With the sustained growth in renewable energy penetration, it is important to incorporate the interval prediction information of the wind and photovoltaic power into the monthly unit commitment model and introduce the system reliable rate as an indicator to measure the system reliability, which make an important contribution to deal with the volatility and randomness of the wind and photovoltaic power and ensure the economy and reliability of the monthly unit commitment. To enhance the practicality of the model and improve the solving ability, the multiobjective function composed by operating cost and reliable rate is transformed into a single-objective function by using the evaluation function based on geometric weighting method. An adaptive genetic algorithm (AGA) is used to solve the above problem when the prohibiting inbreeding strategy is adopted to replace the mutation operator, avoiding the hybridization between close relatives and containing the diversity of the population. Finally, the testing systems verify the validity and accuracy of the proposed model and algorithm.