Research On The Stochastic Optimization Algorithms With Augmented Lagrange Multiplier Method

Optimization design methods have been more and more widely used in modern engineer ing. However, because of the complexity and difficulty of optimization problems increase gradually, especially with the increase of the complexity and difficulty of constrained optimization problem s, the requirements of optimization methods become higher and higher. The diversity of the optimization problems also indicates it is impossible that only one kind of optimization methods can solve all of the optimization problems. In recent years, the traditional optimization methods have the disadvantages of being easily trapped in local optimum with the high dimensional optimization problems, so the study of stochastic optimization methods cause more and more attention. Exploring and improving the methods of stochastic optimization have become an important direction of modern engineering researches and subjects.The key to solve constrained optimization problems is how to effectively deal with the constraints and simplify the optimization problems. However, the traditional methods of handling constraints have their own shortcomings and weaknesses, so they can not be the most effective constraint handling methods in modern engineering optimization problems. So the study of constraints handling methods must also be an important direction for the study of optimization design methods.The stochastic optimization methods of the constrained optimization problems are studied in this paper, which focuses on the subset simulation optimization and the teaching-learning based optimization. In this paper, the augmented Lagrange constraint handling method is used to improve the two optimization methods, and the improved methods have the higher level of accuracy and efficiency in dealing with the constrained optimization problems.Finally, different benchmark problems are used to check the accuracy, efficiency and robustness of improved optimization methods and the results are compared with other optimization methods. Some examples are parametric modeled in Abaqus by Python while the Abaqus is called by Matlab for the finite element analysis to complete the optimization process es.