We used to have a similar problem with ants. The way I fixed it was two fold. First - I cleaned up. All stored food was sealed somehow. No boxes left open, everything in either a tupperware or ziplock bag. Then I made sure to clean after every meal. No crumbs, no dirty dishes. It's a pain, but it's necessary.

That will eventually work. If they don't find food, they'll stop coming. To speed the process however, I would search for and find the trail by which they were entering the food areas. I would then take a spray bottle of rubbing alcohol (not a terrible chemical as chemicals go) and spray the whole path through which they were entering. I would wait for it to kill the ants on the path already then I would wipe it up and spray it again. In doing so I would kill many of the ants who had already invaded, and wipe away the trail that lead them from their entrance to my food areas.

This worked for me because they were limited to a single entrance and path to the food area that was easy for me to clean away. Whenever they showed, I'd spray the path and they'd go away until I got messy and they found their way back to my mess again. Your mileage with this trick may vary.