A regional integrated energy system (RIES) incorporates various energy sources such as wind and solar power, and cooling, heating and electrical loads, as well as batteries, offering advantages like enhancing the utilization of renewable energy. Firstly, considering the uncertainty of wind and solar power output, a robust optimization model with a polytopic uncertainty set is constructed to handle this uncertainty. Secondly, a multi-objective optimization model is established to minimize carbon emissions and operating costs, and a carbon emission penalty factor is introduced to convert the multi-objective into a single-objective for solution. Finally, simulations are conducted using an actual RIES, and the results demonstrate the accuracy and effectiveness of the proposed method. The model effectively balances the environmental protection and economic aspects of the system, better handles uncertainties, and achieves economic optimization of system operation.