Accelerating Extended Benders Decomposition with Quantum-Classical Hybrid Solver
Takuma Yoshihara, Masayuki Ohzeki
TL;DR
The paper addresses solving large-scale MIQP by targeting the master problem bottleneck in extended Benders decomposition, specifically the quadratic term $x^T C x$ over binary variables. It introduces a quantum-classical hybrid approach that solves the EBD master problem using the D-Wave CQM solver by converting the problem to a QUBO via discretization of a continuous variable and augmentation with slack and dual-cut constraints. Experimental results show that the EBD+CQM method achieves near-optimal solutions and, for some instances, can exhibit exponential speedups over a leading classical solver, while quantum annealing alone may not provide the necessary convergence. The work demonstrates notable scalability advantages for large MIQP instances and suggests that this hybrid framework could be impactful for applications like power-system optimization and portfolio selection, with future work aimed at handling more complex continuous variables and larger constraint sets.
Abstract
We propose a quantum-classical hybrid method for solving large-scale mixed-integer quadratic problems (MIQP). Although extended Benders decomposition is effective for MIQP, its master problem which handles the integer and quadratic variables often becomes a computational bottleneck. To address this challenge, we integrate the D-Wave CQM solver into the decomposition framework to solve the master problem directly. Our results show that this hybrid approach efficiently yields near-optimal solutions and, for certain problem instances, achieves exponential speedups over the leading commercial classical solver. These findings highlight a promising computational strategy for tackling complex mixed-integer optimization problems.