Convergence and calculation efficiency analysis of abstract model of nonlinear genetic algorithm based on function group

Through mechanism analysis of genetic algorithm (GAs), every genetic operator of SGA and their combination action can be considered as linear transformations to the corresponding individuals. By modifying the traditional genetic operators, the nonlinear genetic algorithm (NGA) is introduced. In this paper, abstract model of NGA based on function group is discussed in which every function is selected with some probability, and if the function group is correctly selected, then the algorithm can be convergent to global optimal within every given generation number. With this technique the premature convergence and calculation efficiency may be solved.