基于NSGA-II的复杂网络拓扑优化方法

Complex Network Topology Optimization Based on NSGA-II

提出一种基于NSGA-II的保度保边的复杂网络拓扑优化方法,该方法通过保度保边的网络交叉和变异操作,应用非支配层排序和拥挤度计算选择精英父辈网络,以达成最大化网络效率和网络抗毁性。仿真分析表明,该方法能同时显著提高初始网络的抗毁性和网络效率;优化网络效率使得网络度连接呈现负相关,网络呈现出“多核心分散”结构;优化网络抗毁性使得度连接呈现正相关,网络呈现“紧密核心-分散外围”结构;同时优化使得网络呈现“较密核心-大外围”结构。该方法具有较好的理论一般性和实际应用价值。

This paper proposes a complex network topology optimization method based on NSGA-II with degrees and edges number unchanged strategy.By utilizing non-dominated layer sorting and congestion degree calculation of NSGA-II and designing genetic operations with node’s degree and edge’s number unchanged,this method selects elite parent networks to generate latent advantageous children,which accelerates the convergence speed without falling into local optimal solutions,thus achieving the maximum network efficiency and invulnerability.Simulation analysis shows that it can significantly improve both network invulnerability and network efficiency of the initial networks simultaneously.Through network efficiency optimization,the degree connection relationship shows a negative trend,and thus the network presents a“multi-core decentralized”structure;whereas,through optimizing the network invulnerability,the degree connection relationship shows a positive trend,and the network then presents a“close-core and scattered-periphery”structure.Optimizing both indexes,the network presents a“tighter-core and large-periphery”structure.The method proposed is proved with good theoretical generality and practical application value.