A simulated annealing based heuristic for the multi-source single-path multi-commodity network flow problem

In this paper, we introduce the multi-source single-path multi-commodity network flow problem (MSMCF), which arises in the telecommunication system. For each commodity, the MSMCF is to determine its source node, to choose a single path linking this chosen source and destination nodes, and to allocate bandwidth such that the total transportation cost is minimized. Since the MSMCF is NP-hard, we develop a simulated annealing based heuristic to solve it. We evaluate the performance of the proposed algorithm over 175 randomly generated instances. The experimental results show the proposed heuristic is an efficient and effective method for the MSMCF.