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

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  • Weng Kee Wong
  • Ray-Bing Chen
  • Chien-Chih Huang
  • Weichung Wang

Abstract

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].

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0124720
    DOI: 10.1371/journal.pone.0124720
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    References listed on IDEAS

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    1. Min Yang & Stefanie Biedermann & Elina Tang, 2013. "On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1411-1420, December.
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    1. Saeid Pooladsaz & Mahboobeh Doosti-Irani, 2024. "An algorithm for generating efficient block designs via a novel particle swarm approach," Computational Statistics, Springer, vol. 39(5), pages 2437-2449, July.
    2. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. 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.
    4. Aiste Ruseckaite & Peter Goos & Dennis Fok, 2017. "Bayesian D-optimal choice designs for mixtures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 363-386, February.
    5. Masoudi, Ehsan & Holling, Heinz & Wong, Weng Kee, 2017. "Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 330-345.
    6. Haoyu Wang & Chongqi Zhang, 2022. "The mixture design threshold accepting algorithm for generating $$\varvec{D}$$ D -optimal designs of the mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 345-371, April.
    7. Xiao-Dong Zhou & Yun-Juan Wang & Rong-Xian Yue, 2018. "Robust population designs for longitudinal linear regression model with a random intercept," Computational Statistics, Springer, vol. 33(2), pages 903-931, June.

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