Quantum Annealing-Based Algorithm for Efficient Coalition Formation Among LEO Satellites

TL;DR

This paper tackles the challenge of efficiently clustering large LEO satellite networks by formulating the problem as a graph-based coalition structure generation (CSG) task. It introduces GCS-Q, a hybrid quantum-classical algorithm that solves the problem via iterative, QUBO-based bipartitions using quantum annealing on a D-Wave Advantage system, and compares its performance to the classical solver Gurobi. Experiments on synthetic graphs and real Starlink TLE data show that the quantum annealer achieves substantially faster runtimes on dense graphs while delivering solution quality comparable to Gurobi, with potential for on-site deployment to eliminate network latency. The work demonstrates the practical potential of quantum optimization for managing large-scale satellite networks and outlines avenues for future enhancements, including constraint handling and parallelization, to further bolster scalability and real-world impact.

Abstract

The increasing number of Low Earth Orbit (LEO) satellites, driven by lower manufacturing and launch costs, is proving invaluable for Earth observation missions and low-latency internet connectivity. However, as the number of satellites increases, the number of communication links to maintain also rises, making the management of this vast network increasingly challenging and highlighting the need for clustering satellites into efficient groups as a promising solution. This paper formulates the clustering of LEO satellites as a coalition structure generation (CSG) problem and leverages quantum annealing to solve it. We represent the satellite network as a graph and obtain the optimal partitions using a hybrid quantum-classical algorithm called GCS-Q. The algorithm follows a top-down approach by iteratively splitting the graph at each step using a quadratic unconstrained binary optimization (QUBO) formulation. To evaluate our approach, we utilize real-world three-line element set (TLE/3LE) data for Starlink satellites from Celestrak. Our experiments, conducted using the D-Wave Advantage annealer and the state-of-the-art solver Gurobi, demonstrate that the quantum annealer significantly outperforms classical methods in terms of runtime while maintaining the solution quality. The performance achieved with quantum annealers surpasses the capabilities of classical computers, highlighting the transformative potential of quantum computing in optimizing the management of large-scale satellite networks.

Figures (4)

• Figure 1: Architecture for finding the optimal coalition structures using GCS-Q, an iterative algorithm for optimal graph partitioning leveraging quantum annealing hardware. At each step, the optimal graph cut is determined by formulating a QUBO problem, which is embedded onto the annealer hardware. The quantum tunneling phenomenon helps find the lowest energy solution efficiently within the exponentially large solution space. The optimality condition involves choosing the best solution from the sample set output by the annealer that satisfies the use case-specific constraints.
• Figure 2: Comparison of runtimes for the D-Wave Advantage annealer and Gurobi in finding the optimal graph partition for varying edge sparsities, where sparsity = 0 denotes a fully connected graph, and sparsity = 1 indicates the graph is a tree. The graph includes plots for the total runtime for remotely accessing the annealer as a cloud service, the runtime excluding internet latency and service queue waiting time (On-site), and the time taken for Gurobi to run locally. The plot illustrates the mean (represented by a solid line), the range (indicated by the broadly shaded area), and the standard deviation (denoted by the lightly shaded area) of the runtimes aggregated over three sets of synthetic data.
• Figure 3: Comparison of the solution quality for the single split problem across varying levels of graph sparsity. Sparsity = 0 denotes a fully connected graph, sparsity = 0.5 represents a graph with intermediate connectivity, and sparsity = 1 indicates a tree structure. The plots show the cost of bipartition against the number of satellites for one of the seeds, comparing the least cost sampled by the annealer, the most frequently sampled cost by the annealer, and the cost obtained by Gurobi.
• Figure 4: The figure depicts the benefits of coalition formation in terms of the number of communication links. Having a lower number of communication links is preferable as each link has a management cost.