For the problem of calculating a minimum-length string accommodating each subset of a finite alphabet as contiguous substring we propose and investigate a Beam Search. The latter adopts initial symmetry breaking assumptions and carries out a tailored equivalency pruning to thin out the search tree. It works for any subsystem of the power set as well, therefore, on the system of size-k subsets of the finite alphabet, we can compare it to a previously developed metaheuristic approach relying on the Generalized Traveling Salesperson Problem and demonstrate its efficiency.