A clustering-based coordinate exchange algorithm for generating G-optimal experimental designs

Saleh, Moein; Pan, Rong

doi:10.1080/00949655.2015.1077252

Cited by 4 publications

(6 citation statements)

References 26 publications

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“…4 CEXCH, due to its simplicity and ease of use, has become a favored optimal design algorithm. 4,6,8,10,16 It starts with a random design, then individually exchanges design coordinates to optimize the criterion. This results in a locally optimal design based on the initial random point.…”

Section: Exchange Algorithmsmentioning

confidence: 99%

“…Meyer and Nachtsheim (1995) introduced the coordinate exchange (CEXCH) to address this, eliminating the need for a candidate set and allowing continuous factor levels 4 . CEXCH, due to its simplicity and ease of use, has become a favored optimal design algorithm 4,6,8,10,16 . It starts with a random design, then individually exchanges design coordinates to optimize the criterion.…”

Section: Introductionmentioning

confidence: 99%

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Generating optimal designs with user‐specified pure replication structure

Walsh,

Bolton,

Borkowski

2024

Quality & Reliability Eng

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Over recent decades, optimal experimental design has surged in popularity due to affordable computing and efficient algorithms. However, some researchers highlight that this focus has often side‐lined the importance of including pure experimental replication in designs, as many optimality criteria do not inherently suggest designs with replicates. In this study, we introduce an approach that allows the designer to input a desired replication structure into the optimal design search. We list all potential replication structures, indicate the corresponding budget for pure‐error (PE) and lack‐of‐fit (LOF) degrees‐of‐freedom, and use particle swarm optimization to search for the optimal design in each scenario. We demonstrate our approach on various unexplored ‐optimal design scenarios and several scenarios recently discussed in literature. Our findings reveal the existence of highly‐efficient ‐optimal designs with unique replication structures, offering designers informed choices on allocating a limited budget for PE and LOF degrees‐of‐freedom. This method is versatile and compatible with other optimizers, such as the coordinate exchange.

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Section: Exchange Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generating optimal designs with user‐specified pure replication structure

Walsh,

Bolton,

Borkowski

2024

Quality & Reliability Eng

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“…The results provided in [10] have become a 'ground truth' standard data set against which to compare results of newly developed algorithms to solve this problem. Until this point, the exact G-optimal designs of Borkowski (2003) have remained the best-known designs for these scenarios [10] and were subsequently reproduced by [24] via an augmented application of the coordinate exchange, and used as a benchmark dataset for new algorithms proposed by authors [11,26].…”

Section: Literature Review: Algorithm Development and Current Best-kn...mentioning

confidence: 99%

“…The G-vs. I-optimal design question is the subject of ongoing research in the broader literature [27]. Saleh and Pan (2015) recognized the lack of algorithm development on the G-optimal design problem and provide a hybridized point and coordinate exchange algorithm which utilizes clustering to explore the characteristics of SPV over the design space [26]. Their algorithm is termed cCEA and they apply it to linear model and generalized linear model scenarios.…”

Section: Literature Review: Algorithm Development and Current Best-kn...mentioning

confidence: 99%

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Improved G-Optimal Designs for Small Exact Response Surface Scenarios: Fast and Efficient Generation via Particle Swarm Optimization

Walsh

Borkowski

2022

Mathematics

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G-optimal designs are those which minimize the worst-case prediction variance. Thus, such designs are of interest if prediction is a primary component of the post-experiment analysis and decision making. G-optimal designs have not attained widespread use in practical applications, in part, because they are difficult to compute. In this paper, we review the last two decades of algorithm development for generating exact G-optimal designs. To date, Particle Swarm Optimization (PSO) has not been applied to construct exact G-optimal designs for small response surface scenarios commonly encountered in industrial settings. We were able to produce improved G-optimal designs for the second-order model and several sample sizes under experiments with K=1,2,3,4, and 5 design factors using an adaptation of PSO. Thereby, we publish updated knowledge on the best-known exact G-optimal designs. We compare computing cost/time and algorithm efficacy to all previous published results including those generated by the current state-of-the-art (SOA) algorithm, the G(Iλ)-coordinate exchange. PSO is hereby demonstrated to produce better designs than the SOA at commensurate cost. In all, the results of this paper suggest PSO should be adopted by more practitioners as a tool for generating exact optimal designs.

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A non‐approximate method for generating G$G$‐optimal RSM designs

Hansen,

Walsh,

Pan

2024

Quality & Reliability Eng

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We present a nonapproximate computational method for generating ‐optimal designs in response surface methodology (RSM) settings using Gloptipoly, a global polynomial optimizer. Traditional approaches use a grid approximation for computing a candidate design's ‐score. Gloptipoly can find the global optimum of high‐order polynomials thus making it suitable for computing a design's ‐score, that is, its maximum scaled prediction variance, which, for second‐order models, is a quartic polynomial function of the experimental factors. We demonstrate the efficacy and performance of our method through comprehensive application to well‐published examples, and illustrate, for the first time, its application to generating ‐optimal designs supporting models of order greater than 2. This work represents the first non‐approximate computational approach to solving the ‐optimal design problem. This advancement opens new possibilities for finding ‐optimal designs beyond second‐order RSM models.

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A clustering-based coordinate exchange algorithm for generating G-optimal experimental designs

Cited by 4 publications

References 26 publications

Generating optimal designs with user‐specified pure replication structure

Generating optimal designs with user‐specified pure replication structure

Improved G-Optimal Designs for Small Exact Response Surface Scenarios: Fast and Efficient Generation via Particle Swarm Optimization

A non‐approximate method for generating G$G$‐optimal RSM designs

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