Abstract
The application of Genetic Programming (GP) to the
discovery of empirical laws most often suffers from two
limitations. The first one is the size of the search
space; the second one is the growth of non-coding
segments, the introns, which exhausts the memory
resources as GP evolution proceeds. These limitations
are addressed by combining Genetic Programming and
Stochastic Grammars. On one hand, grammars are used to
represent prior knowledge; for instance, context-free
grammars can be used to enforce the discovery of
dimensionally consistent laws, thereby significantly
restricting GP search space. On the other hand, in the
spirit of distribution estimation algorithms, the
grammar is enriched with derivation probabilities. By
exploiting such probabilities, GP avoids the intron
phenomenon. The approach is illustrated on a real-world
like problem, the identification of behavioral laws in
Mechanics.
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