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T-optimality and neural networks: a comparison of approaches for building experimental designs

Authors


Correspondence to: Rossella Berni, Department of Statistics ‘G.Parenti’ University of Florence Viale Morgagni 59, 50134 Florence, Italy.

E-mail: berni@ds.unifi.it

Abstract

This paper deals with optimal experimental design criteria and neural networks in the aim of building experimental designs from observational data. It addresses the following three main issues: (i) the introduction of two radically different approaches, namely T-optimal designs extended to Generalized Linear Models and Evolutionary Neural Networks Design; (ii) the proposal of two algorithms, based on model selection procedures, to exploit the information of already collected data; and (iii) the comparison of the suggested methods and corresponding algorithms by means of a simulated case study in the technological field.

Results are compared by considering elements of the proposed algorithms, in terms of models and experimental design strategies. In particular, we highlight the algorithmic features, the performances of the approaches, the optimal solutions and the optimal levels of variables involved in a simulated foaming process. The optimal solutions obtained by the two proposed algorithms are very similar, nevertheless, the differences between the paths followed by the two algorithms to reach optimal values are substantial, as detailed step-by-step in the discussion. Copyright © 2012 John Wiley & Sons, Ltd.

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