Toward a Theory of Evolution Strategies: The (µ,lambda)-Theory

The multi-membered Evolution Strategy (ES) acting on parents and offspring is analyzed for real-valued, N-dimensional parameter spaces (N ? 30). N-dependent progress rate formulas are derived for (1; ) and (; ) strategies on spherical models. The analytical results obtained are compared with simulation experiments for the (hyper)sphere and the inclined (hyper)plane. Keywords Evolution Strategy(ES), progress rate theory, multi-membered ES, (; )-selection, truncation selection 1 Introduction State-of-the-art Evolution Strategies (ES) for parameter optimization are multi-membered strategies acting on one or more populations of individuals. This paper deals with strategies denoted by (; ), that is, the best offspring of a population (consisting of individuals) are selected to be the parents for the next generation. Such selection schemes are sometimes called `truncation selection' (Muhlenbein & Schlierkamp-Voosen, 1993). Recombination is not included in this paper. It will be trea..