Dual‐objective Optimal Mixture Designs

Zhang, Chongqi; Wong, Woon K.; Peng, Heng

doi:10.1111/j.1467-842x.2012.00670.x

Cited by 10 publications

(5 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We plan to do follow up work in [ 46 ] and [ 47 ] and modify the ProjPSO to search for multiple-objective optimal designs for mixture models and optimal designs for mixture amount models. Multiple-objective optimal designs are desirable because they can incorporate multiple goals of the study at the design stage and deliver a design with efficiencies specified by the user, with more important goals having larger efficiencies.…”

Section: Discussionmentioning

confidence: 99%

A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models

et al. 2015

View full text Add to dashboard Cite

Particle Swarm Optimization (PSO) is a meta-heuristic algorithm that has been shown to be successful in solving a wide variety of real and complicated optimization problems in engineering and computer science. This paper introduces a projection based PSO technique, named ProjPSO, to efficiently find different types of optimal designs, or nearly optimal designs, for mixture models with and without constraints on the components, and also for related models, like the log contrast models. We also compare the modified PSO performance with Fedorov's algorithm, a popular algorithm used to generate optimal designs, Cocktail algorithm, and the recent algorithm proposed by [1].

show abstract

Section: Discussionmentioning

confidence: 99%

A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models

et al. 2015

View full text Add to dashboard Cite

show abstract

“…These operators are only applied to the parents if they pass the probability test. In this research, we have adapted the genetic operators proposed by Limmun et al [26].…”

Section: The Proposed Genetic Algorithmmentioning

confidence: 99%

“…They investigated the conditions under which these two types of designs were equivalent. Zhang et al [26] presented a methodology for constructing dual-objective optimal designs in mixture experiments within a simplex experimental region. They considered two types of dual-objectives: D-and A-optimality, and D-and I-optimality.…”

Section: Introductionmentioning

confidence: 99%

Generating Robust Optimal Mixture Designs Due to Missing Observation Using a Multi-Objective Genetic Algorithm

Limmun,

Chomtee,

Borkowski

2023

Mathematics

View full text Add to dashboard Cite

Missing observation is a common problem in scientific and industrial experiments, particularly in a small-scale experiment. They often present significant challenges when experiment repetition is infeasible. In this research, we propose a multi-objective genetic algorithm as a practical alternative for generating optimal mixture designs that remain robust in the face of missing observation. Our algorithm prioritizes designs that exhibit superior D-efficiency while maintaining a high minimum D-efficiency due to missing observations. The focus on D-efficiency stems from its ability to minimize the impact of missing observations on parameter estimates, ensure reliability across the experimental space, and maximize the utility of available data. We study problems with three mixture components where the experimental region is an irregularly shaped polyhedral within the simplex. Our designs have proven to be D-optimal designs, demonstrating exceptional performance in terms of D-efficiency and robustness to missing observations. We provide a well-distributed set of optimal designs derived from the Pareto front, enabling experimenters to select the most suitable design based on their priorities using the desirability function.

show abstract

“…Subsequent work on finding dual-objectives optimal designs includes Dette [11, 12], Zhu et al [13], Wong [14], Song and Wong [15], Tsai and Zen [16], Atkinson [17], McGree et al [18], Tommasi [19] and, Padmanabhan and Dragalin [20]. A recent application is Zhang et al [21] where they constructed dual-objective optimal designs for a mixture experiment.…”

Section: Multiple-objective Optimal Designsmentioning

confidence: 99%

Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

Hyun

Wong

2015

The International Journal of Biostatistics

View full text Add to dashboard Cite

We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem. We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.

show abstract

Dual‐objective Optimal Mixture Designs

Cited by 10 publications

References 40 publications

A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models

A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models

Generating Robust Optimal Mixture Designs Due to Missing Observation Using a Multi-Objective Genetic Algorithm

Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

Contact Info

Product

Resources

About