Do
not reduce your fishes' food simply to correct a cosmetic algae problem. That is, assuming you're not radically overfeeding your fish. Others here, particularly Sk8r, can give you some specific advice about how much to feed and how often.
Generally, you can expect a nutrient build-up over time in any reef tank without counter measures. You can definitely reduce immediate dissolved nutrient problems with judicious water changes, but especially in a large tank, that can get both tiresome and expensive over the long term. One aspect of the water change issue - make sure that you have an effective RODI system, or a good source to purchase purified water from. Dechlorinated tap water for a reef tank is a no-no (but generally fine for fish-only tanks).
There are several other strategies to deal with dissolved inorganic nutrients (i.e., phosphate and nitrate) that go along with water changes. These focus on either the front end, which is removing organics before they degrade into nitrate and phosphate, or the back end, which is using lifeforms to utilize these nutrients to remove them from the water column.
On the front end is effective skimming, occasional sand washing, water filtration with reef socks, and potentially sump vacuuming to remove excess detritus. The sand washing, in particular will do the dual job of removing built-up organics in your sand as well as removing the cyanobacteria that's on the surface of the sand. The most convenient way to do this is with a
gravel wash tube. One caveat to this - if you've a substantial sandbed, you want to do this in stages of perhaps 20% of the surface area at a time. Otherwise, you can actually cause the formation and release of hydrogen sulfide, which is deadly to the inhabitants of your tank.
On the back end, you've a choice of using denitrifying bacteria to remove the NO3 and PO4, or use algae in a refugium or algae reactor, or both. For the bacteria, one typically encourages their growth with carbon dosing. That can take the form of liquid carbon dosing with vinegar, or it can take the form of solid bio-pellets in a reactor. Personally, I favor the liquid dosing because it's easy and darn near free. For this to work, you will require effective skimming, because it's removing bacteria with a skimmer that removes the nitrate and phosphate that they've taken up that makes it effective.
Refugiums with macro algae or an
actual algae reactor is another approach that's effective. A refugium can be as simple as just placing a light over a compartment in your sump and putting a handful of chaetomorpha algae in it. Or it can take the form of a small tank adjacent to your display tank with an overflow and a small pump from the sump to supply it with tank water. These small tanks can be interesting in and of themselves.