An analyzer-surrogate-hybrid optimization framework for three-dimensional functionally graded material distribution

Abstract

This paper presents a new optimization framework in which the structural analyzer (isogeometric analysis–IGA) and data-driven surrogate model (deep neural network–DNN) are sequentially and repeatedly employed as the evaluation function in the optimization process of the computationally heavy problem of three-dimensional material distribution optimization in functionally graded (FG) plates. The optimization process starts with IGA normally, and the key point is to collect the evaluated candidates as data to build DNNs as surrogates predicting the plate behavior. Then, in the surrogate-assisted phase, based on the best predicted value, one more IGA analysis could be performed to find a new truly best candidate solution. This is also to track the surrogates' accuracy, which is another key feature of the proposed framework. When the prediction becomes less accurate, the optimization process is back to using IGA, more data is collected, and the whole procedure is repeated. Compliance minimization in FG plates under static bending is considered with various plate geometries. Numerical results confirm that the proposed recurrent optimization framework reduces up to 38% computational time whilst ensuring that the best candidate solution is always exact and of highest optimality.