Detecting infinite loop in brainfuck program

Question

I have written a simple brainfuck interpreter in MATLAB script language. It is fed random bf programs to execute (as part of a genetic algorithm project). The problem I face is,

Answer 1

This is not the halting problem, however, it is still not reasonable to try to detect halting even in such a limited machine as a 1000 cell BF machine.

Consider this program:

+[->[>]+<[-<]+]

This program will not repeat until it has filled up the entire of memory which for just 1000 cells will take about 10^300 years.