Solving Even-12, -13, -15, -17, -20 and -22 Boolean Parity Problems using Sub-machine Code GP with Smooth Uniform Crossover, Smooth Point Mutation and Demes

In this paper we describe a recipe to solve very large parity problems, using GP without automatically defined functions. The recipe includes three main ingredients: smooth uniform crossover (a crossover operator inspired by theoretical research), sub-machine-code GP (a technique which allows speeding up fitness evaluation in Boolean classification problems by nearly 2 orders of magnitude), and distributed demes (weakly interacting sub-populations running on separate workstations). We tested this recipe on parity problems with up to 22 input variables (i.e. where the fitness function includes 2^22=4,194,304 fitness cases), solving them with a very high success probability.

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