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

Genetic programming is an often-used technique for symbolic regression:\nfinding symbolic expressions that match data from an unknown function. To make\nthe symbolic regression more efficient, one can also use dimensionally-aware\ngenetic programming that constrains the physical units of the equation.\nNevertheless, there is no formal analysis of how much dimensionality awareness\nhelps in the regression process. In this paper, we conduct a fitness landscape\nanalysis of dimensionallyaware genetic programming search spaces on a subset of\nequations from Richard Feynmans well-known lectures. We define an\ninitialisation procedure and an accompanying set of neighbourhood operators for\nconducting the local search within the physical unit constraints. Our\nexperiments show that the added information about the variable dimensionality\ncan efficiently guide the search algorithm. Still, further analysis of the\ndifferences between the dimensionally-aware and standard genetic programming\nlandscapes is needed to help in the design of efficient evolutionary operators\nto be used in a dimensionally-aware regression.\n