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Identification of planted (Z, d)-motifs is an important and hard challenging problem in computational biology. In this paper, we present an original algorithm that combines genetic algorithm (GA) and random projection strategy (RPS) GARPS to identify (I, d)-motifs. We start with RPS to find good starting positions by introducing position-weight function and constructing a new hash function based on the function and return a set of candidate motifs. Then, we use the results(good candidate motifs) from RPS as the initial population of genetic algorithm to make series of iterations to refine motif candidates. We use the global search capability of GA and RPS are explored in GARPS. Experimental results on simulated data show that GARPS performs better than the projection algorithm and solves the most of challenging planted motif finding problems and improves finding faint motifs.