Abstract
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.
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