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Maximal age in randomized search heuristics with aging

The concept of aging has been introduced and applied in many different variants in many different randomized search heuristics. The most important parameter is the maximal age of search points. Considering static pure aging known from artificial immune systems in the context of simple evolutionary algorithms, it is demonstrated that the choice of this parameter is both, crucial for the performance and difficult to set appropriately. The results are derived in a rigorous fashion and given as theorems with formal proofs. An additional contribution is the presentation of a general method to combine fitness functions into a function with stronger properties than its components. By application of this method we combine a function where the maximal age needs to be sufficiently large with a function where the maximal age needs to be sufficiently small. This yields a function where an appropriate age lies within a very narrow range.