A Stackelberg Game-Theoretic and Mixed Integer Programming Framework for Collaborative Optimization in Multi-Energy Transportation Systems

Abstract

In the context of the deep integration of energy transformation and transportation electrification, multi-energy transportation systems involve electricity, hydrogen energy, natural gas and infrastructures like charging stations, hydrogen refueling stations, with coordinated operation facing challenges from conflicting interests and complex physical constraints. Traditional optimization models often overlook game behaviors among energy suppliers, operators and users, leading to poor executability of scheduling plans. Thus, this study proposes a two-level collaborative optimization framework integrating game theory and MIP: the upper level takes charging/hydrogen station operators as leaders (maximizing daily net revenue via pricing, subject to pricing range and station capacity constraints); the lower level takes EV (31,200 daily trips) and FCEV (8,600 daily trips) users as followers (minimizing total travel costs via station and energy demand selection). To solve the bi-level game, the framework transforms followers’ optimal responses into mathematical constraints via KKT conditions, introduces binary variables and Big-M method to linearize complementary relaxation conditions, and finally forms an MIP model with continuous and integer variables. It uses Gurobi 10.0, with a simulation environment built on MATLAB R2023a and SUMO 1.18.0.Simulation results based on a regional energy internet case (covering 20 charging stations, 10 hydrogen stations, 15 transportation hubs, 24-hour scheduling) show multi-dimensional improvements: vs. single-level centralized optimization, total operating costs down 15.7%, renewable energy utilization up 22.3%; vs. disordered scheduling, user waiting time reduced 31.5%, operators’ revenue up 12.9%; vs. RL models (DQN, PPO) in 50-node systems, optimization time down 57%, total costs further reduced 18.3%. Verified by 1,000 Monte Carlo simulations, the model has a total operational cost fluctuation coefficient of 3.2%, 95.3% constraint satisfaction rate in 100-node dynamic scenarios, and Nash equilibria with fluctuations <5% in 98% of nodes, fully validating its effectiveness and stability in coordinating economy, environmental protection and user experience.