For example, Sitter (1992) proposed minimax optimal designs assuming a known parameter space for the unknown parameters and minimized the maximum inefficiency that arises from using the worst set of values for the model parameters. Minimax types of design criteria are complicated and usually require advanced algorithms to solve nested multimodal continuous optimization problems (see, e.g., Masoudi, Holling, and Wong 2017;Chen et al 2015).…”

Section: Introductionmentioning

confidence: 99%

“…Our interest is in one such algorithm called imperialist competitive algorithm (ICA), which is inspired from the sociopolitical process of humans and proposed in Atashpaz-Gargari and Lucas (2007). Our choice of ICA is in part due to our earlier positive experience, where we were successful in our search for hard-to-find minimax and standardized maximin optimal designs for different nonlinear models and where we experienced fewer premature convergence issues (Masoudi, Holling, and Wong 2017). Furthermore, as a state-of-the-art optimization algorithm, ICA: (a) does not require the design space to be discretized, (b) is a multi-start or population-based derivativefree algorithm and usually is not sensitive to the starting designs, and (c) can be easily modified to find other types of optimal designs.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the traditional quadrature methods, the hcubature algorithm provides an estimation error that is used to build stopping rules to determine if and when to increase the reliability of the approximations. To emphasize the difference between the previous minimax algorithm in Masoudi, Holling, and Wong (2017) and the current version, we call the algorithm proposed here Bayesian imperialist competitive algorithm (BICA). Our work is novel because this is the first study that hybridizes a subregion adaptive algorithm with a metaheuristic algorithm to find Bayesian optimal designs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Masoudi

Holling

Duarte

et al. 2019

Journal of Computational and Graphical Statistics

Self Cite

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Section: Ica For Bayesian Optimal Design Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Masoudi

Holling

Duarte

et al. 2019

Journal of Computational and Graphical Statistics

Self Cite

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“…Such criteria are mathematically equivalent to "pseudo-Bayesian" design criteria, see Section 3. This package uses the meta-heuristic imperialist competitive algorithm (Masoudi et al 2017). For special classes of nonlinear models, locally optimal designs, with a point mass prior for γ and utility functions not depending on y, can be found by packages LDOD (Masoudi et al 2013), designGLMM (Bush and Ruggiero 2016) and PopED (Nyberg et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Design of Experiments Using Approximate Coordinate Exchange

Overstall

Woods

2017

Technometrics

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The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional design spaces. We provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm. This methodology uses a Gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps. It has flexibility to address problems for any choice of utility function and for a wide range of statistical models with different numbers of variables, numbers of runs and randomization restrictions. In contrast to existing approaches to Bayesian design, the method can find multi-variable designs in large numbers of runs without resorting to asymptotic approximations to the posterior distribution or expected utility. The methodology is demonstrated on a variety of challenging examples of practical importance, including design for pharmacokinetic models and design for mixed models with discrete data. For many of these models, Bayesian designs are not currently available. Comparisons are made to results from the literature, and to designs obtained from asymptotic approximations.

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Optimal designs of accelerated degradation tests with random shock failures and measurement errors

Wu,

Zhou,

Yue

2024

Appl Stoch Models Bus & Ind

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Accelerated degradation tests (ADTs) are widely used for assessing the reliability of long‐life products. During an ADT, accelerated stresses not only expedite the degradation of test products but also increase the likelihood of encountering traumatic shocks. Moreover, it is important to acknowledge that measurement errors can be inevitable during the observation process of an ADT. Unfortunately, these errors are often overlooked in the optimal design of the ADT, especially when multiple competing failure modes are present. In this article, we propose a new approach to design ADTs when measurement errors exist and test products suffer from degradation failures and random shock failures. We utilize the Wiener process to model the degradation path, incorporating normally distributed measurement errors, and an exponential distribution to fit the time between random shock failures. Given the number of test products and the termination time, we optimize the ADT plans under three common design criteria. The equivalence theorem is used to verify the optimality of the optimal ADT plans. A real‐life example and sensitivity analysis are provided to illustrate our proposed method. The results demonstrate that when competing failure modes are present, the optimal ADT plans, which account for measurement errors, differ significantly from those that do not consider such errors.

show abstract

Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs

Cited by 21 publications

References 39 publications

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

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

Bayesian Design of Experiments Using Approximate Coordinate Exchange

Optimal designs of accelerated degradation tests with random shock failures and measurement errors

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