These 2 tables show that the model finds paths that are not much longer than the shortest possible paths, but that overlap very little not only with the shortest path but with all of the other paths found so far.

Table 1. The Four Shortest Paths from Beijing to Kunming
 
Path
Length
(km)
Distance Shared With
Distance + Max Shared Distance
Ratio:

Maxj[2ds+dn]/d(P1)
P1 P2 P3
P1 3016 NA NA NA 3016 1.000
P2 3016 2783 NA NA 5799 1.922
P3 3019 2776 2542 NA 5795 1.921
P4 3019 2546 2779 2786 5805 1.925

Table 2. The Four Optimal* Differentiated Paths from Beijing to Kunming
 
Path
Length
(km)
Distance Shared With
Distance + Max Shared Distance
Ratio:

Maxj[2ds+dn]/d(P1)
P1 P2 P3
P1 3016 NA NA NA 3016 1.000
P2 3098 289 NA NA 3387 1.123
P3 3177 419 307 NA 3596 1.192
P4 3152 867 0 642 4019 1.333

*For m=100, =1.0, =1.0.

NA=Not Applicable