Cumulative Updating of Network Reliability with Diameter Constraint and Network Topology Optimization

Reliability-based optimization of a network topology is to maximize the network reliability within certain constraints. For modeling of unrelaible networks we use random graphs due to their good applicability, wide facilities and profound elaborating. However, graph optimization problems in conditions of different constraints are NP-hard problems mostly. These problems can be effectively solved by optimization methods based on biological processes, such as genetic algorithms or clonal selection algorithms. As a rule, these techiques can provide an applicable solution for network topology optimization within an acceptable time. In order to speed up fitness function calculation, we improve operators of a genetic algorithm and a clonal selection algorithm by using the method of cumulative updating of lower and upper bounds of network reliability with diameter constraint. This method allows us to make a decision about the network reliability (or unreliability) with respect to a given threshold without performing the exhaustive calculation. Based on this method, we obtain the genetic algorithm and the clonal selection algorithm for network topology optimization. Some computational results are also presented for demonstration of an applicability of the proposed approach.