IC-D2S: A Hybrid Ising-Classical-Machines Data-Driven QUBO Solver Method

We present a heuristic algorithm designed to solve Quadratic Unconstrained Binary Optimization (QUBO) problems efficiently. The algorithm, referred to as IC-D2S, leverages a hybrid approach using Ising and classical machines to address very large problem sizes. Considering the practical limitation on the size of the Ising machine(IM), our algorithm partitions the QUBO problem into a collection of QUBO subproblems (called subQUBOs) and utilizes the IM to solve each subQUBO. Our proposed heuristic algorithm uses a set of control parameters to generate the subQUBOs and explore the search space. Also, it utilizes an annealer based on cosine waveform and applies a mutation operator at each step of the search to diversify the solution space and facilitate the process of finding the global minimum of the problem. We have evaluated the effectiveness of our IC-D2S algorithm on three large-sized problem sets and compared its efficiency in finding the (near-)optimal solution with three QUBO solvers. One of the solvers is a software-based algorithm (D2TS), while the other one (D-Wave) employs a similar approach to ours, utilizing both classical and Ising machines. The results demonstrate that for large-sized problems (>= 5000) the proposed algorithm identifies superior solutions. Additionally, for smaller-sized problems (= 2500), IC-D2S efficiently finds the optimal solution in a significantly faster manner.