Unified description of evolutionary strategies over continuous parameter spaces

Several standard processes for searching minima of potential functions, such as thermodynamical strategies (simulated annealing) and biologically motivated self-reproduction strategies, are reduced to Schrödinger eigenvalue problems. 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. The connection between thermodynamical strategies and biologically motivated self-reproduction is analyzed and interpreted in the above context. In this way we introduce mixing of both strategies as a new powerful tool of optimization.