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

2025-02-19

AI Summary

To address the scalability bottleneck of large-scale Quadratic Unconstrained Binary Optimization (QUBO) problems on Ising machines with limited hardware size, this paper proposes IC-D2S, a hybrid solving framework. IC-D2S synergistically integrates Ising hardware annealing with classical heuristic search, featuring a control-parameter-driven adaptive subproblem partitioning mechanism, cosine-annealing scheduling, and generation-wise genetic mutation operators to enhance global exploration efficiency. By enabling parallel subproblem solving and tight software–hardware co-optimization, IC-D2S achieves superior performance: it significantly outperforms D2TS and D-Wave on instances with ≥5,000 variables, and converges to optimal solutions faster than competing methods on 2,500-variable problems. The framework balances scalability, solution efficiency, and accuracy, establishing a practical hybrid computing paradigm for ultra-large-scale QUBO.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Solving large-scale QUBO problems efficiently using a hybrid Ising-classical approach
• Partitioning QUBO into subproblems solvable by Ising machines within size limits
• Enhancing solution space diversity via annealing and mutation for global minima

Innovation

• Hybrid Ising-classical approach for large QUBO problems
• Partitions QUBO into subproblems solved by Ising machine
• Uses cosine-annealer and mutation operator for solution diversity