An Analysis of the (µ+1) EA on Simple Pseudo-Boolean Functions

Evolutionary Algorithms (EAs) are successfully applied for optimization in discrete search spaces, but theory is still weak in particular for population-based EAs. Here, a first rigorous analysis of the (μ + 1) EA on pseudo-Boolean functions is presented. For three example functions well-known from the analysis of the (1 + 1) EA, bounds on the expected runtime and success probability are derived. For two of these functions, upper and lower bounds on the expected runtime are tight, and the (μ + 1) EA is never more efficient than the (1 + 1) EA. Moreover, all lower bounds grow with μ. On a more complicated function, however, a small increase of μ provably decreases the expected runtime drastically.

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