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Different energy requirements of the residential sector are varied, such as electricity, heating, cooling, water, etc., and these necessities are met by multi-energy systems using various energy sources and converters. In this paper, an optimal day-ahead operation of a large residential demand sector is presented based on the energy hub (EH) model with combined heat and power (CHP) as a cogeneration system. The purpose of the optimization is to maximize social welfare (SW) and minimize environmental emissions subjected to numerous technical constraints. To explore the effectiveness of the proposed model, real cases were studied and results were analyzed. Moreover, to evaluate the efficiency of the proposed methodology, the Archimedes optimization algorithm (AOA) is implemented for optimizing the EH system. The performance of the AOA is compared with the genetic algorithm, and the results depict that the AOA is better in terms of convergence speed and global search ability. Implementation of the proposed framework shows that the total SW is increased by 27.44% and environmental emissions are reduced by 18.36% compared to the base case without the EH. Additionally, there is 512.26 MWh and 149.4 m3 as a surplus in the electricity and water that are sold to every network, respectively.