Results of computational experiments: solving (r|p)HCPuPW using BVNS-based solution approach

The computational experiments are conducted using the instancesgenerated from the well-known CAB dataset, composed and published by O'Kelly in 1987. All mathematical programs were implemented in Python 3.8 (as a part of Anaconda package). The Gurobi Optimizer 9.0 was used as an integer linear programming solver, installed on the Windows 10 operating system. The hardware platform for computation was Intel(R) Core(TM) i7-7700 CPU @ 3.60GHz with 24.0 GiB of DDR4 RAM. When it comes to the size of instance, three batches were considered: 15, 20, and 25 node instances. The discount factors chi and delta were set to 1, and alpha took values from the set {0.2, 0.4, 0.6, 0.8}, as usual for the CAB data set. The price sensitivity factor Theta took values from a set {3, 6, 9, 12, 15}, which are modified values from. The difference is that the values are integer and equally separated in range from 3 to 15. When it comes to the hub backbone size, two cases were addressed: 1. the number of hubs for both competitors is equal (i.e., r = p); 2. the competitors locate unequal number of hubs (i.e., r <> p). In the first case, the size of hub backbone in experiments was taken to be 2, 3, 4, and 5. The time limit t_max is set as: + when |N| = 15, t_max = 45 minutes; + when |N| = 20, t_max = 1.5 hours; + when |N| = 25, t_max = 2 hours. In total, 240 instances were examined. For every one of them, the VNS algorithm has been executed for 10 times, i.e., 2400 tests were performed. In the second case, only extreme parameter values were considered, i.e., alpha from {0.2, 0.8}, Theta from {3, 15}, (r,p) from {(2, 5), (5, 2)}. In other words, the second case is presented just for illustration purposes, because such considerations are not presented in the majority of research literature. These data is stored in three csv files: different-15.csv, different-20.csv, different-25.csv. Besides this, a situation in which leader ignores the follower is addressed. Two classic hub--location networks are considered as the leader's strategic option: p-HMLP and p -HCLP. For these networks, VNS algorithm has not been executes. Only the optimal follower's solution was determined. For this situation, 480 tests were performed. The corresponding filenames have prefix C, or suffix M.