Bayesian optimization-based topology optimization using moving morphable bars for flexible structure design problems

Abstract

This paper presents a Bayesian optimization (BO) based topology optimization to solve flexible structure design problems in highly nonlinear design spaces. Our primary interest is to avoid topology optimization’s strong dependency on initial designs, which is inevitable when employing gradient-based optimizers. In order to do this, BO is used as a gradient-free optimizer that uses a probabilistic model to trade off exploration and exploitation in order to balance global and local search with a minimal number of iterations. Because of the curse of dimensionality in BO, a moving morphable bar (MMB) is used as a primitive member for a low-dimensional surrogate. We verified that BO could handle dozens of design parameters using the MMB through mean compliance minimization problems with known global optimum layouts. The effect of the BO trade-off parameter in the acquisition function, balancing the optimizer’s exploration, is also investigated. Numerical examples show that the proposed BO-based topology optimization method has suggested better optimum solutions for flexible structures than the MMA-based topology optimization. The performance of the proposed method is also compared with other global optimization methods, showing better performance in terms of minimized objective functions as well as the number of analyses for convergence.