Abstract: Developing a comprehensive energy system with the power grid as the core, which integrates electricity, heat, and gas with complementary and coordinated supply, is an important means to implement the "dual carbon" goals. However, there are economic and stability problems in the operation of the integrated energy system with combined electricity-heat-gas, which need to be addressed. This paper aims to use machine learning algorithms to solve the economic problems of the electricity-heat-gas co-generation system while ensuring operational stability.First, the paper models the comprehensive energy system incorporating energy storage and power-to-gas devices. It combines the general framework of optimizing objectives and constraints in the optimization operation problem, considering factors such as power balance, output limits of various units, ramping rate limits, and capacity constraints in the constraints.Next, the paper designs a solution strategy for the optimization operation problem of the electricity-heat-gas co-generation system based on deep reinforcement learning（DRL）. The algorithm combines the advantages of reinforcement learning policy selection and deep learning environment simulation. In the algorithm design, it carefully considers five major modules: action space, reward function, state space, DRL algorithm, and DRL network.Finally, the paper designs four case studies, combining typical daily operating conditions of the electricity-heat-gas co-generation system, to verify that the co-generation supply mode of electricity-heat-gas can effectively achieve multi-energy complementarity and reduce energy consumption costs. Moreover, the DRL method designed in this paper can effectively solve the optimization operation problem of the electricity-heat-gas co-generation system.