I would also throw out your garbage more often.
Fruit flies lay their eggs in soft materials (often meat, rotting vegetables or fruit) and that's what results in them showing up in your kitchen rather than any other room. They may just be congregating around the ice maker because it's a source of drinking water for them.
Also, if your kitchen drain pipe is leaking badly, solids from your kitchen sink will spill out (perhaps onto the crawl space below), and fruit flies will lay their eggs in that mass of rotting putrifaction. In that case, however, you'd see them throughout your house.
I would clean the area where you see these bugs congregating with bleach, and I would definitely hang up some fly paper. Fly paper is really sticky, so that it traps flies when they land on the paper and then can't take off again. That will break the breeding cycle so that once your existing crop of flies is stuck to the paper, you won't have a new crop.