A general rule for pool is, the closer vegetation is to the pool, the more maintenance the pool will require. Grass next the pool looks nice, but is high maintenance.

Operating your pump and filter, and bringing your chlorine up will tend to reduce the population. Using a cheap and foamy algaecide will reduce, and may eliminate the population. And, unlike dish soap, cheap algaecide is broken down by chlorine -- in fact, you have to watch your chlorine levels, because adding cheap algaecide will cause chlorine to drop.

Longer term, a deck around the pool will generally lower maintenance. Meanwhile, you'll probably need a more with a pick-up bag.