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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Stephen J. Walsh & John J. Borkowski, 2022. "Improved G -Optimal Designs for Small Exact Response Surface Scenarios: Fast and Efficient Generation via Particle Swarm Optimization," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4245-:d:971295
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    References listed on IDEAS

    as
    1. Weng Kee Wong & Ray-Bing Chen & Chien-Chih Huang & Weichung Wang, 2015. "A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-23, June.
    2. Chen, Ray-Bing & Hsu, Yen-Wen & Hung, Ying & Wang, Weichung, 2014. "Discrete particle swarm optimization for constructing uniform design on irregular regions," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 282-297.
    3. Yu Shi & Zizhao Zhang & Weng Kee Wong, 2019. "Particle swarm based algorithms for finding locally and Bayesian D-optimal designs," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-17, December.
    4. Chang Li & Daniel C. Coster, 2014. "A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, March.
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