Demonstrating Quantum Scaling Advantage in Approximate Optimization for Energy Coalition Formation with 100+ Agents

TL;DR

This work benchmarks quantum and classical solvers on an energy-coalition-formation problem by transforming Coalition Structure Generation (CSG) into an Induced Subgraph Game (ISG) and then into a QUBO. The authors compare quantum annealing on D-Wave against classical solvers (Gurobi, Tabu, simulated annealing, QB-solve) and IBM QAOA for approximate optimization over networks with 100+ agents, demonstrating a scaling advantage for D-Wave and underperformance of 1-round QAOA on hardware. They show that ISG-based approximations closely track the original CSG solutions, report dense graph characteristics ($>90\%$ connectivity) and Gaussian-weight distributions around zero, and provide evidence that D-Wave can achieve solutions comparable to best classical solvers up to about 150–100 prosumers with favorable runtime scaling. The conclusion highlights a practical quantum advantage for dense, real-world optimization tasks and outlines pathways to scale to larger instances and to further improve quantum-classical hybrid approaches for energy-cooperation problems.

Abstract

The formation of energy communities is pivotal for advancing decentralized and sustainable energy management. Within this context, Coalition Structure Generation (CSG) emerges as a promising framework. The complexity of CSG grows rapidly with the number of agents, making classical solvers impractical for even moderate sizes. This suggests CSG as an ideal candidate for benchmarking quantum algorithms against classical ones. Facing ongoing challenges in attaining computational quantum advantage for exact optimization, we pivot our focus to benchmarking quantum and classical solvers for approximate optimization. Approximate optimization is particularly critical for industrial use cases requiring real-time optimization, where finding high-quality solutions quickly is often more valuable than achieving exact solutions more slowly. Our findings indicate that quantum annealing (QA) on DWave can achieve solutions of comparable quality to our best classical solver, but with more favorable runtime scaling, showcasing an advantage. This advantage is observed when compared to solvers, such as Tabu search, simulated annealing, and the state-of-the-art solver Gurobi, in finding approximate solutions for energy community formation involving over 100 agents. DWave also surpasses 1-round QAOA on IBM hardware. Our findings represent the largest benchmark of quantum approximate optimizations for a real-world dense model beyond the hardware's native topology, where D-Wave demonstrates a scaling advantage.

Figures (5)

• Figure 1: (a) Schematic representation of the workflow: The Distribution System Operator (DSO) strategically evaluates the potential of prosumer communities, aiming to minimize network management costs through optimized power flow analysis. The DSO's decision-making involves partitioning prosumers into net-metered coalitions, treating it as a Coalition Structure Generation (CSG) problem to optimize overall network efficiency. We transform the CSG formulation into the Induced Subgraph Game (ISG). An approximate solution to the ISG is found through iterative splitting coalitions to bipartitions until no value-increasing bipartitions remain. In the benchmarking phase, the efficiency of both quantum and classical solvers is assessed in the iterative splitting process.
• Figure 2: Benchmarking classical solvers against quantum solvers in energy coalition formation: (a) Solution quality of different solvers on ISG formulation where the baseline is w.r.t. the solution determined with the Gurobi on the same formulation. (b) The solution quality of different solvers on ISG formulation w.r.t. the solution determined with IDP on the original CSG formulation. (c) Run time of different solvers on ISG formulations as well as run time of improved dynamical programming (IDP) on CSG formulation. (d) QAOA circuit depth on quantum hardware for different numbers of prosumers (number of qubits). Note that results for each number of prosumers showcase averages across 20 realizations except for IBM hardware and random solver with $2^{12}$ shots where results are shown for a single problem instance per data point. The light blue histogram on the lower right shows the weight distribution after transferring CSG to ISG.
• Figure 3: Benchmarking classical solvers against DWave in energy coalition formation for randomly generated problem instances. (a) The solution quality versus the number of prosumers. (b) Run time versus number of prosumers. (c) The number of physical qubits versus logical qubits (number of prosumers) on DWave hardware for the first split of the grand coalition into two partitions. Note that results for each number of prosumers showcase averages across 20 realizations. (d) Energy distribution sampled from DWave, QAOA, and a random sampler for the first split of the grand coalition to two partitions for a randomly generated instance with 100 prosumers (100 qubits). The dashed vertical line shows the solution found by Gurobi.
• Figure S1: Schematic representation of QA and QAOA.
• Figure S2: Schematic representation of the network with 9 prosumers and one external grid.