Hybrid Quantum Benders' Decomposition For Mixed-integer Linear Programming

TL;DR

This paper introduces a hybrid quantum-classical Benders' decomposition algorithm that reformulates the master problem into a QUBO model and solves it with a quantum annealer, aiming to improve solutions for complex MILP problems.

Contribution

It presents a novel hybrid quantum Benders' decomposition method that leverages quantum annealing for the master problem in MILP, enhancing solution quality.

Findings

Quantum annealer effectively solves the QUBO-formulated master problem.

The hybrid algorithm guarantees solution quality for MILP.

Feasibility analysis shows potential for quantum-enhanced optimization.

Abstract

The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders' decomposition can be described as a strategy of divide and conquer. The Benders' decomposition algorithm has been employed in a variety of applications such as communication, networking, and machine learning. However, the master problem in Benders' decomposition is still NP-hard, which motivates us to employ quantum computing. In the paper, we propose a hybrid quantum Benders' decomposition algorithm. We transfer the Benders' decomposition's master problem into the quadratic unconstrained binary optimization (QUBO) model and solve it by the state-of-the-art quantum annealer. Then, we analyze the computational results and discuss the feasibility of the proposed algorithm. Due to our reformulation in the master problem in Benders' decomposition, our hybrid algorithm, which takes advantage of both classical and quantum computers, can guarantee the solution quality for solving MILP problems.