3 The Great Deluge (GD)

The great deluge algorithm is founded on the assumption, that a person can walk through a hilly country and a tyde is slowly rising. She can not see much forward, only her nearest neighborhood. So she tries to change her way a little for not getting wet boots on the way. So she walks up and down the hills until she is trapped in the flooding, that surround her.
The great deluge algorithm can not promise that the solution, that it finds, is the global optimum. It can be a local optimum. That depends on the rising of the tyde and where the person and the tyde started. But the solution that can be found is sometimes almost as good as the global optimum and much faster than finding it by an algorithm like branch and bound (BB). It also has a solution after each step. This is advantageously because the algorithm can be stopped and can return the best solution it has found until now.
In our case we are searching the minimal length of a way through an amount of cities which are allowed to be visited only once. Only the startpoint is allowed to be visited again at the end of the path.
This is a little different than described above, where we were looking for a maximum. Now we are looking for a minimum, so the tyde is falling. The person is now like a fish in the water and looks for the deepest valley to survive while the tyde is falling.
We are using a graph to describe the problem. A graph exists on knots and edges. Knots are our cities and the edges are the ways from one city to another. A solution is a path through all cities without visiting one city twice, except the city we are starting with.