Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

Abstract In engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, weight and cost. We consider biobjective shape optimization problem maximizing ceramic component under tensile load while minimizing volume. Stability is thereby modeled using Weibull-type formulation probability failure external loads. The PDE state equation discretized by finite element method on regular grid. To solve we suggest hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints formulation. FurthIn this section, general properties hypervolumeermore, dominated supports decision maker in identifying compromise solutions. investigate relation scalarization weighted sum direct multiobjective descent methods. Since gradient information efficiently obtained solving adjoint equation, scalarized solved ascent algorithm. evaluate our approach 2 D test case representing straight joint load.