  Symbolic regression is a powerful system identification technique in
industrial scenarios where no prior knowledge on model structure is available.
Such scenarios often require specific model properties such as
interpretability, robustness, trustworthiness and plausibility, that are not
easily achievable using standard approaches like genetic programming for
symbolic regression. In this chapter we introduce a deterministic symbolic
regression algorithm specifically designed to address these issues. The
algorithm uses a context-free grammar to produce models that are parameterized
by a non-linear least squares local optimization procedure. A finite
enumeration of all possible models is guaranteed by structural restrictions as
well as a caching mechanism for detecting semantically equivalent solutions.
Enumeration order is established via heuristics designed to improve search
efficiency. Empirical tests on a comprehensive benchmark suite show that our
approach is competitive with genetic programming in many noiseless problems
while maintaining desirable properties such as simple, reliable models and
reproducibility.
