Theory of Genetic Algorithms with Α-selection

Genetic algorithms are random heuristic search (RHS) algorithms for adaptive systems with a wide range of applications in search, optimisation, pattern recognition and machine learning as well as signal processing. Despite their widespread use a general theory is still lacking. A promising approach is offered by the dynamical system model which describes the stochastic trajectory of a population under the dynamics of a genetic algorithm with the help of an underlying deterministic heuristic function and its fixed points. However, even for the simple genetic algorithm (SGA) with fitnessproportional selection, crossover and mutation the determination of the population trajectory and the fixed points of the heuristic function is unfeasible for practical problem sizes. In order to simplify the mathematical analysis α-selection is introduced in this paper. Based on this strong selection scheme it is possible to derive the dynamical system model and the respective fixed points in closed form. In addition to the theoretical analysis experimental results are presented.