生命线工程网络抗震优化算法研究

Research on Seismic Topology Optimization of Lifeline Networks

摘要:

以生命线工程网络系统造价为优化目标，网络拓扑结构为优化参数，网络节点抗震连通可靠度为约束条件，建立了生命线工程网络系统的抗震拓扑优化模型。同时，介绍了利用递推分解算法来获得单元重要度的方法。进而利用遗传算法、模拟退火算法和遗传-模拟退火混合算法进行了生命线网络系统的抗震拓扑优化分析。其中，遗传算法通过对种群进行选择、交叉和变异操作不断进化以获得优化解。模拟退火算法则通过扰动当前解产生新解来获得优化解。遗传-模拟退火混合算法则通过将遗传算法中的变异操作用模拟退火操作代替来获得优化解。利用三种优化方法对两个算例进行了生命线工程网络系统的抗震拓扑优化分析。计算结果对比表明，遗传-模拟退火混合算法具有最好的优化能力。

Abstract:

Taking network cost and nodal reliability as optimization object and restriction, a network topology optimization model is presented for the aim to achieve the best topologies of lifeline networks under earthquake. In order to speed up the optimization process, the element investment importance is introduced based on recursive decomposition algorithm. As this model is a typical combinatorial optimization problem, three approaches, genetic algorithm (GA), simulated annealing algorithm (SAA) and simulated annealing genetic algorithm (SAGA), are used to solve it. When GA is used, a generation including many genes is initially created with each gene representing a network. Then by using selection, crossover and mutation operators, a new generation is evolved. After a number of iterations or when some criteria are met, a near-global optimal solution could usually be found. SAA takes a network topology as its current solution and produce a new solution by perturbing. If the perturbation result is an improved solution, it is accepted and the current solution is updated accordingly. Otherwise, it can also be accepted at a probability. The perturbations and updates repeat until some criteria are met. Replacing the mutation operator in GA with perturbations and updates in SAA, SAGA is established to solve the optimization model. Moreover, two example networks are evaluated to compare the efficiency of these algorithms. The results indicate that SAA performs best.