To address the challenges of low efficiency in energy transmission networks and the difficulty of multi-agent interest coordination in integrated energy systems, a bi-level collaborative optimization method coupling “physical-economic” layers was proposed. At the physical layer, an energy network graph model was constructed based on the max-flow min-cut theorem to dynamically identify critical transmission bottlenecks, optimize electricity and heat transmission paths, and calculate real-time flows. Additionally, the costs incurred by network losses and congestion are quantified to measure the efficiency loss during transmission, thereby improving energy transmission efficiency. At the economic layer, a stackelberg game model was established, with the integrated energy system operator as the leader and load aggregators and shared energy storage operators as followers. Through dynamic pricing and demand response mechanisms, each agent was guided to engage in strategic interactions and interest balancing while satisfying physical constraints, thus achieving coordinated optimization of energy supply and demand. To solve the model, the adaptive differential evolution algorithm was improved by introducing a spatiotemporal two dimensional crossover probability mechanism, which effectively balanced global exploration and local exploitation capabilities, thereby enhancing the algorithm’s convergence speed and solution accuracy. Finally, the model was implemented in MATLAB and solved using the Yalmip toolbox and CPLEX solver, with its performance validated through comparative case studies. The results demonstrate that the proposed method effectively reduces the peak-valley difference of electrical and thermal loads, improves economic benefits, resolves the disconnection between network optimization and market decisions found in traditional studies, and achieves synergistic unification of physical network constraints and economic gaming behaviors, providing a theoretical foundation for the efficient operation of integrated energy systems.