A Divide-and-conquer Evolutionary Algorithm for Large-scale Virtual Network Embedding

The subgraph isomorphism problems, which aim to map subgraphs to a given graph, are widely seen in many applications and are usually nondeterministic polynomial-time complete (NP-complete). As a representative extension of the subgraph isomorphism problem, virtual network embedding (VNE) is a key problem in datacenter scheduling and network virtualization. Existing metaheuristic approaches to VNE problems tend to schedule networks as a whole. But when the problem scale grows, the performance of these approaches may degenerate due to the curse of dimensionality. In this article, we intend to propose a divide-and-conquer evolutionary algorithm with overlapping decomposition (ODEA) to solve large-scale VNE problems. First, realizing the fact that the decision variables in graph-based optimization problems like VNE are usually nonseparable, an overlapping decomposition method is introduced by investigating the characteristic of the network structure. In this method, the critical elements which have tight connections to many other nodes can belong to multiple subcomponents. As a result, the decision variables with tight connections can always be evolved together in multiple subcomponents. Second, to combine the subsolutions into a complete feasible solution, a competitive strategy is devised. Through the competition among critical elements, the optimizing information is shared among subcomponents, which can further improve the effectiveness of ODEA. The proposed ODEA can adopt different metaheuristics as the optimizer, and we conduct experiments on both the scenarios with a single virtual network and with a series of online networks. The experimental results verify that ODEA can significantly improve the performance of different metaheuristics in large-scale VNE problems.