  In order to formulate mathematical conjectures likely to be true, a number of
base cases must be determined. However, many combinatorial problems are NP-hard
and the computational complexity makes this research approach difficult using a
standard brute force approach on a typical computer. One sample problem
explored is that of finding a minimum identifying code. To work around the
computational issues, a variety of methods are explored and consist of a
parallel computing approach using Matlab, a quantum annealing approach using
the D-Wave computer, and lastly using satisfiability modulo theory (SMT) and
corresponding SMT solvers. Each of these methods requires the problem to be
formulated in a unique manner. In this paper, we address the challenges of
computing solutions to this NP-hard problem with respect to each of these
methods.
