A mathematical design of genetic operators on \(\mathrm{GL}_n(\mathbb Z_2)\) (Q1718634)

Summary: We study the space that consists of all nonsingular binary matrices, that is, \(\mathrm{GL}_n(\mathbb Z_2)\). The space is quite important in that it is used for the change of basis in binary representation, which is the encoding typically adopted in genetic algorithms. We analyze the properties of \(\mathrm{GL}_n(\mathbb Z_2)\) and theoretically design possible encodings and their corresponding recombination operators for evolutionary algorithms. We present approaches based on elementary matrices of linear algebra as well as typical two-dimensional ones.