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arXiv · 2407.06773

Evaluating Quantum Optimization for Dynamic Self-Reliant Community Detection

David Bucher·Daniel Porawski·Benedikt Wimmer·Jonas Nüßlein·Corey O'Meara·Naeimeh Mohseni·Giorgio Cortiana·Claudia Linnhoff-Popien
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Abstract

Power grid partitioning is an important requirement for resilient distribution grids. Since electricity production is progressively shifted to the distribution side, dynamic identification of self-reliant grid subsets becomes crucial for operation. This problem can be represented as a modification to the well-known NP-hard Community Detection (CD) problem. We formulate it as a Quadratic Unconstrained Binary Optimization (QUBO) problem suitable for solving using quantum computation{\color{blue}, which is expected to find better-quality partitions faster. The formulation aims to find communities with maximal self-sufficiency and minimal power flowing between them}. To assess quantum optimization for sizeable problems, we apply a hierarchical divisive method that solves sub-problem QUBOs to perform grid bisections. Furthermore, we propose a customization of the Louvain heuristic that includes self-reliance. In the evaluation, we first demonstrate that this problem examines exponential runtime scaling classically. Then, using different IEEE power system test cases, we benchmark the solution quality for multiple approaches: D-Wave's hybrid quantum-classical solvers, classical heuristics, and a branch-and-bound solver. As a result, we observe that the hybrid solvers provide very promising results, both with and without the divisive algorithm, regarding solution quality achieved within a given time frame. Directly utilizing D-Wave's Quantum Annealing (QA) hardware shows inferior partitioning.

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David Bucher, Daniel Porawski, Benedikt Wimmer, Jonas Nüßlein, Corey O'Meara, Naeimeh Mohseni, Giorgio Cortiana, Claudia Linnhoff-Popien. 2024-07-09. Evaluating Quantum Optimization for Dynamic Self-Reliant Community Detection. https://arxiv.org/abs/2407.06773

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