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Optimal Designs for Antoine’s Equation: Compound Criteria and Multi-Objective Designs via Genetic Algorithms

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  • Carlos de la Calle-Arroyo

    (Escuela de Ingeniería Industrial y Aeroespacial de Toledo, Instituto de Matemática Aplicada a la Ciencia y a la Ingeniería, Universidad de Castilla-La Mancha, E-45071 Toledo, Spain
    Instituto de Ciencia de los Datos e Inteligencia Artificial (DATAI), Universidad de Navarra, E-31009 Pamplona, Spain)

  • Miguel A. González-Fernández

    (Departamento de Informática, Universidad de Oviedo, E-33204 Gijón, Spain)

  • Licesio J. Rodríguez-Aragón

    (Escuela de Ingeniería Industrial y Aeroespacial de Toledo, Instituto de Matemática Aplicada a la Ciencia y a la Ingeniería, Universidad de Castilla-La Mancha, E-45071 Toledo, Spain)

Abstract

Antoine’s Equation is commonly used to explain the relationship between vapour pressure and temperature for substances of industrial interest. This paper sets out a combined strategy to obtain optimal designs for the Antoine Equation for D- and I-optimisation criteria and different variance structures for the response. Optimal designs strongly depend not only on the criterion but also on the response’s variance, and their efficiency can be strongly affected by a lack of foresight in this selection. Our approach determines compound and multi-objective designs for both criteria and variance structures using a genetic algorithm. This strategy provides a backup for the experimenter providing high efficiencies under both assumptions and for both criteria. One of the conclusions of this work is that the differences produced by using the compound design strategy versus the multi-objective one are very small.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:693-:d:1050979
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Hamada M. & Martz H. F. & Reese C. S. & Wilson A. G., 2001. "Finding Near-Optimal Bayesian Experimental Designs via Genetic Algorithms," The American Statistician, American Statistical Association, vol. 55, pages 175-181, August.
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