  In this report, we describe three encodings of the multiple constant
multiplication (MCM) problem to pseudo-boolean satisfiability (PBS), and
introduce an algorithm to solve the MCM problem optimally. To the best of our
knowledge, the proposed encodings and the optimization algorithm are the first
formalization of the MCM problem in a PBS manner. This report evaluates the
complexity of the problem size and the performance of several PBS solvers over
three encodings.
