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Multi-objective optimisation of split-plot designs

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  • Borrotti, Matteo
  • Sambo, Francesco
  • Mylona, Kalliopi

Abstract

Modern experiments allow scientists to tackle scientific problems of increasing complexity. Often experiments are characterised by factors that have levels which are harder to set than others. A possible solution is the use of a split-plot design. Many solutions are available in the literature to find optimal designs that focus solely on optimising a single criterion. Multi-criteria approaches have been developed to overcome the limitations of the one-objective optimisation, however they mainly focus on estimating the precision of the fixed factor effects, ignoring the variance component estimation. The Multi-Stratum Two-Phase Local Search (MS-TPLS) algorithm for multi-objective optimisation of designs of experiments is extended, in order to ensure pure-error estimation of the variance components. The proposed solution is applied to two motivating problems and the final optimal Pareto front and related designs are compared with other designs from the relevant literature. Experimental results show that the designs from the obtained Pareto front represent good candidate solutions based on the different objectives.

Suggested Citation

  • Borrotti, Matteo & Sambo, Francesco & Mylona, Kalliopi, 2023. "Multi-objective optimisation of split-plot designs," Econometrics and Statistics, Elsevier, vol. 28(C), pages 163-172.
    • Handle: RePEc:eee:ecosta:v:28:y:2023:i:c:p:163-172
    DOI: 10.1016/j.ecosta.2022.04.001
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    References listed on IDEAS

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    1. Steven G. Gilmour & Luzia A. Trinca, 2012. "Optimum design of experiments for statistical inference," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(3), pages 345-401, May.
    2. MACHARIA, Harrison & GOOS, Peter, 2010. "D-optimal and D-efficient equivalent-estimation second-order split-plot designs," Working Papers 2010011, University of Antwerp, Faculty of Business and Economics.
    3. Bradley Jones & Peter Goos, 2009. "D-optimal design of split-split-plot experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 67-82.
    4. JONES, Bradley & GOOS, Peter, 2012. "I-optimal versus D-optimal split-plot response surface designs," Working Papers 2012002, University of Antwerp, Faculty of Business and Economics.
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