I have a bit of a strange question. Can anyone tell me where to find information about, or give me a little bit of an introduction to using shortest path algorithms that use a hill-climbing approach? I understand the basics of both, but I can't put the two together. Wikipedia has an interesting part about solving the Travelling Sales Person with hill climbing but doesn't provide a more in-depth explanation of how to go about it exactly.
For example, hill climbing can be applied to the traveling salesman problem. It is easy to find a solution that visits all the cities but will be very poor compared to the optimal solution. The algorithm starts with such a solution and makes small improvements to it, such as switching the order in which two cities are visited. Eventually, a much better route is obtained.
As far as I understand it, you should pick any path and then iterate through it and make optimizations along the way. For instance, going back and picking a different link from the starting node and checking whether that gives a shorter path.
I am sorry - I did not make myself very clear. I understand how to apply the idea of Travelling Salesperson. I would like to use it in the shortest distance algorithm.