Efficient Hypomixability Elimination in Recombinative Evolutionary Systems∗

We submit that adaptation in recombinative evolutionary systems is powered by an implicit form of computation called Hypomixability Elimination. We describe hypomixability elimination, and provide evidence that it can be performed efficiently by recombinative evolutionary systems. Specifically we show that hypomixability elimination in a simple genetic algorithm can be used to obtain optimal bounds on the time and queries required to solve a subclass (k = 7, η = 1/5) of a familiar computational learning problem: PAC-learning parities with noisy membership queries; where k is the number of relevant attributes and η is the oracle’s noise rate. We show that a simple genetic algorithm that treats the noisy membership query oracle as a fitness function can be rigged to PAC-learn the relevant variables in O(log(n/δ)) queries and O(n log(n/δ)) time, where n is the total number of attributes and δ is the probability of error. To the best of our knowledge, this is the first time optimally efficient non-trivial computation has been shown to occur in an evolutionary algorithm. The optimality result and indeed the implicit implementation of hypomixability elimination by a simple genetic algorithm depends crucially on recombination. This dependence yields a fresh, unified explanation for sex, adaptation, speciation, and the emergence of modularity in recombinative evolutionary systems. Compared to other explanations, Hypomixability Theory is exceedingly parsimonious. For example, it does not assume deleterious mutation, a changing fitness landscape, or the existence of building blocks.