  Classical benchmark problems utilize multiple transformation techniques to
increase optimization difficulty, e.g., shift for anti centering effect and
rotation for anti dimension sensitivity. Despite testing the transformation
invariance, however, such operations do not really change the landscape's
"shape", but rather than change the "view point". For instance, after rotated,
ill conditional problems are turned around in terms of orientation but still
keep proportional components, which, to some extent, does not create much
obstacle in optimization. In this paper, inspired from image processing, we
investigate a novel graphic conformal mapping transformation on benchmark
problems to deform the function shape. The bending operation does not alter the
function basic properties, e.g., a unimodal function can almost maintain its
unimodality after bent, but can modify the shape of interested area in the
search space. Experiments indicate the same optimizer spends more search budget
and encounter more failures on the conformal bent functions than the rotated
version. Several parameters of the proposed function are also analyzed to
reveal performance sensitivity of the evolutionary algorithms.
