Grammar-guided genetic programming and dimensional consistency: application to non-parametric identification in mechanics

Although genetic programming has often successfully been applied to non-parametric modeling, it is frequently impaired by the huge size of the search space explored. Domain knowledge is a powerful way to trim out the size of the space, by restricting the search to a priori relevant models. A most natural domain knowledge in scientific modeling is known as dimensional analysis, stipulating that the models must be consistent with regards to the variable measurement units.In this paper, it is shown that dimensional analysis can automatically be expressed as a context free grammar. Dimensionally-aware GP is thus achieved by employing the dimensional grammar within the grammar-guided GP framework first investigated by Gruau [On using syntactic constraints with genetic programming, in: P. Angeline, K.E. Kinnear Jr. (Eds.), Advances in Genetic Programming II, MIT Press, Cambridge, MA, 1996, pp. 377–394.].However, grammar-guided genetic programming encounters severe difficulties when it involves a complex grammar, which might explain why this approach has not been widely used so far. The drawback is blamed on the initialization step, which hardly constructs a sufficiently diversified initial population, thus hindering the success of evolution. This limitation is addressed by a new CFG compliant initialization procedure.The approach is validated on two problems related to the identification of mechanical properties of materials