The present paper develops a multi–dimensional genetic algorithm for the Resource constrained project scheduling problem. This algorithm performs a series of perturbations in an attempt to improve the current solution, applying some problem dependant genetic operators. The procedure used is efficient and easy to implement. The approach was tested on sets of standard problems freely available on the Internet (PSPLIB) and the results were compared to those found in the literature. It was found that the algorithm used is able to generate competitive results compared to the best methods known so far and computes, for the first time, four optimal solutions for four benchmark instance.