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The performance of genetic algorithms (GAs) is dependent on many factors. In this paper, we have isolated one factor: the crossover operator. Commonly used crossover operators such as one-point, two-point and uniform crossover operator are likely to destroy the information obtained previously because of their random choices of crossover points. To overcome this defect, RSO, a new adaptive crossover operator based on the rough set theory, is proposed. By using RSO, useful schemata can be found and have a higher probability of surviving recombination regardless of their defining length. In this paper, the mechanism of RSO is discussed and its performance is compared with two-point crossover operator on several typical function optimization problems. The experimental results show that the proposed operator is more efficient.