Time dependent sheet metal forming optimization by using Gaussian process assisted firefly algorithm

For a sheet metal forming optimization problem, time related design variables are seldom considered in practice. The purpose of this work is to handle time dependent sheet metal forming problems. Because it is difficult to investigate all time points during the entire forming procedure, some key time points should be extracted. Therefore, the number of design variables should be significantly increased due to introduce auxiliary time design variables. However, curse of dimensionality is a formidable difficult issue to be solved. To solve such medium-scale problems, Gaussian Process Assisted Firefly Algorithm (GPFA) is suggested. The main idea of the suggested method is to construct a surrogate model-aware search mechanism with Firefly Algorithm (FA) for simulation-based optimization efficiently. Compared with other FAs, the distinctive characteristic of GPFA is to generate new sample points adaptively based on maximum Expected Improvement (EI) criterion, so that the local and global search can be well balanced, and a small promising area can be quickly focused on. Numerical studies on benchmark problems with 20 variables and a real-world application of time dependent sheet metal forming optimization reveal that the GPFA is capable to solve such similar problems.