To further improve the low-carbon performance and economic efficiency of integrated energy systems, an optimal dispatch model considering Power-to-Gas and Carbon Capture Systems (P2G-CCS) is proposed. First, an integrated energy system coupling electricity, gas, cooling, heating, and hydrogen is constructed, incorporating P2G-CCS, hydrogen fuel generators, and combined heat and power systems. Second, based on a tiered carbon trading mechanism, an optimal dispatch model for the integrated energy system is developed to minimize the total cost, including energy purchase cost, operation and maintenance cost, carbon emission cost, and the cost of curtailed wind and solar energy. Then, the improved Marine Predators Algorithm is proposed, which integrates reinforcement learning and an adaptive spiral search strategy to select optimal actions, thereby further enhancing the convergence speed and optimization accuracy. Finally, four different scenarios are designed for case studies, and the proposed model is solved using the improved algorithm. The results demonstrate that the proposed model can effectively reduce system carbon emissions and overall operating costs.