A combinatorial optimization problem is a problem finding a combination of variables that optimizes an objective function while satisfying its given constraints.For solving the problem, Ising machines have gained attention as a prominent architecture.However, due to limited computational resources, using only Ising machines may not be able to obtain quasi-optimal solutions.This dissertation proposes two state-of-the-art methods that hybridly utilize an Ising machine and a classical computer.These methods are applicable to various combinatorial optimization problems and can effectively achieve quasi-optimal solutions.Experimental results demonstrated that the proposed methods outperform existing approaches and achieve optimal solutions in several instances.
A combinatorial optimization problem is a problem finding a combination of variables that optimizes an objective function while satisfying its given constraints.For solving the problem, Ising machines have gained attention as a prominent architecture.However, due to limited computational resources, using only Ising machines may not be able to obtain quasi-optimal solutions.This dissertation proposes two state-of-the-art methods that hybridly utilize an Ising machine and a classical computer.These methods are applicable to various combinatorial optimization problems and can effectively achieve quasi-optimal solutions.Experimental results demonstrated that the proposed methods outperform existing approaches and achieve optimal solutions in several instances.
An emerging class of specialized hardware called Ising machines offers a novel approach to tackling computationally intractable combinatorial optimization problems.Specifically, Ising machines are designed to solve problems formulated as the quadratic unconstrained binary optimization (QUBO) problem.However, their widespread practical adoption is currently hindered by several critical obstacles, including the challenge of achieving high solution accuracy, the absence of fair and robust comparative frameworks against traditional optimization methods, and limitations in handling large-scale problems.This dissertation addresses these fundamental challenges through a software-centric approach centered on preprocessing and postprocessing techniques applied to the input and output of Ising machines.This work makes three key contributions.First, a novel preprocessing methodology is proposed to improve accuracy and scalability by linearizing QUBO problems.This technique reduces quadratic terms in the input problem through the extraction of variable ordering relationships, which simplifies the problem structure, enables compact embedding, and offers broader applicability than existing variable reduction methods.The method is successfully validated on QUBO and multi-dimensional knapsack problem instances.Second, a twostage postprocessing methodology is developed to yield feasible, high-quality solutions for constrained problems by adapting basic heuristic principles.This enabled the first fair benchmark of a state-of-the-art Ising machine against traditional heuristics on the quadratic knapsack problem, successfully obtaining high-quality solutions on instances of size up to 2,000 variables.Finally, coefficient reduction techniques for suppressing errors in quantum annealers under realistic minor-embedding conditions are systematically validated.Our findings clarify the practical effectiveness of these methods in improving sample quality on real devices, a crucial area that had been largely unexamined.Collectively, these contributions provide essential software methodologies that bridge the gap between the theoretical promise of Ising machines and their effective real-world application, establishing a foundation for future advancements of Ising machines such as software-hardware co-design to achieve greater improvements in accuracy and scalability.
A combinatorial optimization problem is the problem of minimizing the energy function among many combinations of variables, which is often difficult to solve with conventional classical computers. Recently, Ising machines, including quantum annealers, have gained attention as a promising architecture for efficiently solving combinatorial optimization problems. Among various methods for solving such problems using Ising machines, one prominent approach is the three-stage annealing method. The approach effectively solves a combinatorial optimization problem, utilizing an initial solution, but it performs the annealing process only once. Repeating the annealing process several times may enhance the solution more efficiently. In this paper, we propose a novel hybrid iterative annealing method that consists of an initial process using a classical computer, an annealing process using a quantum annealer, and a correction process/selection process using a classical computer. The proposed method repeats the annealing process and the correction process/selection process until the solution is sufficiently converged. In the experimental evaluations through the three types of typical combinatorial optimization problems, the proposed method shows improvements by up to 54.0% compared to the three-stage annealing method.
One of the problems that conventional computers, such as those based on central processing units, cannot solve is the combinatorial optimization problem, the solution to which is a pattern from among a huge number of combinations of patterns that satisfies a certain condition.Operating on the basis of a new principle, an Ising machine is a computer that specializes in solving this problem.However, there are many challenges to using an Ising machine, such as converting real-world problems into a format that the Ising machine can handle.Research and development of a software development kit and computing system that overcome these challenges are introduced in this article.
This research is concerned with an annealing processor for efficiently solving a combinatorial optimization problem.\nIn order to realize a smart society, optimization of people and thingssuch as transportation networks, power networks, human resource allocationand routes is indispensable. Many of these problems are called combinatorial optimization problems and are known as very important problems in modern society. However, it is known that the combinatorial optimization problem is NP-hard and it is difficult to efficiently solve it with a conventional Neumann computer.\nIn recent years, the miniaturization of the process of manufacturing computer chips is approaching the physical limit. Therefore, especially in the solution by the full search, the improvement in speed due to the calculation speed of the computer cannot be expected. From such a background, dedicated hardware capable of solving a combination optimization problem at high speed and with low power consumption has been attracting attention.\nThe annealing processor is a general-purpose combination optimization solver that utilizes the property that the ground state of the optimization problem expressed by using the Ising model and the optimal solution of the combination optimization problem match. The Ising model is a ferromagnetic model in statistical physics expressed by spins having an upward and downward state, spin-spin interactions occurring between the spins, and an external magnetic field acting on each spin. The Ising model can express a combinatorial optimization problem by expressing a control target and a cost using these parameters. The annealing processor updates the spin state while slowly lowering the temperature parameters based on simulated annealing,which is an optimization method learned from natural phenomena generally called annealing. Eventually, the spin will reach the ground state with a high probability and obtain the optimal solution.\nAnnealing processors are classified into two types, the nearest neighbor type and the fully connected type, depending on the shape of the Ising model simulated on the hardware. In the nearest neighbor type, the coupling between spins is limited to only between adjacent spins, and in the full coupling type, coupling exists between arbitrary spins. The nearest neighbor type realizes high parallel processing by reducing the data spin required by simulated annealing by reducing the proximity spin. In addition, since data transfer is limited to adjacent spins, the scalability is high. However, since the spin-to-spin interaction is sparse, there is a problem that the class of combinatorial optimization problems that can be dealt with is limited, or that the problem requires deformation processing to match the Ising model of hardware. The fully connected type can solve any class of problems as long as the number of spins permits, however it requires connections between arbitrary spins.Therefore, scalability is low. Because there there is a dependency on all spins,the number of spins that can be updated at one time is always limited to only one regardless of the total number of spins. Therefore, it takes time to converge to the ground state.\nIn this research, we propose a method of increasing the number of spins for this annealing processor by using (1) a spatially-expanded time-division processing mechanism architecture based on a loosely-coupled type, (2) An algorithm for applying a fully coupled Ising network to a more complex Ising network using the nearest neighbor Ising network and an annealing method that can be updated in parallel, (3)We conducted a study on the architecture of a fully coupled annealing processor for parallel updating annealing.\nAs described above, the research described in this paper contributes to the improvement of the efficiency of the annealing processor for solving the large-scale combinatorial optimization problem from both the fundamental algorithm and the hardware architecture. I hope that this research will solve the combinatorial optimization problem that is expected to increase in demand in the future and contribute to the development of human society.
A combinatorial optimization problem is the problem of minimizing the energy function among many combinations of variables, which is often difficult to solve with conventional classical computers. Recently, Ising machines, including quantum annealers, have gained attention as a promising architecture for efficiently solving combinatorial optimization problems. Among various methods for solving such problems using Ising machines, one prominent approach is the three-stage annealing method. The approach effectively solves a combinatorial optimization problem, utilizing an initial solution, but it performs the annealing process only once. Repeating the annealing process several times may enhance the solution more efficiently. In this paper, we propose a novel hybrid iterative annealing method that consists of an initial process using a classical computer, an annealing process using a quantum annealer, and a correction process/selection process using a classical computer. The proposed method repeats the annealing process and the correction process/selection process until the solution is sufficiently converged. In the experimental evaluations through the two types of typical combinatorial optimization problems, the proposed method shows improvements by up to 50.5% compared to the three-stage annealing method.