Parallelizable Search-Space Decomposition for Large-Scale Combinatorial Optimization Problems Using Ising Machines

2026-02-26

AI Summary

This work addresses the computational intractability of large-scale combinatorial optimization problems arising from their exponentially sized search spaces by proposing a structure-aware parallel decomposition framework. The approach constructs a constrained maximum-cut model based on variable interaction structures, reformulates it as a QUBO problem, and leverages an Ising machine to efficiently cluster variables for automatic problem decomposition. The resulting subproblems are then solved in parallel using mathematical optimization solvers. This method uniquely integrates structure-aware clustering with Ising-based computation, substantially reducing the effective problem size. Experimental results on the capacitated vehicle routing problem demonstrate up to a 95.32% reduction in variable count, achieving within one minute the solution quality that conventional methods require thirty minutes to attain, while significantly improving the rate of feasible solutions.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Combinatorial optimization problems are crucial in industry. However, many COPs are NP-hard, causing the search space to grow exponentially with problem size and rendering large-scale instances computationally intractable. Conventional solvers typically treat problems as monolithic entities, leading to significant efficiency degradation as structural complexity increases. To address this issue, we propose a novel search-space decomposition method that leverages the inherent structure of variables to systematically reduce the size of the master problem. We formulate interaction costs between variables and individual variable costs as a constrained maximum cut problem and convert it into a quadratic unconstrained binary optimization formulation using penalty terms. An Ising-model solver is used to rapidly decompose the problem into independent small-scale subproblems, which are subsequently solved in parallel using mathematical optimization solvers. We validated this method on the capacitated vehicle routing problem. Results demonstrate three significant benefits: a substantial enhancement in feasible solution rates, accelerated convergence, achieving in 1 min the accuracy that the naive method required 30 min to reach, and a variable reduction of up to 95.32\%. These findings suggest that search-space decomposition is a promising strategy for efficiently solving large-scale combinatorial optimization problems.

Problem

• combinatorial optimization
• search-space decomposition
• large-scale
• NP-hard
• Ising machines

Innovation

• search-space decomposition
• Ising machine
• combinatorial optimization
• parallelization
• QUBO