  Linear functions play a key role in the runtime analysis of evolutionary
algorithms and studies have provided a wide range of new insights and
techniques for analyzing evolutionary computation methods. Motivated by studies
on separable functions and the optimization behaviour of evolutionary
algorithms as well as objective functions from the area of chance constrained
optimization, we study the class of objective functions that are weighted sums
of two transformed linear functions. Our results show that the (1+1) EA, with a
mutation rate depending on the number of overlapping bits of the functions,
obtains an optimal solution for these functions in expected time O(n log n),
thereby generalizing a well-known result for linear functions to a much wider
range of problems.
