Affiliations: Department of Mathematics, Wayne State University, Detroit, MI 48202 | Dortmund Informatik Centrum, Joseph-von-Frounhofer-Str. 20, D-44227, Dortmund, Germany | Dortmund University, FB Informatik 11, D-44221, Dortmund, Germany
Note: [] This research was supported in part by the National Science Foundation under grant DMS-9224372, and in part by the Deutscher Akademischer Austauschdienst.
Note: [] The research of this author was supported by BMFT under grant 01 IB 403A, project EVOALG.
Abstract: This work is our first attempt in establishing the connections between evolutionary computation algorithms and stochastic approximation procedures. By treating evolutionary algorithms as recursive stochastic procedures, we study both constant gain and decreasing step size algorithms. We formulate the problem in a rather general form, and supply the sufficient conditions for convergence (both with probability one, and in the weak sense). Among other things, our approach reveals the natural connection of the discrete iterations and the continuous dynamics (ordinary differential equations, and/or stochastic differential equations). We hope that this attempt will open up a new horizon for further research and lead to in depth understanding of the underlying algorithms.
