A
genetic algorithm is created by running an intelligent
trial-and-error system which rewards
efficiency. You take a model of the
problem, create
random algorithms, then try each of them. The best few algorithms are then slightly modified by either
random mutation or by combining to create "child" algorithms. This process is repeated for a while; eventually you should get a highly efficient algorithm (if you wait long enough). These algorithms may find
logical quirks that we may not think of, or find strange "hot spots" in efficiency that are part of a system that is too
chaotic for us to find ourselves.
A good example of a problem which I think could be solved by genetic algorithms is the elevator algorithm.