Impact of commutative and non-commutative functions on symbolic regression with ACGP

Genetic Programming, as other evolutionary methods, uses selection to drive its search toward better solutions, but its search operators are uninformed and perform uniform search. Constrained GP methodology changes this exploration to pruned non-uniform search, skipping some representation subspaces and giving preferences to others, according to provided heuristics. The heuristics are position-fixed or position-independent and are just preferences on some specific labeling. Adaptable Constrained GP ACGP is a methodology for discovery of such useful heuristics. Both methodologies have previously demonstrated their surprising capabilities using only parent-child and parent-children heuristics. This paper illustrates how the ACGP methodology applies to symbolic regression; demonstrate the power of low-order local heuristics, while also exploring the differences in evolutionary search between commutative and non-commutative functions.