Application of simulated annealing method to pressure and force loading optimization in tube hydroforming process

► A novel optimization procedure is developed for tube hydroforming process using Simulated Annealing method. ► Optimal pressure and force loading paths are obtained for a copper tube with an axisymmetric final shape. ► Optimized results are validated using experiments and another literature. ► Less wall thinning and better shape conformation are obtained through the multi-linear pressure and force loading paths.