I'm presuming that by "tile" you mean ceramic tile and not vinyl composition tile.
Janitorial services will clean ceramic tile floors with a floor machine like this:
You can get rotary brushes for floors in a wide variety of aggressiveness;
(the above shows two rotary brushes with their bristles pressed together)
everything from soft thin nylon bristles to stiff nylon bristles impregnated with abrasives.
If this is a kitchen floor, then I'd expect all of the soil on it is likely to be removed with just a detergent and water. I'd just use Mr. Clean & water.
You may have a problem with soft foods getting mooshed into porous grout. They can be a problem to remove from the grout, but it can be done by dissolving the grout with an acidic cleaner like CLR. If you do that, however, then definitely seal your grout with an acrylic film forming sealer after it's clean so you don't have to do that again. Use Google to find a product called "Grout Sealer" made by the Glaze 'N Seal Company of California.
That will prevent soft foods from getting into the grout underfoot in the first place.
But, be aware that unless you take an artist's paint brush and paint sealer over the grout lines only, a coat of sealer on the tiles will make them smoother, make the tile floor both look darker and glossier and will make the tile floor slippery when wet. You really only need to seal the grout lines to prevent soft foods from getting into it's porous surface.