In this paper a novel genetic algorithm is presented for the dyad motif finding problem. The genetic algorithm uses a multi-objective fitness function based on the sum of pairs, the number of matches, and the information content. The individuals required for the population pool in the genetic algorithm are optimized by Gibbs sampling method. Also, new crossover and mutation operators are designed. The algorithm is implemented and tested on the different types of real datasets. The results are compared with other well-known algorithms and the effectiveness of our algorithm is shown.