I forgot to mention that one key to not having algae pop up is not having places for it to get a foothold. Rocks with film algae, film bacteria, live and growing coralline, etc. do not have hair algae growing on them. When you use chemicals like h2o2, you kill everything on the surface of the rock and the stuff can come right back. Bio diversity is the key but it has to be able to colonize. The urchins/snails will eat the algae down but not sterilize the rock where nothing wants to grow again but the algae.
Unfortunately, dry/dead rock is a great place for algae to find a foothold. Nobody tells you this when they sell it to you, but in the end some cultured rock from Florida is often better and cheaper since it is covered in stuff and algae doesn't take hold very well to it. Mined limestone or other rocks painted purple and sprayed with bacteria are also sterile and a good pitri dish for algae.
Like The Real Chris said, any direct killing is temporary and the algae will come back.
In the end, a pack of diverse things, substrate, mud from IPSF or the like will win, but it takes time. You can also just order a 10-20 pound pack of real live rock from Florida to help get things going. Any of these needs lower levels of residual no3 and po4 since they are poisons to inverts at higher levels... they don't have to be like ocean-like levels, but also cannot be just out of control.