AutoQUBO v2: Towards Efficient and Effective QUBO Formulations for Ising Machines

The QUBO framework provides a way to model, in principle, any combinatorial optimization problem and enables the use of Ising machines to solve it. Ising machines are devices designed to quickly find good solutions to QUBO problems. In previous work, Auto-QUBO was designed to automatically generate QUBO formulations from a high-level problem description. We address two shortcomings of this method. It only works on a per-instance basis, making repeated formulations for similar problems inefficient, and relies on the user to specify penalty weights. This work introduces symbolic sampling, which provides QUBO formulations for entire problem classes. We demonstrate the speedup that can be achieved with this approach using instances of the maximum clique problem. Additionally, we use proven methods to compute valid penalty weights automatically to simplify the translation process. By providing a user-friendly way to generate QUBO formulations in an efficient manner, both in terms of time and problem difficulty, we enable more people to use Ising machines for combinatorial optimization.