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

Figure 9

Visualization of CSA problems for the TR dataset with , , and , AP dataset with , , and , and CAB dataset with , , and : red points are hubs and blue points are nonhub nodes. The red links are hub links. For the TR dataset, CPLEX-LP provides a feasible solution only, and therefore the assignment is rather useless. The results obtained by GA, LR, and RCBS are quite similar to each other. For the AP dataset, CPLEX-LP and RCBS provide poor solutions, while the results of GA and LR are different regarding one hub. For the CAB dataset, CPLEX-LP, GA, and LR are all up to the optimality, while RCBS selects Detroit (DTT) as a hub because of its high node importance instead of Dallas (DFW).

(a) TR dataset with LP (108.55%)

(b) TR dataset with GA (0.67%)

(c) TR dataset with LR (0%)

(d) TR dataset with RCBS (1.49%)

(e) AP dataset with LP (186.43%)

(f) AP dataset with GA (0%)

(g) AP dataset with LR (2.45%)

(h) AP dataset with RCBS (2.73%)

(i) CAB dataset with LP (0%)

(j) CAB dataset with GA (0%)

(k) CAB dataset with LR (0%)

(l) CAB dataset with RCBS (5.29%)