Tadashi Kadowaki

Tadayoshi Matsumori, Masato Taki, Tadashi Kadowaki

Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We employed the BBO methods to design a printed circuit board for resonance avoidance. This design problem is formulated to maximize natural frequency and simultaneously minimize the number of mounting points. The natural frequency, which is the bottleneck for the QUBO formulation, is approximated to a quadratic model in the BBO method. We demonstrated that BBO using a factorization machine shows good performance in both the calculation time and the success probability of finding the optimal solution. Our results can open up QUBO solvers' potential for other applications in structural designs.

Tadashi Kadowaki, Mitsuru Ambai

In edge computing, suppressing data size is a challenge for machine learning models that perform complex tasks such as autonomous driving, in which computational resources (speed, memory size and power) are limited. Efficient lossy compression of matrix data has been introduced by decomposing it into the product of an integer and real matrices. However, its optimisation is difficult as it requires simultaneous optimisation of an integer and real variables. In this paper, we improve this optimisation by utilising recently developed black-box optimisation (BBO) algorithms with an Ising solver for integer variables. In addition, the algorithm can be used to solve mixed-integer programming problems that are linear and non-linear in terms of real and integer variables, respectively. The differences between the choice of Ising solvers (simulated annealing, quantum annealing and simulated quenching) and the strategies of the BBO algorithms (BOCS, FMQA and their variations) are discussed for further development of the BBO techniques.

Yusuke Hama, Tadashi Kadowaki

Quantum computing and machine learning are state-of-the-art technologies which have been investigated intensively in both academia and industry. The hybrid technology of these two ingredients is expected to be a powerful tool to solve complex problems in many branches of science and engineering such as combinatorial optimization problems and accelerate the creation of next-generation technologies. In this work, we develop an algorithm to solve a black-box optimization problem by improving Factorization Machine Annealing (FMA) such that the training of a machine learning model called Factorization Machine is performed not by a full dataset but by a subdataset which is sampled from a full dataset: Subsampling Factorization Machine Annealing (SFMA). According to such a probabilistic training process, the performance of FMA on exploring a solution space gets enhanced. As a result, SFMA exhibits balanced performance of exploration and exploitation which we call exploitation-exploration functionality. We conduct numerical benchmarking tests to compare the performance of SFMA with that of FMA. Consequently, SFMA certainly exhibits the exploration-exploitation functionality and outperforms FMA in speed and accuracy. In addition, the performance of SFMA can be further improved by sequentially using two subsampling datasets with different sizes such that the size of the latter dataset is substantially smaller than the former. Such a substantial reduction not only enhances the exploration performance of SFMA but also enables us to run it with correspondingly low computational cost even for a large-scale problem. These results indicate the effectiveness of SFMA in a certain class of black-box optimization problems of significant size: the potential scalability of SFMA in solving large-scale problems with correspondingly low computational cost.