Quantum computing (QC) is emerging as a new computing resource that could be superior to conventional computing (CC) for certain classes of optimization problems. However, in principle QC can only solve unconstrained binary programming problems, while mixed-integer linear programming (MIP) is of most interest in practice. We attempt to bridge the gap between the capability of QC and real-world applications by developing a new approach for MIP. The idea is decomposing the MIP into binary programming and linear programming (LP) problems, which are respectively solved by QC and conventional computing. We formalize a decomposition approach that ensures that with a sufficient number of back and forth iterations, the algorithm can reach the optimal solution of the original MIP problem. The algorithm is tested on a 2000Q D-Wave quantum processing units (QPU) and is shown to be effective for small-scaled test cases.
Quantum computing (QC) is emerging as a new computing resource that could be superior to conventional computing (CC) for certain classes of optimization problems. However, in principle QC can only solve unconstrained binary programming problems, while mixed-integer linear programming (MIP) is of most interest in practice. We attempt to bridge the gap between the capability of QC and real-world applications by developing a new approach for MIP. The idea is decomposing the MIP into binary programming and linear programming (LP) problems, which are respectively solved by QC and conventional computing. We formalize a decomposition approach that ensures that with a sufficient number of back and forth iterations, the algorithm can reach the optimal solution of the original MIP problem. The algorithm is tested on a 2000Q D-Wave quantum processing units (QPU) and is shown to be effective for small-scaled test cases.
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to solve unconstrained binary programming problems, while mixed-integer linear programming is of most interest in practice. We attempt to bridge the gap between the capability of quantum computing and real-world applications by developing a new approach for mixed-integer programming. The approach applies Benders decomposition to decompose the mixed-integer programming into binary programming and linear programming sub-problems, which are solved by a noisy intermediate-scale quantum processor and conventional processor, respectively. The algorithm is provably able to reach the optimal solution of the original mixed-integer programming problem. The algorithm is tested on a D-Wave 2000Q quantum processing unit and is shown to be effective for small-scaled test cases. We also test the algorithm on a mixed-integer programming inspired by power system applications. Many insights are drawn from the numerical results for both the capabilities and limitations of the proposed algorithm.
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 can give a direct solution to this problem, as it has been experimentally shown that it can provide significant speedups in solving 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.
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.
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 can give a direct solution to this problem, as it has been experimentally shown that it can provide significant speedups in solving 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.
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.
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer programming. State-of-the-art integer programming algorithms can compute strong relaxation bounds even for hard instances, but may have to enumerate a large number of subproblems for determining an optimum solution. If the potential of quantum computing is realized, it can be expected that in particular finding high-quality solutions for hard problems can be done fast. Still, near-future quantum hardware considerably limits the size of treatable problems. In this work, we go one step into integrating the potentials of quantum and classical techniques for combinatorial optimization. We propose a hybrid heuristic for the weighted maximum-cut problem and for quadratic unconstrained binary optimization. The heuristic employs a linear programming relaxation, rendering it well-suited for integration into exact branch-and-cut algorithms. For large instances, we reduce the problem size according to a linear relaxation such that the reduced problem can be handled by quantum machines of limited size. Moreover, we improve the applicability of depth-1 QAOA, a parameterized quantum algorithm, by deriving a parameter estimate for arbitrary instances. We present numerous computational results from real quantum hardware.