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Classification-based Optimization and Reliability Assessment Using LS-OPT

Simulation-based design often involves the use of metamodeling techniques that provide a cheap surrogate model to replace expensive evaluations. Several types of metamodels are available in LS-OPT, e.g. Radial Basis Function Networks, Feed Forward Neural Networks, Kriging etc. These metamodels use different basis functions and optimization criteria to find the "best" approximation of the actual expensive model. These approximations are then used for optimization and probabilistic analysis. However, the use of response approximations is difficult in certain scenarios, especially when binary (pass/fail) or discontinuous responses (e.g. discontinuity in displacement due to buckling) are present. The above issues can be resolved if classification-based methods are used instead of response approximation. The basic idea is to classify the designs into feasible/infeasible or safe/failed using an explicit decision boundary based on pre-defined constraints. Instead of trying to approximate the response function values, these methods only require and predict the class of a design for training and classification. Several classification methods exist such as k-nearest neighbors (KNN), convex hull, support vector machine (SVM), relevance vector machine (RVM) etc. SVMs and RVMs can provide explicit equations of decision boundaries that are high nonlinear and non-convex. In this work SVMs will be used to perform reliability assessment using LS-OPT. In addition, a new classification-based methodology for multiobjective optimization, which can be seen as an interesting case of binary behavior (dominated vs. non-dominated), will also be presented. The paper will end with a broad perspective on various possible applications of classification methods including but not limited to buckling, biomechanical problems, aero-elastic applications and multi-responses with runtime jumps in the response definition.