## 1 Introduction
This paper will use a robust optimization method to improve the robustness of IES. The articles above are aimed at the optimization of energy suppliers, ignoring the autonomy of energy consumers (users) and the interest interaction between users and IES energy suppliers. Up to now, a large number of scholars have studied MIES under the framework of game theory. Connecting multiple IESs to form MIES can realize complementary coordination of different energies Hou et al. (2018). With the development of multi-energy market mechanism, each IES belongs to different operating entities, so it is urgent to clarify the energy interaction mechanism between IESs and within each IES Hou et al. (2018). At the same time, it is also necessary to explore the cooperative scheduling mechanism suitable for MIES, so that each subject can obtain the optimal revenue. In the cooperative game, the participants generate cooperation surplus through signing a mandatory contract. This way focuses on the overall benefits of the alliance and essentially belongs to centralized optimization. From the perspective of MIES cooperation, an MIES trading model was established in [PERSON] et al. (2018) based on a cooperative game, in which MIES were equated to an IES combination, called IES alliance and the Shapley value was used to distribute the gains of each IES. This model improves the benefits of the IES alliance, but equating MIES to an IES alliance fails to consider the constraints from power transmission between different IESs and ignores the impact of energy storage devices. From the perspective of MIES, the economic dispatch of MIES for cold, heat, and electricity were examined in [PERSON] et al. (2018), through fully evaluating the impacts of an energy storage battery, a heat and electricity cogeneration unit, a waste heat boiler, and other devices on the collaborative dispatch of MIES. The analysis results showed that the total operation cost of the system could be significantly reduced through interconnection among MIES. In consideration of the influence of demand response on MIES collaborative operation under various factors, it was further revealed in [PERSON] et al. (2018) that to demand response can effectively reduce the operation cost of the system and increase the renewable energy consumption rate. It should be noted that Refs. [PERSON] et al. (2018); [PERSON] et al. (2018); [PERSON] et al. (2018)intended to explore how to improve the overall benefits of the IES alliance. What should be done in the following stage is only to distribute the cooperation surplus obtained by the IES alliance according to a specific distribution method (such as the Shapley value method), so that the benefits of the IES alliance can be higher than the sum of benefits from independent operation, which meets the condition of cooperative game. However, the MIES collaborative trading operation models studied in these references cannot reflect the degree of fairness, and they mostly use the traditional method of Nash bargaining (NB) and the Shapley value distribution method. In fact, under the collaborative operation of MIES, some participants sacrifice their own benefits to maximize the benefits of the IES alliance. Nevertheless, these two distribution methods mean that such participants may gain more from participating in market competition alone than those in cooperation. The traditional model of NB mentioned above cannot further characterize the contribution of each participant, making it difficult to reflect the specific contributions of each participant. In this regard, the model of asymmetric NB overcomes the limitations of the alliance game [26]. The optimization method proposed in this paper belongs to the research field of asymmetric NB. However, Refs. [27; 28; 29; 30; 31; 32; 33; 34] all adopted the centralized solution method, which ignores the privacy protection of each network and the multi-agent characteristics of IES. The alternating direction method of multipliers (ADMM) algorithm can solve the distribution issue of the model in this paper.