一种基于网格的多目标优化方法

摘要

工程设计优化大多为多目标、非线性和隐函数的数学规划问题,通常需要用黑箱商用或专用有限元分析软件的模拟结果进行目标评估.这种计算密集型任务导致巨大的计算消耗.为此,将黑箱优化方法和网格计算技术用于工程优化设计领域.首先,通过拉丁超立方取样在设计域内得到了一个分布相对均匀的样本集合,利用这些样本建立工程优化的克里格（Kriging）替代模型;然后,发展了一种与网格计算技术相结合的优化权系数的网格黑箱多目标优化方法（GBMO）,并获得一系列按权系数分布的Pareto解.该方法已经在中国国家网格（CNGrid）环境中实现.工程优化实例表明,该方法有很高的优化效率和加速比,适用于国家网格计算环境下的工程设计优化.%Engineering design optimization problems are mostly multi-objective,nonlinear and implicit mathematical programming issues,and their evaluation requires the resolution of the finite element analysis performed by a black-box commercial or professional software.These computation intensive works result in huge computational consumptions.Therefore,the black-box optimization method and grid computing technology are developed in the engineering optimization field.A set of fairly well-distributed samples is first obtained by Latin hypercube sampling(LHS),and a Kriging approximate model for the engineering optimization is constructed by using these sampling points.Then,a combination of the optimal weighted expected improvement and grid computing technology,named grid-based multi-objective optimization method(GBMO),is developed to obtain a series of Pareto solutions according to the weight coefficient distribution.An implementation of the method on the China national grid(CNGrid)is discussed.The engineering optimization examples are given,and the results show that the method has very high speed-up and efficiency and can be applied to the engineering design optimizations under CNGrid environment.