Boltzmann Machine Is Useful for Enhancing Search Performance of Ising Machines

Various methods for formulating practical combinatorial optimization problems as an Ising model have been developed, expanding real-world applications of Ising machines. Nevertheless, the usability of Ising machines remains limited since the formulation process involves complicated tasks, such as fine-tuning parameters or selecting options, which can be challenging for non-expert users. Moreover, the existing formulation technique is often insufficient to design an Ising model that facilitates efficient solution search by Ising machines. This paper proposes a novel approach in which the Boltzmann machine, an energy-based machine learning model, autonomously optimizes the Ising model based on solutions obtained from an Ising machine. The proposed combinatorial optimization flow iteratively alternates between solution search by the Ising machine and model refinement by the Boltzmann machine, gradually improving solution quality without manual adjustments of parameters or options. Experimental results demonstrate that the proposed method consistently outperforms the standalone Ising machine in several benchmark problems, achieving superior solution quality under a comparable computational budget.