Understanding transforms of pseudo-boolean functions

There exist general transforms that convert pseudo-Boolean functions into k-bounded pseudo-Boolean functions, for all k ≥ 2. In addition to these general transforms, there can also exist specialized transforms that can be applied in special cases. New results are presented examining what happens to the "bit flip" neighborhood when transforms are applied. Transforms condense variables in a particular order. We show that different variable orderings produce different results in terms of problem difficulty. We also prove new results about the embedding of the original function in the new k-bounded function. Finally, this paper also looks at how parameter optimization problems can be expressed as high precision k-bounded pseudo-Boolean functions. This paper lays a foundation for the wider application of evolutionary algorithms to k-bounded pseudo-Boolean functions.