Scalable and Robust Energy Routing Optimization in Stochastic Vehicular Energy Network

A vehicular energy network (VEN) enables energy transfer by leveraging electric vehicles as mobile carriers through wireless exchange across large geographic areas. This article presents a scalable and robust framework for energy routing in stochastic VENs with the objective of minimizing transmission loss. The problem is formulated as a graph generalized flow optimization, solvable to global optimality via linear programming. To ensure scalability, a flow-guided graph reduction method is proposed, which preserves critical supply-demand connectivity by prioritizing high-impact routes based on vehicular flow patterns. Building upon this, a route-guided time-expanded graph construction strategy is developed to avoid exhaustive temporal replication by generating only time-relevant nodes and arcs along active routes. To address long-horizon stochasticity, a long short-term memory-based model predictive control framework is designed, which captures both randomness and uncertainty via data-driven forecasting and residual-aware robust correction under a rolling-horizon decomposition. The proposed methods are validated on 100 real-world U.S. datasets, demonstrating significant gains in computational efficiency, scalability, and solution robustness across both time-invariant and time-varying VENs.