Finding -Hub Median Locations: An Empirical Study on Problems and Solution Techniques

Figure 10

Visualization of ISA problems for the TR dataset with , , , and , AP dataset with , , , and , and CAB dataset with , , , and : red points and blue points are hubs and nonhub nodes. The red links are the links between hubs. For the TR dataset, the structures of links obtained by three methods are similar to each other. For the AP dataset, the optimal solution is obtained with CPLEX-LP and GA while RCBS selects node 35 and node 16 as hubs because of their high importance. For the CAB dataset, CPLEX-LP provides an optimal solution. The solutions of GA and CPLEX-LP only have a difference of 1.33% while having significantly different hub assignments in the figures. RCBS still selects Detroit (DTT) as a hub instead of Dallas (DFW).

(a) TR dataset with CPLEX-LP (0%)

(b) TR dataset with GA (3.35%)

(c) TR dataset with RCBS (2.23%)

(d) AP dataset with CPLEX-LP (0%)

(e) AP dataset with GA (0%)

(f) AP dataset with RCBS (3.65%)

(g) CAB dataset with CPLEX-LP (0%)

(h) CAB dataset with GA (1.33%)

(i) CAB dataset with RCBS (4.37%)