Why would you use GA for shortest path problem. Unless you have some unknown twist to the definition of the problem shortest path is a O(n log m) problem?! And to my experience I would not suggest GA for this kind of problem due to the complexity issue. GA are simply got good with that kind of problems to my experience. It’s always tempting to try! =)

http://silyeek-tech.blogspot.com/2006/03/genetic-algorithm-in-solving-vehicle.html