Gradient-Free Distribution Network Reconfiguration via Discrete Structural Annealing: Exhaustive Proof and Near-Linear Scaling for Edge Computing

Distribution Network Reconfiguration (DNR) is a typical non-convex combinatorial optimization problem. Traditional methods rely on Mixed-Integer Nonlinear Programming (MINLP), Deep Reinforcement Learning (DRL), or long-term heuristic iterations, which are difficult to deploy in edge-computing scenarios. This paper proposes Discrete Structural Annealing (DSA)—a gradient-free simulated annealing framework that strictly preserves the radial tree structure. On the IEEE 33-bus system, DSA independently finds the literature optimum (139.55 kW) and mathematically proves that the feasible region for V_min ≥ 0.95 p.u. is an empty set by exhaustively enumerating all 435,897 topologies. On the IEEE 69-bus system, this paper completes the exhaustive enumeration of C(73,5) = 15,003,780 topologies, yielding a theoretical optimum of 66.11 kW under the MATPOWER load version. Meanwhile, through cross-validation on dual load versions, it reproduces the 98.59 kW benchmark of the general reconfiguration literature. In synthetic scaling tests, as the number of nodes increases from 33 to 528, the state space spans approximately 96 orders of magnitude, while the single-start execution time only increases by 13.8 times (99 ms → 1364 ms), demonstrating strict near-linear time scaling. The native C++ single-threaded implementation completes 5000 annealing steps for the 69-bus system in only about 0.26 s, requiring neither GPUs nor commercial solvers.