Analytical and numerical investigations of evolutionary algorithms in continuous spaces

We investigate the biologically motivated selfreproduction strategies, by numerical and analytical calculations. In the analytical part we show that each of these strategies can be reduced to a eigenvalue problem of Sturm-Liouville-type. The properties of the landscape and the dynamics of the optimization are encoded in the spectrum of the Hamiltonian, which is different in both cases. We discuss some model cases with exact solutions and compare it with simulations.