Trajectory Stability in the Traveling Salesman Problem

Figure 3

Parameter dependence of rank diversity. We analyze how changing parameter values affects the rank diversity for two time-dependent versions of the TSP. For panels (a)–(d) we consider . Starting with the bTSP and , we (a) vary the number of observations while keeping the total time , (b) fix the number of time steps while varying the total time, and (c) fix the value of while changing the number of time steps (and thus the total time). For the rTSP, we also (d) show how changing the number of time steps alters the diversity. Curves are averages over 100 realizations. Panels (e) and (f), respectively, show the rank diversity for the bTSP when sites are allowed to move and for the rTSP when sites are reallocated at each time step, with both and . For the bTSP the total time is , which leads to . We choose this value of so that the ranges of the diversity in (e) and (f) resemble each other. Results in (f) are averages over 1000 realizations. Horizontal lines correspond to , the maximum value of the diversity given in (1). In (b), (d), (e), and (f) all curves have the same bound, whereas in (a) and (c) color is used to indicate the bounds of each curve.

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