Trajectory Stability in the Traveling Salesman Problem

Figure 1

Time-dependent traveling salesman problem with moving sites and with reallocation of sites. Rank distribution for the TSP. (a) Diagram showing the two generalizations of the TSP considered here. By allowing nodes to shift in time, the static TSP (center) becomes time dependent. In the TSP with moving sites (left), these are displaced in a small interval . In the TSP with reallocation of sites (right), they are displaced to random positions after one time step. In these TSP variations, nodes do not move during path traversals; that is, the optimization problem of finding paths is solved for a static situation. Shortest paths are shown with lines between sites. (b) Rank distribution according to the inverse path length , for to sites in particular but representative instances of the TSP. Not all points are shown in the figure, so the best fit to a beta function (continuous line) can be clearly seen. We include a proportionality factor to such function to account for the fact that is not a probability density.

(a)

(b)