An adaptive RBF-based multi-objective optimization method for crashworthiness design of functionally graded multi-cell tube

Multi-objective optimization (MOO) problems involving expensive black-box functions are common in various engineering design problems. Currently, metamodel-based multi-objective optimization methods using static metamodels are routinely used to solve these MOO problems. The major challenge to static metamodel-based MOO methods lies in solution accuracy, which heavily depends on the accuracy of the metamodels. While sequential or successive methods can be used to improve the accuracy of a metamodel in a small local region, they are not appropriate for MOO problems because the Pareto optima do not fall into the same small region in the design space. In this study, a novel metamodel-based MOO method using adaptive radial basis functions (ARBFs) was developed for efficiently and effectively solving MOO problems. The ARBFs are globally metamodels that are adaptively improved at various local regions where the Pareto optimal designs are located. The performance of this novel method was first evaluated using six mathematical functions. In addition, the ARBF-based MOO method was also used in a practical application, i.e., the crashworthiness optimization of a new kind of thin-walled structure named functionally graded multi-cell tube (FGMT) that was shown to be a good energy absorber in vehicle bodies.