.. _parity: =================== Even-Parity Problem =================== Parity is one of the classical GP problems. The goal is to find a program that produces the value of the Boolean even parity given n independent Boolean inputs. Usually, 6 Boolean inputs are used (Parity-6), and the goal is to match the good parity bit value for each of the :math:`2^6 = 64` possible entries. The problem can be made harder by increasing the number of inputs (in the DEAP implementation, this number can easily be tuned, as it is fixed by a constant named PARITY_FANIN_M). For more information about this problem, see :ref:`refPapersParity`. Primitives set used =================== Parity uses standard Boolean operators as primitives, available in the Python operator module : .. literalinclude:: /../examples/gp/parity.py :lines: 49-55 In addition to the *n* inputs, we add two constant terminals, one at 0, one at 1. .. note:: As Python is a dynamic typed language, you can mix Boolean operators and integers without any issue. Evaluation function =================== In this implementation, the fitness of a Parity individual is simply the number of successful cases. Thus, the fitness is maximized, and the maximum value is 64 in the case of a 6 inputs problems. .. literalinclude:: /../examples/gp/parity.py :pyobject: evalParity `inputs` and `outputs` are two pre-generated lists, to speedup the evaluation, mapping a given input vector to the good output bit. The Python :func:`sum` function works on booleans (false is interpreted as 0 and true as 1), so the evaluation function boils down to sum the number of successful tests : the higher this sum, the better the individual. Conclusion ========== The other parts of the program are mostly the same as the :ref:`Symbolic Regression algorithm `. The complete :example:`gp/parity`. .. _refPapersParity: Reference ========= *John R. Koza, "Genetic Programming II: Automatic Discovery of Reusable Programs", MIT Press, 1994, pages 157-199.*