Detecting outlying subspaces is a relatively new research problem in outlier-ness analysis for high-dimensional data. An outlying subspace for a given data point p is the subspace in which p is an outlier. Outlying subspace detection can facilitate a better characterization process for the detected outliers. It can also enable outlier mining for highdimensional data to be performed more accurately and efficiently. In this paper, we proposed a new method using genetic algorithm paradigm for searching outlying subspaces efficiently. We developed a technique for efficiently computing the lower and upper bounds of the distance between a given point and its kth nearest neighbor in each possible subspace. These bounds are used to speed up the fitness evaluation of the designed genetic algorithm for outlying subspace detection. We also proposed a random sampling technique to further reduce the computation of the genetic algorithm. The optimal number of sampling data is specified to ensure the accuracy of the result. We show that the proposed method is efficient and effective in handling outlying subspace detection problem by a set of experiments conducted on both synthetic and real-life datasets.