Optimal distribution of reliability for a large network based on connectivity

Abstract

It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms (GA). Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.