# VNS with other heuristic algorithms (some examples)

The second set of experiments is designed to compare VNSMR1 with four other existing multicast routing algorithms in terms of both the quality of the solution generated and computational time. The four algorithms include BSMA, CDKS, QDMR, which are DCLC multicast routing algorithms, and DKSLC which uses Dijkstra’s shortest path algorithm to construct the least cost multicast tree without delay constraint. We randomly generate 20 different network topologies for each size of 20, 50, 100, 200 and 300 networks. For each network topology, the source node and the destination nodes are randomly selected.

1. Network Size = 20, Group Size = 2

 BSMA (Tree Cost = 154, Time = 0s) QDMR (Tree Cost = 118, Time = 0s) CDKS (Tree Cost = 118, Time = 0s) DKSLC (Tree Cost = 118, Time = 0s) VNSMR1 (Tree Cost = 118, Time = 0s)

2.Network size = 50, Group size = 10

 BSMA (Tree Cost = 653, Time = 0.078s) QDMR (Tree Cost = 671, Time = 0s) CDKS (Tree Cost = 695, Time = 0.016s) DKSLC (Tree Cost = 695, Time = 0s) VNSMR1 (Tree Cost = 584, Time = 0.046s)

# 3.Network Size = 100, Group Size = 10

 BSMA (Tree Cost = 620, Time = 0.797s) QDMR (Tree Cost = 586, Time = 0s) CDKS (Tree Cost = 619, Time = 0.078s) DKSLC (Tree Cost = 619, Time = 0s) VNSMR1 (Tree Cost = 521, Time = 0.593s)

# 4.Network Size = 200, Group Size = 20

 BSMA (Tree Cost = 1562, Time = 58.016s) QDMR (Tree Cost = 1877, Time = 0.015s) CDKS (Tree Cost = 1742, Time = 0.672s) DKSLC (Tree Cost = 1722, Time = 0.016s) VNSMR1 (Tree Cost = 1422, Time = 54.657s)
 BSMA (Tree Cost = 839, Time = 147.487s) QDMR (Tree Cost = 852, Time = 0.015s) CDKS (Tree Cost = 1170, Time = 0.188s) DKSLC (Tree Cost = 1215, Time = 0.016s) VNSMR1 (Tree Cost = 814, Time = 44.282s)