Your constant hunger is as much a result of habits or boredom as of an empty stomach.
When I did my masters, I was forced to use the crappy MS Fortran compiler of the day, and resolved I will not go to lunch before the code compiles. Turns out that I reached this state only at 3 or 4 in the afternoon when the canteen had long closed. Did that for a week and felt no hunger around lunchtime anymore.
So your habit of stuffing something in your mouth every two hours makes sure you will feel hungry after the next two hours. Yes, it does cost some discipline to break that habit, but you will be surprised how quickly you will adapt and will be able to work for a longer stretch. Same with boredom - your visit at the fridge is as much a result of desiring variety as of being hungry. Kick that habit, do something that keeps your mind occupied, and you will go without feeling the need to eat something for much longer stretches.
It is a matter of eating less, after all.