Rey,
I have a large deck made of pressure treated SYP. It's on the north side of my house which sits on a heavily wooded lot, and thus the deck is prone to mildew growth. To look its best, the stained deck needs to be touched up each year and fully restained every other year [despite using Behr water dispersed oil base stain which is advertised to have a longer life]. The best method I have found to clean it to remove the mildew/algae is a pressure washer with cleaner chemicals. Also very effective is a product named Jomax [available at HD or Lowe's] which is mixed with household [chlorine] bleach and water prior to application with a garden sprayer, followed by a light scrubbing with a brush, then rinsing with water. If done according to manufacturer instructions, the Jomax/bleach/water solution won't your grass or landscaping plants -- just wet them down before you start and rinse them again when you are done cleaning the wood.
Dave R.