  Combinatorial optimization problems are ubiquitous in various disciplines and
applications. Many heuristic algorithms have been devoted to solve these types
of problems. In order to increase the efficiency for finding the optimal
solutions, an application-specific hardware, called digital annealer (DA) has
been developed for solving combinatorial optimization problems using quadratic
unconstrained binary optimization (QUBO) formulations. In this study, we
formulated the number partitioning problem and the graph partitioning problem
into QUBO forms and solved such problems with the DA developed by Fujitsu Ltd.
The QUBO formulation of the number partitioning problem is fully connected. The
DA found the overall runtime for the optimal solution to be less than 30
seconds for 6500 binary variables. For the graph partitioning problem, we
adopted modularity as the metric for determining the quality of the partitions.
For Zachary's Karate Club graph, the modularity obtained was 0.445, a 6%
increase against D-wave Quantum Annealer and Simulated Annealing. Moreover, to
explore the DA's potential applications to real-world problems, we used the
search for communities or virtual microgrids in a power distribution network as
an example. The problem was formulated into graph partitioning. It is shown
that the DA effectively identified community structures in the IEEE 33-bus and
IEEE 118-bus network.
