Optimal Network Topology Based on Natural Connectivity and Improved Genetic Algorithm

Abstract

Invulnerability study is an important research content of complex network. On the basis of analysis and comparison of other traditional inadequate measurements of invulnerability, natural connectivity was used as the invulnerability measurement of network topology and an optimal network topology model based on natural connectivity has been proposed. Based on the basic idea of genetic algorithms, we designed an improved algorithm based on genetic algorithm and cloud mode to solve the model. Simulation experiments analyzed the invulnerability changes before and after the network topology optimization and verified the rationality of network topology optimization model and algorithm. Introduction An important purpose of complex network research is to design a good network topology and invulnerability is an important measurement to check the network. Currently, the study of complex network invulnerability is based on graph theory. The graph theory based invulnerability indicators mainly include toughness [1], integrity [2], tenacity [3], algebraic connectivity [4][5], etc., but these indicators have their disadvantages [6][7]. Chvatal initially used tenacity to study Hamiltonicity a graph. Later, it was used to measure the graph invulnerability, but Bauer et al demonstrated that the calculation of toughness was a NP problem. The integrity does not only consider the degree of difficulty of network destruction, but also takes into account of the scale of the largest piece after being destroyed, but the calculation of integrity is also a NP problem. Similarly, tenacity does not solely focus on the degree of difficulty of network destruction, but also takes into account of the scale of the maximum connectivity piece scale and the number of connectivity pieces, but the calculation of tenacity is also a NP problem. Algebraic connectivity is obviously inadequate, and not suitable for large-scale networks. Nature connectivity proposed by Literature [8] focused on proceeding from the internal network topology properties to describe the redundancy of alternative path by the method of closed path amount weighing, with clear physical significance and in concise mathematical form. It can be directly obtained by calculating the characteristic spectrum of the adjacent matrix, with a relatively low calculation complexity. Moreover, the edge adding and removal of natural connectivity is in strict monotonic increase or decrease, which has obvious advantages by comparing with other indicators and can well measure the invulnerability of network topology. Therefore, this paper uses natural connectivity as the invulnerability measurement to establish network topology optimization model, design the algorithm based on genetic algorithm and cloud model, which does not only speed up the search speed of the algorithm, but also reduces the possibility of local optimum. 5th International Conference on Information Engineering for Mechanics and Materials (ICIMM 2015) © 2015. The authors Published by Atlantis Press 1175 Network Topology Invulnerability Optimization Model Network topology representation. Complex network topology can be represented as the Figure G=(V,E)composed of node set V and edge set E, where V is a node set, represented as { } 1 2 , , , N V v v v =  , edge set represented as { } 1 2 , , , W E e e e V V = ⊆ ×  , indicating node connectivity. N V = is used to represent node quantity, whereas W E = represents edge quantity, ( ) ( ) ij N N E G a × = means the adjacent matrix of G, where ij a represents the connection between network node i and j: 1 0 ij i and j is connected a otherwise  =   (1) λ − is the natural connectivity of Figure G, where