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

Stephen J. Walsh () and John J. Borkowski
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Stephen J. Walsh: Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
John J. Borkowski: Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA

Mathematics, 2022, vol. 10, issue 22, 1-17

Abstract: 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 ( I λ ) -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.

Keywords: coordinate exchange; Genetic Algorithms; Particle Swarm Optimization; G -optimality; response surface designs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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