  In symbolic regression, the search for analytic models is typically driven
purely by the prediction error observed on the training data samples. However,
when the data samples do not sufficiently cover the input space, the prediction
error does not provide sufficient guidance toward desired models. Standard
symbolic regression techniques then yield models that are partially incorrect,
for instance, in terms of their steady-state characteristics or local behavior.
If these properties were considered already during the search process, more
accurate and relevant models could be produced. We propose a multi-objective
symbolic regression approach that is driven by both the training data and the
prior knowledge of the properties the desired model should manifest. The
properties given in the form of formal constraints are internally represented
by a set of discrete data samples on which candidate models are exactly
checked. The proposed approach was experimentally evaluated on three test
problems with results clearly demonstrating its capability to evolve realistic
models that fit the training data well while complying with the prior knowledge
of the desired model characteristics at the same time. It outperforms standard
symbolic regression by several orders of magnitude in terms of the mean squared
deviation from a reference model.
