Fitness Landscape Analysis of Dimensionally-Aware Genetic Programming Featuring Feynman Equations

Abstract: Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic programming that constrains the physical units of the equation. Nevertheless, there is no formal analysis of how much dimensionality awareness helps in the regression process. In this paper, we conduct a fitness landscape analysis of dimensionallyaware genetic programming search spaces on a subset of equations from Richard Feynmans well-known lectures. We define an initialisation procedure and an accompanying set of neighbourhood operators for conducting the local search within the physical unit constraints. Our experiments show that the added information about the variable dimensionality can efficiently guide the search algorithm. Still, further analysis of the differences between the dimensionally-aware and standard genetic programming landscapes is needed to help in the design of efficient evolutionary operators to be used in a dimensionally-aware regression.