This paper proposes a hybrid multi-objective optimization and game-theoretic approach (HMOGTA) to achieve the optimal operation of integrated energy systems (IESs) consisting of electricity and natural gas (E&G) utility networks

multiple distributed energy stations (DESs)

and multiple energy users (EUs). The HMOGTA aims to solve the coordinated operation strategy of the electricity and natural gas networks considering the demand characteristics of DESs and EUs. In the HMOGTA

a hierarchical Stackelberg game model is developed for generating equilibrium strategies of DESs and EUs in each district energy network (DEN). Based on the game results

we obtain the coupling demand constraints of electricity and natural gas (CD-CENs) which reflect the relationship between the amounts and prices of electricity and cooling (E&C) that DESs purchase from utility networks. Furthermore

the minimization of conflicting costs of E&G networks considering the CDCENs are solved by a multi-objective optimization method. A case study is conducted on a test IES composed of a 20-node natural gas network

a modified IEEE 30-bus system

and 3 DENs

which verifies the effectiveness of the proposed HMOGTA to realize fair treatment for all participants in the IES.