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Response Surface Models are often used as a surrogate for expensive black-box functions during optimization to reduce computational cost. Often, the CAE analysis models are highly nonlinear and multi-modal. A response surface approximation of such analysis as a result is highly multi-modal; i.e. it contains multiple local optima. A gradient-based optimizer working with such a response surface will often converge to the nearest local optimum. There does not exist any method to guarantee a global optima for non-convex multi-modal functions. For such problems, we propose an efficient algorithm to find as many distinct local optima as possible. The proposed method is specifically designed to work in large dimensions (about 100 ∼ 1000 design variables and similar number of constraints) and can identify most of the locally optimal solutions in a reasonable amount of time.

The Hybrid Cellular Automaton (HCA) algorithm is a generative design approach used to synthesize conceptual designs of crashworthy vehicle structures with a target mass. Given the target mass, the HCA algorithm generates a structure with a specific acceleration-displacement profile. The extended HCA (xHCA) algorithm is a generalization of the HCA algorithm that allows to tailor the crash response of the vehicle structure. Given a target mass, the xHCA algorithm has the ability to generate structures with different acceleration-displacement profiles and target a desired crash response. In order to accomplish this task, the xHCA algorithm includes two main components: a set of meta-parameters (in addition target mass) and surrogate model technique that finds the optimal meta-parameter values. This work demonstrates the capabilities of the xHCA algorithm tailoring acceleration and intrusion through the use of one meta-parameter (design time) and the use of Kriging-assisted optimization.