Robust Pareto Design of GMDH-type Neural Networks for Systems with Probabilistic Uncertainties. N. Nariman-zadeh, F. Kalantary, A. Jamali, F. Ebrahimi

Abstract. In this paper, multi-objective evolutionary Pareto optimal design of Group Method of Data Handling (GMDH)-type neural networks have been used for modelling of systems using input-output data sets with probabilistic uncertainties. In this way, A Monte Carlo Simulation (MCS) is first performed to generate input-output data set using some probabilistic distributions. Multi-objective genetic algorithms (GAs) are then used for Pareto optimization of GMDH-type neural networks. The important conflicting objectives of GMDH-type neural networks that are considered in this work are, namely, the mean and variance of both Training Error (TE) and Prediction Error (PE) of such neural networks. It is shown that a robust GMDH-type neural network can be simply obtained using a criterion based on four values of means and variances of both TE and PE. The probabilistic evolved GMDH model exhibits much more robustness to the uncertainties involved within the input-output data sets than that of the deterministic evolved GMDH model. It is shown that GMDH-type neural networks can be successfully applied for input-output data set with uncertainties so that a robust polynomial neural network can be compromisingly obtained from some non-dominated optimum GMDH models.

Keywords. Multi-objective optimization, Genetic algorithms, GMDH, Pareto, _MonteCarlo, Uncertainties.

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