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

TL;DR

IC-D2S addresses large-scale QUBO optimization by decomposing a dense problem into subQUBOs that fit an Ising machine, enabling hybrid Ising-classical search. It combines Tabu-search driven subproblem generation, a data-driven control parameter framework ($\eta$, $\Delta$, $\gamma$), and a cosine-annealed mutation strategy to explore the full solution space. Empirical results on Beasley and Palubeckis benchmarks show superior solution quality for $n\ge 5000$ and faster convergence for $n=2500$ compared with D$^2$TS and D-Wave, highlighting the method's efficiency with limited Ising hardware. The work demonstrates the practical impact of intelligent subproblem construction and adaptive search in hybrid architectures for large-scale QUBO problems.

Abstract

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.

Figures (6)

• Figure 1: The procedure of Call_IM_Solution_Set() fucntion
• Figure 2: Extracting the control parameters.
• Figure 3: Comparing the efficiency of the two simplified versions of the proposed heuristic compared to the original version.
• Figure 4: Impact of different values of a) $c$, b) $z$ and c) $\alpha$ on the effectiveness of the proposed heuristic on solving the Q2 problem of Beasley problem set.
• Figure 5: Overall comparison of three different algorithms on the problems with a size of 5000 and varying densities.