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.Optimal designs are basically model dependent; therefore, model discrimination has received great attention in literature also following different approaches, which can be grouped according to the methodological approach. The first class of contributions deals with model discrimination together with other issues, in particular the parameter estimation. In this regard, following the seminal contributions by [14,15] and [7], constrained optimality based on D-optimality is introduced, and the concept of canonical moments is expounded in order to find an optimal design and to choose the best model. In [16], an optimal robust design for polynomial regression models is developed by eliciting priors onˇ-coefficients as weight, as previously introduced in [15].In addition, in [17], generalization of previous optimality measures, such as in [4], is developed; while in [18], further issues are studied for the Fourier regression model and the power of the F -test. It must be noted that in [18], for discriminating among designs/models, the weights and the power of tests are evaluated by considering D-optimal restricted criterions.Undoubtedly, modeling discrimination and parameter estimation compared with T-optimality, as stated in [19], share common features and properties but, at the same time, the sequential nature of T-optimality may be viewed as a specific characteristic that is not a fundamental feature when applying D-optimality [1,5]. Nonetheless, as in [20] and [21], the T-optimality algorithm works through an adaptive sequential scheme, and the power of the F -test is affected by this selection process.A different approach for efficiently designing experimental strategies is to adopt an evolutionary paradigm [22][23][24][25][26][27]. This approach is fundamentally led by an optimization process that iteratively evolves the initial design toward some op...