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Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs

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  • Masoudi, Ehsan
  • Holling, Heinz
  • Wong, Weng Kee

Abstract

Finding optimal designs for nonlinear models is complicated because the design criterion depends on the model parameters. If a plausible region for these parameters is available, a minimax optimal design may be used to remove this dependency by minimizing the maximum inefficiency that may arise due to misspecification in the parameters. Minimax optimal designs are often analytically intractable and are notoriously difficult to find, even numerically. A population-based evolutionary algorithm called imperialist competitive algorithm (ICA) is applied to find minimax or nearly minimax D-optimal designs for nonlinear models. The usefulness of the algorithm is also demonstrated by showing it can hybridize with a local search to find optimal designs under a more complicated criterion, such as standardized maximin optimality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:330-345
    DOI: 10.1016/j.csda.2016.06.014
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    References listed on IDEAS

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    Cited by:

    1. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    2. Chen, Ping-Yang & Chen, Ray-Bing & Chen, Yu-Shi & Wong, Weng Kee, 2023. "Numerical Methods for Finding A-optimal Designs Analytically," Econometrics and Statistics, Elsevier, vol. 28(C), pages 155-162.
    3. Lei He & Rong-Xian Yue, 2022. "$$I_L$$ I L -optimal designs for regression models under the second-order least squares estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 53-66, January.
    4. Carlos de la Calle-Arroyo & Miguel A. González-Fernández & Licesio J. Rodríguez-Aragón, 2023. "Optimal Designs for Antoine’s Equation: Compound Criteria and Multi-Objective Designs via Genetic Algorithms," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    5. Xin Liu & Rong‐Xian Yue & Weng Kee Wong, 2022. "Equivalence theorems for c and DA‐optimality for linear mixed effects models with applications to multitreatment group assignments in health care," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1842-1859, December.

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