Edit: I've answered a few critics below.
The problem for the commercial traveler is: "Given the number of cities and the cost of traveling from one city to another, what is the cheapest round trip that visits each city exactly once?"
I've used the open source classes listed under the link below to create a treatment program to solve the problem of Traveling Saleman with the help of genetic algorithms. Reused paths (corresponding to chromosomes) increase visibility when they are reused. They erase otherwise, which means that the paths "emerge" when certain chromosomes become more dominant.
The problem is considered "resolved" when a hundred generations have passed without a more optimal solution being found.
I've also created the problem in 3D, just because … well, everything looks prettier in 3D and, to be honest, it's incredibly easy to program, given the course that I'm 39 I used from the link below. I would have made it a lot prettier but I'm running out of time / unemployed because I'm starting a new job soon, so I made it work and I left it.
Update: Hello Reddit and Wired. The published simulation does not claim to be the "perfect" solution for the specified layout. The execution of the program repeatedly produces not only different "solutions", but also a large variation in the number of generations required to create a "solution" – from 800 to 5,000, depending entirely on the initial randomized population and of their genetic constitution.
Classes of genetic algorithms: http://www.heatonresearch.com
Traveler Traveler: http://en.wikipedia.org/wiki/Traveling_salesman_problem