A Three-Stage Annealing Method Solving Slot-Placement Problems Using an Ising Machine

Ising machines are promising alternatives to solve combinatorial optimization problems, which search for their quasi-optimal solutions with high speed and high accuracy. However, the obtained solution much depends on the initial spin states, since the computation time is finite. Moreover, due to their probabilistic nature, they cannot always satisfy the constraints given to combinatorial optimization problems. In this paper, we propose a three-stage annealing method, targeting a slot-placement problem as a typical but difficult example of combinatorial optimization problems. The proposed method is composed of an initial process, an annealing process, and a correction process. The initial process and the correction process are executed by a classical computer while the annealing process is executed by an Ising machine. In the initial process, we give initial spin values that lead to a relatively good solution to the combinatorial optimization problem, which satisfies the given constraints. Then, the annealing process is executed by an Ising machine, and the solution obtained by the annealing process is further corrected to satisfy the constraints. The experimental results demonstrate that the proposed method reduces a minimum total weighted wiring length by 0.0898%-2.45% on average depending on the initial process methods used, compared to the existing method. The mean total weighted wiring length is reduced by 2.79%-7.08% on average depending on the initial process methods used.