HQC-Bend: A Python Package of Hybrid Quantum-Classical Multi-cuts Benders’ Decomposition Algorithm

This article introduces the Hybrid Quantum-Classical Multi-Cut Benders’ Decomposition (HQC-Bend) algorithm, an efficient, open-source Python script designed to tackle complex Mixed-Binary Linear Programming (MBLP) problems with a block structure by integrating quantum and classical computing methods. HQC-Bend decomposes large MBLP models into a master problem and smaller, manageable subproblems, iteratively refining solutions to accelerate convergence. By leveraging quantum computing for specific computational tasks and classical methods for others, the algorithm significantly enhances efficiency. Supported by D-Wave for quantum solving and Gurobi for classical solving, the demonstration includes two primary modes of problem solving: a purely classical iteration and a hybrid quantum-classical approach. Experimental validations on real-world cases demonstrate the algorithm’s effectiveness and offer practical insights, highlighting its potential for broad adoption across various topics and fields.