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    The high dimensional nature of the experimental research space is increasingly present in a variety of scientific areas, and characterizes at the moment most of biochemical experimentation. High dimensionality may pose serious problems in design the experiments because of the cost and feasibility of a large number of experiments, as requested by classical combinatorial design of experiments. In this work we propose a predictive approach based on neural network stochastic models where the design is derived in a sequential evolutionary way. From a set of neural networks trained on an initial random population of experiments, the best predictive net is chosen on a different validation set of experiments and adopted to predict the unknown space. The experiments which satisfy a predefined optimality criterion are then chosen and added to the initial population to form a second generation of experiments. The algorithm then proceeds through generations with a stopping rule on the convergence of the result. This approach, that allows to investigate large experimental spaces with a very small number of experiments, has been evaluated with a simulation study and shows a very good performance also in comparison with the genetic algorithm's approach.