Try to keep the nutrient in the (pitch) dark. That will stop the growth of algae.

So the algae is inevitable if kept in the light? Considering the system is outside I see no way that I would be able to keep it in complete darkness. Is there any way to restrict its growth then?

There is no other way to restrict algae growth. Not unless you want to use a UV steriliser.
If there's gaps of daylight in your raft system, try to cover them with perlite.

Actually, there are a couple of easy solutions.

Aerate your water. That means pump regular old air through air stones (like in a fish tank) submerged in your nutrient sump. You just can't have too much oxygen in the water. The air inhibits the growth of algae and boosts your plants' growth mega-fold.

Try spraying a 3% to 5% solution of hydrogen peroxide on the surface of your growing medium. If that's a float, so be it. Also, you can "foliar spray" the plants themselves. This adds oxygen to the plants and "bleaches", if you will, the algae.

I know this sounds corny, but I do it and it works for me. It'll work for you too.

Light is the enemy. Aeration will help, but it won't do it all. (Hydrogen Peroxide is another way to aerate things - it adds oxygen which kills bad stuff.)

I'm guessing the light is getting in around the edges of your float - gaps between it and the walls of the reservoir that are necessary to allow the float to move up and down freely.

First off, you definitely have to aerate the solution if you aren't already. It supercharges the growth of your plants, but mostly just keeps things from going pear-shaped on you like you're seeing right now.

But to block off those gaps you need something completely opaque but still flexible. You know those plastic metallic bags that Doritos come in? Those are perfect. Duct tape them all the way around the sides of the bin so that you can fold the top edges down onto your float. Either tape them down, or preferably weight them down a little. If you clipped some clothespins to the edges they'd want to fall down onto the raft, but you wouldn't have to worry about them slipping out from under the weights. (You can fold the corners and clip them to help keep the wind from blowing it over the wrong way.)

Of course whatever your bin is made out of should be light-proofed as well - most rubbermaids aren't even if they look like they should be. Cover them with more bags, aluminum tape, whatever works best.

Oh, and those reflective solutions also help to keep the water cooler, which helps cut down on the growth of bad stuff.