A hybrid Quantum-Classical Algorithm for Mixed-Integer Optimization in Power Systems
Petros Ellinas, Samuel Chevalier, Spyros Chatzivasileiadis
TL;DR
The paper presents a general quantum-classical framework to accelerate mixed-integer linear programs in power systems via an enhanced Benders decomposition that splits MILPs into a binary Master Problem and a linear Subproblem. It provides two acceleration strategies: Method I uses Pareto-optimal cuts and core-point stabilization to reduce convergence time, while Method II leverages quantum sampling by evaluating multiple QC-provided SP solutions per iteration. The MP is transformed into a QUBO formulation through HOBO reductions and discretization, enabling quantum devices to contribute to the optimization, and two benchmarks—Optimal Transmission Switching and Neural Network verification for DC-OPF—are used to evaluate performance on both small (IEEE 6/14-bus) and larger scales. The results show quantum-accelerated BD can outperform classical BD on small problems, while scalability to larger problems requires reductions in circuit depth and qubit usage; the authors also release a public Python tutorial to promote reproducibility and further research.
Abstract
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs' sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid ``quantum-classical'' approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum-classical algorithms for power system mixed integer optimization problems.