This talk begins with a brief look into the origins of the evolution strategies and then provides a contemporary ( ,,, )-variant for numerical optimization purposes. Since theoretical analyses so far have mostly dealt with real-valued variables, Gaussian mutations, averaging or discrete multi-recombination, and deterministic selection (( , )-selection, corresponding to a setting of = 1 , or ( + )-selection, corresponding to = ), an overview of the corresponding results will be given. This concerns non-convergence for fixed mutation strength, conditions for global convergence with probability one, and convergence rates for some prototypic n -dimensional fitness landscapes. Recent results about theoretical benefits of multi-recombination ( = ) are mentioned as well as a couple of open questions.

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1996-1997 Mathematics in High Performance Computing