Isn't that a NP problem? If it is, you cannot find the fastest one without testing all possibilities, which would take rather long.
The problem is similar to the Traveling Sales Man, IMHO. The best known solution for this problem so far is the Ant Colony Solution. This solution does not guarantee to always find the best solution possible, but it will find at least a pretty good solution within an acceptable amount of time.
I think it may be possible to modify the Ant Colony Solution to also address your problem, by taking the bonus points into account somehow. Probably not the answer you hopped to hear, but the best one I have to offer at the moment.