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Modeling of real world data requires many choices to be made, about the size and type of model used parameter value settings and validation criteria. The group method of data handling, GMDH, builds a data-driven polynomial model by constructing a hierarchy of increasingly complex terms. At each level, terms which perform baldly on independent validation data are rejected. Thus the GMDH algorithm performs a search over a small set of different models to find the best. Drawbacks of this method are that the model is conditioned to fit the validation data set and so may not be able to generalize well, and its ability to find a good model is affected by the choice of polynomial terms used. In the work described in this paper, we demonstrate a new method of optimizing the basic GMDH approach using genetic algorithms which avoids an exhaustive search of all possible polynomials. Specifically, multi- objective genetic algorithms can be used to optimize the model to several different constraints, encouraging a good bias- variance trade-off. To illustrate this, the method is tested on data arising from the financial markets and the weather.
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