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. 1 Introduction The optimization problem appears in several fields of physics and mathematics. It is known from mathematics that every local minimum of a convex function defined over a convex set is also the global minimum of the function. But the main problem is to find this optimum. From the physical point of view every dynamical process can be considered in terms of finding the optimum of the action functional. The best example is the trajectory of the free point mass in mechanics which follows the shortest way between..