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 m...