Regulation-Aware Combinatorial Optimization of Energy Community Formation Under Geographic Proximity Constraints

Renewable Energy Communities (RECs) enable collective self-consumption by allowing geographically proximate households to share locally generated renewable energy. While most existing studies optimize the operation of a pre-defined community, the prior problem of how to partition a set of households into multiple regulation-compliant communities remains underexplored. This paper formalizes REC formation as a pre-operational combinatorial design problem: households are partitioned under a strict diameter-based proximity constraint derived from European national regulatory rules. Within this feasible space, we minimize the quadratic imbalance of yearly community energy balances, a structural proxy for self-consumption potential equivalent to variance minimization over community balances, and prove it tightens the theoretical upper bound of annual aggregate self-consumption. The problem is shown to be NP-hard via reduction from 3-Partition. A hybrid particle swarm optimization (PSO) framework with strict feasibility repair and local memetic refinement is proposed. Experiments on residential data from two urban zones of Murcia, Spain (N = 200, N = 151 households; 130 profiles from the FlexCHESS European project) under the Spanish regulatory distance cap of 2 km (Real Decreto-ley 29/2021) demonstrate 86-93 % reduction in quadratic imbalance over random and geographic baselines, and 7-9 % over greedy local search (Wilcoxon p < 0.004, 10 independent runs). Hourly validation on independently generated PVGIS-calibrated profiles (annual balances derived a posteriori, eliminating reconstruction circularity) reveals a strong negative correlation between annual imbalance and hourly self-consumption (rho = -0.42, p < 1e-5, rho^2 = 0.18), supporting the annual proxy as a useful pre-operational structural criterion. Ablation studies confirm robustness to PSO hyperparameters, and climate sensitivity analysis shows PSO dominance across irradiance levels from 1000 to 1900 kWh/kWp. Beyond solution quality, the proposed framework is intended as a pre-operational planning and screening tool that can assist municipalities, community organizers, and Distribution System Operators in identifying promising community configurations before undertaking detailed network-constrained or operational studies.