Requirement prioritization in complex software system often involves multiple stakeholders and needs to satisfy several different stakeholders' requirements. In this paper, we define multi-stakeholder tradeoffs in requirements optimization as a multi-objective optimization problem and introduce an archived Non-Dominated Sorted Genetic Algorithm-Ⅱ (NSGA-Ⅱ) to the automated analysis of requirements assignments. The results show that the proposed method can generate a set of optimal requirements satisfying multiple stakeholders with the constraints of the resources and the cost. Comparing with the baseline methods, our approach shows better performance on all evaluation metrics, such as average, minimum satisfaction and variance in satisfaction. In summary, the archived NSGA-Ⅱ algorithm could provide a scientific and reasonable result for the software requirements engineering.