In this paper, two heuristic algorithms are proposed to solve the direct aperture optimisation problem (DAO) in radiation therapy for cancer treatment. In the DAO problem, the goal is to find a set of deliverable aperture shapes and intensities so we can irradiate the tumor according to a medical prescription without producing any harm to the surrounding healthy tissues. Unlike the traditional two-step approach used in intensity modulated radiation therapy (IMRT) where the intensities are computed and then the apertures shapes are determined by solving a sequencing problem, in the DAO problem, constraints associated to the number of deliverable aperture shapes as well as physical constraints are taken into account during the intensities optimisation process. Thus, we do not longer need any leaves sequencing procedure after solving the DAO problem. We try our heuristic algorithms on a prostate case and compare the obtained treatment plan to the one obtained using the traditional two-step approach. Results show that our algorithms are able to find treatment plans that are very competitive when considering the number of deliverable aperture shapes.