Runtime Analysis Of The (1+1) Evolutionary Algorithm On Strings Over Finite Alphabets

In this work, we investigate a (1+1) Evolutionary Algorithm for optimizing functions over the space {0, ... , r}(n), where r is a positive integer. We show that for linear functions over {0, 1, 2}(n), the expected runtime time of this algorithm is O(n log n). This result generalizes an existing result on pseudo-Boolean functions and is derived using drift analysis. We also show that for large values of r, no upper bound for the runtime of the (1+1) Evolutionary Algorithm for linear function on {0, ... , r}(n) can be obtained with this approach nor with any other approach based on drift analysis with weight-independent linear potential functions.