  This paper provides a systematic investigation into the various nonlinear
objective functions which can be used to explore the feasible space associated
with the optimal power flow problem. A total of 40 nonlinear objective
functions are tested, and their results are compared to the data generated by a
novel exhaustive rejection sampling routine. The Hausdorff distance, which is a
min-max set dissimilarity metric, is then used to assess how well each
nonlinear objective function performed (i.e., how well the tested objective
functions were able to explore the non-convex power flow space). Exhaustive
test results were collected from five PGLib test-cases and systematically
analyzed.
