In a negative survey, a category which does not agree with the fact of each participant is collected. Hence, data collectors cannot acquire the realistic data of participants, and this can efficiently protect participants' private information and sensitive data. However, existing approaches used to estimate the distribution of positive surveys from negative surveys are not practical and time-consuming. This paper proposed a method in order to acquire practical estimation results with a lower computing cost, namely fastNStoPS. Usually, privacy and utility are used to measure the performances of negative surveys, and they are two conflicting metrics. Users have different demands on privacy (or utility) under different circumstances. The optimal negative surveys are a Pareto font of these two objectives. To demonstrate its practicability, the proposed fastNStoPS method is embedded into a Differential Evolution (DE), which is used to find the optimal negative surveys. The experiment results show that the DE has a much better performance on find the optimal negative surveys, and the computing cost is very low.