An adaptive method of moving asymptotes for topology optimization based on the trust region

Abstract

A novel gradient-based optimizer, which makes use of Trust Region based Moving Asymptotes and is abbreviated as TRMA method, is proposed for the topology optimization. Compared with the most frequently used optimizer, the method of moving asymptotes (MMA), the step-based subproblem adopted in the TRMA method shows better accuracy in approximating the response surface near the current iterative point. Also, a criterion to judge the quality of the trial step is introduced in the trust region scheme which is regarded as an adaptive process for automatically adjusting the expansion parameters of the moving asymptotes. The above features endow the TRMA method with inherent numerical robustness and efficiency. Three benchmark problems (including the compliance minimization problem and the stress constraint problem) are considered to investigate the performance of the TRMA method. Although those problems are well addressed by many other creative strategies, which always involve modification of the optimization formulations, few studies focus on the development of the algorithms directly. Hence, the inherent complexity of those formulations (like the high nonlinearity introduced by aggregation and the large-scale constraints when the aggregation-free formulation is adopted) is still a great difficulty for the existing optimizers. Results show that the TRMA method is a powerful optimizer for handling problems with high nonlinearity and large-scale constraints and may promote the exploration and application of the topology optimization methods, even when the traditional MMA becomes inefficient.