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To initialize a high dimensional system design process, it is very important to be able to develop an initial estimate of its design parameters to satisfy designer required specifications. For new emerging designs, this estimate has to be made based on a limited available set of examples. Moreover, a practical estimate prediction strategy should be flexible enough having no distinction between input (specified constraints) and outputs (parameters required to be estimated), since these vary from one design case to another. In other words, the same design parameter may be a specified constraint in a certain application and it may be the desired design parameter that we seek to estimate to achieve a certain design goal in another application. Conventional regression-based techniques, which are usually employed to provide the required estimates, lack this flexibility. Furthermore, they suffer from low accuracy in case of a small number of available examples. In addition to that, they fail to capture the interrelation between different design parameters. To overcome these limitations and others, the present paper proposes a new approach based on a system of artificial neural-networks (ANNs). The paper uses a ship design case study for demonstrating the merits of the proposed approach. An additional contribution of the paper is that it defines new assessment measures suitable for evaluating the performance and the reliability of any design methodology. This is to be considered a necessary asset for judging the adequacy of new proposed design methodologies before actually employing them in the design of real-life challenging practical applications.