Fig. 1. An example of six-node network.

Fig. 2. State-space tree construction based on branch-and-bound algorithm.

Fig. 3. The branch-and-bound based optimal algorithm.

Fig. 4. A partial path of length L.

Fig. 5. The branch-and-bound based heuristic procedure.

Fig. 6. Tabu-search based heuristic procedure.

Fig. 7. A network topology.

Fig. 8. A 16-node mesh.

Fig. 9. The success ratio and CPU time versus the L_max/L_min for the tabu-search based algorithm.

Fig. 10. The success ratio versus the number of constraints for an 8×8 mesh.

Table 1. The first set of success ratio comparisons for ANSNET

The number of feasible paths found by all algorithms is based on 1000 benchmarks, which are generated by method (a) in Section 6.1. w₀,w₁=0–10; L_max/L_min=10/5.

Table 2. The second set of success ratio comparisons for ANSNET

The number of feasible paths found by all algorithms is based on 1000 benchmarks, which are generated by method (b) in Section 6.1. w₀,w₁=0–10; L_max/L_min=10/5.

Table 3. The first set of success ratio comparisons for N×N meshes

The number of feasible paths found by all algorithms is based on 1000 benchmarks, which are generated by method (a) in Section 6.1. w₀,w₁=0–10; L_max/L_min=10/5.

Table 4. The second set of success ratio comparisons for N×N meshes

The number of feasible paths found by all algorithms is based on 1000 benchmarks, which are generated by method (b) in Section 6.1. w₀,w₁=0–10; L_max/L_min=10/5.

Table 5. Efficiency comparisons based on N×N meshes

The number of feasible paths found by all algorithms is based on 100 benchmarks, which are generated by method (a) in Section 6.1. Each CPU time is a summation of all the executing times of 100 benchmarks. The CPU time is marked as “n/a”, if it is over 7200 s. α (%)=(number of feasible paths by TK_MK method)/(number of feasible paths by Tabu method)×100.