Description of Evolutionary Strategies over continous Parameter

Several standard processes for searching minima of potential functions, such as thermodynamical strategies (simulated annealing) and biologically motivated self-reproduction strategies, are reduced to Schrr odinger eigenvalue problems. The properties of the landscape and the dynamics of the optimization are encoded in the spectrum of the Hamiltonian, which is diierent in both cases. We discuss some model cases with exact solutions. The connection between thermodynamical strategies and biologically motivated self-reproduction strategies is analyzed and interpreted in the above context. In this way we introduce mixing of both strategies as a new powerful tool of optimization.