GPU-based Ising Machine for Solving Combinatorial Optimization Problems with Enhanced Parallel Tempering Techniques

Ising machines (IMs) are hardware solvers designed to tackle computationally complex combinatorial optimization problems (COPs), harnessing physical processes such as quantum annealing to simulate the Ising model, enabling these specially designed solvers to tackle a wide range of computationally complex NP-hard problems in real-world applications, such as portfolio optimization and logistics planning. While prior works propose to fabricate dedicated integrated circuits for building IMs, we leverage off-the-shelf Graphics Processing Unit (GPU) chips for implementing Ising algorithms for quick development. In this work, we explore parallel tempering (PT), an Ising algorithm, which shows promise owing to its capability for parallel processing of multiple independent searches for the optimal solution, each with a different amount of randomness that allows escaping local minima. We propose several optimization strategies, including addressing the dependency problem in PT to enhance algorithm parallelism and integrating genetic algorithm (GA)-like operations to increase the diversity of the search process for effective solution discovery. Empirical evaluations demonstrate that our proposed Parallel Quantum-inspired Search (PQS) solver achieves a $2.66 \times$ speedup over the state-of-the-art GPU-based solution without sacrificing solution quality.