February 15, 2020
Grammatical Evolution, Evolutionary Computing
Crossover in Evolutionary computing is considered as a computing concept and currently has little theoretical framework. Crossover Magma is introduced as the beginning of Lie Algebra-like theoretical foundation for not only Evolutionary computing but hopefully as a formal language for all discourses in any Evolution theory. Crossover Magma is non-Commutative and non-Associative with familiar algebraic structures which easily could expand as a new theory. Non-Associativity imbues the Evolutionary computing with a novel concept of a computable Curvature based upon the Associator. The latter Curvature of Evolution flags the failure of Monoidal Categorification of Crossover. Therefore any theory of Evolution fails to Categorify except at null Curvature offsprings. And the larger the Curvature of the Evolution the more varied offsprings, the smaller the Curvature the more stable or stagnate offsprings. In summary the Crossover non-Associative Magma structures a geometry for an Evolutionary system including Left Translations and Curvature. Left Translations evolve the parent down the evolutionary tree, so to say, and Curvature shapes the amount of variations in regions of the Evolution's geometry. In conclusion, every Evolution synthesizes an emergent evolved space with familiar spatial attributes e.g. translations and curvature.