On the Impact of the Differential Evolution Parameters in the Solution of the Survivable Virtual Topology-Mapping Problem in IP-Over-WDM Networks

Abstract In IP-over-WDM networks, a virtual topology is placed over the physical topology of the optical network. Given that a simple link failure or a node failure on the physical topology can cause a significant loss of information, an important challenge is to make the routing of the virtual topology onto the physical topology survivable. This problem is known as survivable virtual topology mapping (SVTM) and is an NP-complete problem. So far, this problem has been optimally solved for small instances by integer linear programming, and suboptimally solved for large instances by heuristic strategies such as ant colony optimization or genetic algorithms. In this chapter, we introduce the application of differential evolution (DE) to solve the SVTM problem. An illustrative example is presented to clearly understand the method. The method requires the manipulation of a few DE parameters such as population size ( NP ), mutation constant ( M ), and recombination constant ( RC ). A detailed analysis of the impact of the DE parameters on the quality of solutions is presented using the NSF and Japan test bench optical topologies. Results show the effectiveness and efficiency of the proposed algorithms. The chapter concludes with a set of recommended DE parameter values for this specific application.