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Generating Robust Optimal Mixture Designs Due to Missing Observation Using a Multi-Objective Genetic Algorithm

Author

Listed:
  • Wanida Limmun

    (Center of Excellence in Data Science for Health Study, Department of Mathematics and Statistics, Walailak University, Thasala, Nakhon Si Thammarat 80161, Thailand)

  • Boonorm Chomtee

    (Department of Statistics, Kasetsart University, Chatuchak, Bangkok 10900, Thailand)

  • John J. Borkowski

    (Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA)

Abstract

Missing observation is a common problem in scientific and industrial experiments, particularly in a small-scale experiment. They often present significant challenges when experiment repetition is infeasible. In this research, we propose a multi-objective genetic algorithm as a practical alternative for generating optimal mixture designs that remain robust in the face of missing observation. Our algorithm prioritizes designs that exhibit superior D-efficiency while maintaining a high minimum D-efficiency due to missing observations. The focus on D-efficiency stems from its ability to minimize the impact of missing observations on parameter estimates, ensure reliability across the experimental space, and maximize the utility of available data. We study problems with three mixture components where the experimental region is an irregularly shaped polyhedral within the simplex. Our designs have proven to be D-optimal designs, demonstrating exceptional performance in terms of D-efficiency and robustness to missing observations. We provide a well-distributed set of optimal designs derived from the Pareto front, enabling experimenters to select the most suitable design based on their priorities using the desirability function.

Suggested Citation

  • Wanida Limmun & Boonorm Chomtee & John J. Borkowski, 2023. "Generating Robust Optimal Mixture Designs Due to Missing Observation Using a Multi-Objective Genetic Algorithm," Mathematics, MDPI, vol. 11(16), pages 1-33, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3558-:d:1219377
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    References listed on IDEAS

    as
    1. Peter Goos & Bradley Jones & Utami Syafitri, 2016. "I-Optimal Design of Mixture Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 899-911, April.
    2. Qiang Long & Changzhi Wu & Xiangyu Wang & Lin Jiang & Jueyou Li, 2015. "A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-17, September.
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