增广拉格朗日子集模拟优化方法

Augmented Lagrangian Subset Simulation Optimization Method

传统的工程结构优化设计方法在求解多设计变量、多约束条件的结构优化设计问题时,存在诸多不足,针对上述问题,基于增广拉格朗日约束处理方法和子集模拟优化方法发展一种新的结构优化设计方法——增广拉格朗日子集模拟优化方法(ALSSO)。该方法首先利用拉格朗日乘子法处理多重约束条件,然后利用子集模拟优化方法对转化后的无约束优化问题进行求解;对罚函数因子的更新方法进行改进,以保证收敛过程的稳定性;利用两个算例对该方法的计算精度、稳健性以及计算效率进行验证,并与其他优化方法进行对比。结果表明:增广拉格朗日子集模拟优化方法具有非常优秀的寻优性能。

In solving the structural optimization problems with multiple design variables and multiple constraints,traditional optimization design method of engineering structure has many disadvantages.A new structural optimization method,which is based on subset simulation optimization（SSO）and the Lagrangian multiplier method,is developed to solve structural optimization problems under constraints.The Lagrangian multiplier method is used to handle multiple constraints.Then,SSO is used to solve the transformed unconstrained problem and search for the global optimum.In order to guarantee the robustness of convergence,the updating method of penalty factor is modified for this purpose.The accuracy,robustness and efficiency of the proposed method are demonstrated by two examples.The optimization results of proposed method are compared with those obtained by other optimization methods available in the literature.It indicates that the proposed method has excellent performance on searching for the global optimum.