Adaptive Drift Analysis

We show that the (1+1) evolutionary algorithm using an arbitrary mutation rate p = c/n, c a constant, finds the optimum of any n-bit pseudo-Boolean linear function f in expected time Θ(n log n). Since previous work shows that universal drift functions cannot exist for c larger than a certain constant, we define drift functions depending on p and f. This seems to be the first time in the theory of evolutionary algorithms that drift functions are used that take into account the particular problem instance.

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