論文

Constrained combinatorial optimization problems (CCOPs) are challenging to solve due to the exponential growth of the solution space. When tackled with Ising machines, constraints are typically enforced by the penalty function method, whose coefficients must be carefully tuned to balance feasibility and objective quality. Variable-reduction techniques such as sample persistence variable reduction (SPVAR) can mitigate hardware limitations of Ising machines, yet their behavior on CCOPs remains insufficiently understood. Building on our prior proposal, we extend and comprehensively evaluate multi-penalty SPVAR (MP-SPVAR), which fixes variables using solution persistence aggregated across multiple penalty coefficients. Experiments on benchmark problems, including the quadratic assignment problem and the quadratic knapsack problem, demonstrate that MP-SPVAR attains higher feasible-solution ratios while matching or improving approximation ratios relative to the conventional SPVAR algorithm. An examination of low-energy states under small penalties clarifies when feasibility degrades and how encoding choices affect the trade-off between solution quality and feasibility. These results position MP-SPVAR as a practical variable-reduction strategy for CCOPs and lay a foundation for systematic penalty tuning, broader problem classes, and integration with quantum-inspired optimization hardware as well as quantum algorithms.

Black-box (BB) optimization problems aim to identify an input that minimizes the output of a function (the BB function) whose input-output relationship is unknown. Factorization machine with annealing (FMA) is a promising approach to this task, employing a factorization machine (FM) as a surrogate model to iteratively guide the solution search via an Ising machine. Although FMA has demonstrated strong optimization performance across various applications, its performance often stagnates as the number of optimization iterations increases. One contributing factor to this stagnation is the growing number of data points in the dataset used to train FM. It is hypothesized that as more data points are accumulated, the contribution of newly added data points becomes diluted within the entire dataset, thereby reducing their impact on improving the prediction accuracy of FM. To address this issue, we propose a novel method for sequential dataset construction that retains at most a specified number of the most recently added data points. This strategy is designed to enhance the influence of newly added data points on the surrogate model. Numerical experiments demonstrate that the proposed FMA achieves lower-cost solutions with fewer BB function evaluations compared to the conventional FMA.

To tackle combinatorial optimization problems using an Ising machine, the objective function and constraints must be mapped onto a quadratic unconstrained binary optimization (QUBO) model. While QUBO involves binary variables, combinatorial optimization problems frequently include integer variables, which require encoding by binary variables. This process, known as binary-integer encoding, includes various methods, one of which is domain-wall encoding - a recently proposed approach. Experiments on a quantum annealing machine have demonstrated that domain-wall encoding outperforms the commonly used one-hot encoding in terms of objective function value and the probability of obtaining the optimal solution. In a digital Ising machine, domain-wall encoding required less computation time to reach optimal solutions compared to one-hot encoding. However, its practical effectiveness in digital Ising machines remains unclear. To address this uncertainty, the performance of one-hot and domain-wall encoding methods was evaluated on a digital Ising machine using the quadratic knapsack problem (QKP). The comparison focused on the dependency of penalty coefficient and sensitivity to computation time. Domain-wall encoding demonstrated a higher feasible solution rate when relative penalty coefficients for the two constraint terms were adjusted, a strategy not commonly used in previous studies. Additionally, domain-wall encoding obtained higher performance practical evaluation metrics for QKPs with large knapsack capacities compared to one-hot encoding. Furthermore, it was observed to be more sensitive to computation time than one-hot encoding.

In elementary schools, immunologically immature students come into close contact with each other and are susceptible to the spread of infectious diseases. To analyze pathogen transmission among students, it is essential to obtain behavioral data. Questionnaires and wearable sensor devices were used for communication behavior and swab sampling was employed for contact behavior. However, these methods have been insufficient in capturing information about the processes and actions of each student that contribute to pathogen transmission. Therefore, in this study, actual behavioral data were collected using video recordings to evaluate droplet and contact transmission in elementary schools. The analysis of communication behavior revealed the diverse nature of interactions among students. By calculating the droplet transmission probabilities based on conversation duration, the risk of droplet transmission was quantified. In the contact behavior, we introduced a novel approach for constructing contact networks based on contact history. According to this method, well-known items, such as students’ desks, doors, and faucets, were predicted to be potential fomite. In addition, students’ shirts and shared items with high contact frequency and high centrality metrics in the network, which were not evaluated in swab sampling surveys, were identified as potential fomites. The reliability of the predictions was demonstrated through micro-simulations. The micro-simulations replicated virus transmission scenarios in which virus-carrying students were present in the actual contact history. The results showed that a significant amount of virus adhered to the items predicted to be fomites. Interestingly, the micro-simulations indicated that most viral copies were transmitted through single items. The analysis of contact history, contact networks, and micro-simulations relies on videorecorded behavioral data, highlighting the importance of this method. This study contributes significantly to the prevention of infectious diseases in elementary schools by providing evidence-based information about transmission pathways and behavior-related risks.

To enhance the performance of quantum annealing machines, several methods have been proposed to reduce the number of spins by fixing spin values through preprocessing. We proposed a hybrid optimization method that combines a simulated annealing (SA)-based non-quantum-type Ising machine with a quantum annealing machine. However, its applicability remains unclear. Therefore, we evaluated the performance of the hybrid method on large-size Ising models and analyzed its characteristics. The results indicate that the hybrid method improves upon solutions obtained by the preprocessing SA, even if the Ising models cannot be embedded in the quantum annealing machine. We analyzed the method from three perspectives: preprocessing, spin-fixed sub-Ising model generation method, and the accuracy of the quantum annealing machine. From the viewpoint of the minimum energy gap, we found that solving the sub-Ising model with a quantum annealing machine results in a higher solution accuracy than solving the original Ising model. Additionally, we demonstrated that the number of fixed spins and the accuracy of the quantum annealing machine affect the dependency of the solution accuracy on the sub-Ising model size.

Ising machines have been developed as fast and highly accurate solvers for combinatorial optimization problems. They are classified based on their internal algorithms, with examples including simulated-annealing-based Ising machines (non-quantum-type Ising machines) and quantum-annealing-based Ising machines (quantum annealers). Herein, we have investigated the performance of a hybrid optimization method that capitalizes on the advantages of both types, utilizing a non-quantum-type Ising machine to enhance the performance of the quantum annealer. In this method, the non-quantum-annealing Ising machine initially solves an original Ising model multiple times during preprocessing. Subsequently, reduced-size sub-Ising models, generated by spin fixing, are solved by a quantum annealer. Performance of the method is evaluated via simulations using Simulated Annealing (SA) as a non-quantum-type Ising machine and D-Wave Advantage as a quantum annealer. Additionally, we investigate the parameter dependence of the hybrid optimization method. The method outperforms the preprocessing SA and the quantum annealer alone in fully connected random Ising models.

Ising machines have attracted attention as efficient solvers for combinatorial optimization problems, which are formulated as ground-state (lowest-energy) search problems of the Ising model. Due to the limited bit-width of coefficients on Ising machines, the Ising model must be transformed into a bit-width reduced (BWR) Ising model. According to previous research, the bit-width reduction method, which adds auxiliary spins, ensures that the ground state of the BWR Ising model is theoretically the same as the Ising model before bit-width reduction (original Ising model). However, while the dynamical process is closely related to solution accuracy, how the BWR Ising model progresses towards the ground state remains to be elucidated. Therefore, we compared the dynamical processes of these models using simulated annealing (SA). Our findings reveal significant differences in the dynamical process across models. Analysis from the viewpoint of statistical mechanics found that the BWR Ising model has two characteristic properties: an effective temperature and a slow relaxation. These properties alter the temperature schedule and spin flip probability in the BWR Ising model, leading to differences in the dynamical process. Therefore, to obtain the same dynamical process as the original Ising model, we proposed SA parameters for the BWR Ising model. We demonstrated the proposed SA parameters using a square lattice Ising model, in which all coefficients were set uniformly to the same positive values or randomly. Our experimental evaluations demonstrated that the dynamical process of the BWR and original Ising model became closer.