In this paper, a new hybrid multiobjective algorithm, namely, the modified bald eagle search Algorithm (MBES), integrated with the grasshopper optimization algorithm, is proposed to solve the unit commitment (UC) problem. We consider a standard 10-unit power system with two wind farms, two photovoltaic farms, and flexible loads for optimization purposes. The UC problem is tackled under uncertainties related to demand and renewable generation capacities. To account for these uncertainties, probability density functions (PDFs) are assigned to the sources of uncertainty, and Monte Carlo simulation (MCS) is employed to select several scenarios with specific probability coefficients. Additionally, two innovative objective functions based on operation cost and emissions are introduced, with each scenario weighted based on its occurrence probability. To assess the performance of the proposed MOGOA-MBES algorithm, simulations are conducted across three scenarios with varying conditions, and the results are compared against those obtained from several multiobjective algorithms. Our findings, supported by optimization results and the S-metric index, demonstrate that the proposed MOGOA-MBES algorithm outperforms other algorithms in terms of reducing operation cost and emissions. Furthermore, the simulation results reveal that uncertainties lead to an increase in cost and emissions, whereas the inclusion of flexible loads and their participation in the UC program can effectively mitigate cost and emission levels.