Optimal Distribution of Reliability for Large Network Based on Connectivity
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摘要: 由于网络连通可靠度计算属于NP-hard问题，当系统可靠度无法显式表达时，基于连通可靠度的大型复杂网络优化通常只能采用启发式优化算法解决．通过对复杂网络连通可靠度算法结构的分析，给出了系统连通可靠度的Taylor方程．采用遗传算法，由系统连通可靠度的Taylor方程确定种群适应值，得到一个系统最优可靠度分配方案；将最优解带入改进Minty算法或递推分解算法中，计算该最优解的连通可靠度精确值和对应的连通可靠度的Taylor展开方程；再次采用遗传算法求最优解．当最优解对应的可靠度精确值和Taylor方程算得得近似值误差小于指定精度时，则此最优解为最终的系统最优可靠度分配方案A·D2将此优化过程称为迭代遗传算法．算例显示迭代遗传算法不仅可用于大型网络的连通可靠度最优分配，而且优化迭代过程中可以得到多组阶段最优解，这些解均落在最优解附近，构成了近似最优解群，在实际工程优化中拓展了选择面．Abstract: It is a non-polynomial complexity problem to calculate the connectivity of the complex network. When the reliability of the system can not be expressed as the function of the element reliability,some heuristic methods were applied to do the optimization based on connectivity of the network.The calculation structure of connectivity of complex network was analysed.The coefficient matrixes of Taylor second order expansion of the system connectivity was generated based on the calculation structure of connectivity of complex network.A optimal schedule is achieved based on genetic algorithms(GA).The fitness of seeds was calculated using the Taylor expansion function of system connectivity.The 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 the error between the approximate connectivity and the precise value exceeds the assigned precision,optimize process was continued using GA and the Taylor function of system connectivity need renewal.The optimum process was called iterative GA.One case is illustrated iterative GA which can be used in the large network for optimal reliability attribution.One temporary optimal result will be generated every time in iteration process.These temporary optimal results approach the real optimal results.They can be regarded as the group of the approx imate optimal results that is useful in the real project.
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