Trajectory Stability in the Traveling Salesman Problem

Figure 4

Stability of ranks under reallocation of sites. (a) Particular instance of the rTSP with and . Black points represent fixed sites, whereas the white one represents the site to be reallocated. The shortest trajectory is indicated as a dashed cyan line. When the white point is reallocated in the orange area , the shortest trajectory remains unchanged, while if a node is reallocated in any part of the blue area, the shortest trajectory changes. (b) Same realization of the rTSP, but for the trajectory with an intermediate rank (). The orange area is much smaller in this case. (c) Same realization of the rTSP, but for the longest trajectory (), where the orange area is again big. In panels (d), (e), and (f) we show the probability distributions of for and the three previous values of , as well as its mean value, .

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(b)

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(f)