Analytic Investigations of Random Search Strategies for Parameter Optimization

Abstract

Several standard processes for searching minima of potential functions, such as thermodynamical strategies (simulated annealing) and biologically motivated selfreproduction strategies, are reduced to Schr\"odinger problems. The properties of the landscape are encoded in the spectrum of the Hamiltonian. We investigate this relation between landscape and spectrum by means of topological methods which lead to a possible classification of landscapes in the framework of the operator theory. The influence of the dimension $d$ of the search space is discussed. The connection between thermodynamical strategies and biologically motivated selfreproduction strategies is analyzed and interpreted in the above context. Mixing of both strategies is introduced as a new powerful tool of optimization.