I wrote the solver code used here as an example for the JuMP modeling package for Julia, which is available at https://github.com/JuliaOpt/JuMP.jl. The specific TSP example code is available at https://github.com/JuliaOpt/JuMP.jl/blob/master/examples/tsp..., and more general information about optimization in Julia is available at http://juliaopt.org

Here's a link which explains how this works:

http://forio.com/about/blog/route-optimizer-julia-google-map...

The really unfortunate thing about that post is it completely fails to understand the essential part of solving the TSP this way, which are the lazily-added subtour elimination constraints. I don't think the blog author at Forio really understood the code they were using, hopefully they will update it one day!

What is the computational complexity of this solution?

This is amazing! I wish there was such a thing for simple A -> B routing taking into consideration the traffic.

Surely this can just be achieved by simply increasing the length of congested roads to normalize travel times.