Performance enhancing of hybrid quantum-classical Benders approach for MILP optimization

TL;DR

This paper introduces a hybrid quantum-classical Benders' decomposition algorithm for large-scale MILP problems, leveraging quantum annealers to improve solution efficiency and scalability in transmission network planning.

Contribution

It presents a hardware-agnostic, enhanced Benders' decomposition method integrating quantum annealing, with novel embedding and stopping strategies, for better performance on large MILP problems.

Findings

Quantum-enhanced Benders' algorithm outperforms classical methods on benchmark problems.

Embedding process reductions significantly decrease pre-processing time.

The approach effectively handles current quantum hardware limitations.

Abstract

Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.