  Benchmarking plays a major role in the development and analysis of
optimization algorithms. As such, the way in which the used benchmark problems
are defined significantly affects the insights that can be gained from any
given benchmark study. One way to easily extend the range of available
benchmark functions is through affine combinations between pairs of functions.
From the perspective of landscape analysis, these function combinations
smoothly transition between the two base functions.
  In this work, we show how these affine function combinations can be used to
analyze the behavior of optimization algorithms. In particular, we highlight
that by varying the weighting between the combined problems, we can gain
insights into the effects of added global structure on the performance of
optimization algorithms. By analyzing performance trajectories on more function
combinations, we also show that aspects such as the scaling of objective
functions and placement of the optimum can greatly impact how these results are
interpreted.
