Distributed Hybrid Genetic Programming for Learning Boolean Functions

When genetic programming (GP) is used to find programs with Boolean inputs and outputs, ordered binary decision diagrams (OBDDs) are often used successfully. In all known OBDD-based GP-systems the variable ordering, a crucial factor for the size of OBDDs, is preset to an optimal ordering of the known test function. Certainly this cannot be done in practical applications, where the function to learn and hence its optimal variable ordering are unknown. Here, the first GP-system is presented that evolves the variable ordering of the OBDDs and the OBDDs itself by using a distributed hybrid approach. For the experiments presented the unavoidable size increase compared to the optimal variable ordering is quite small. Hence, this approach is a big step towards learning well-generalizing Boolean functions.