Hybrid Kriging-assisted Level Set Method for Structural Topology Optimization

Elena Raponi, Mariusz Bujny, Markus Olhofer, Simonetta Boria, Fabian Duddeck

Abstract

This work presents a hybrid optimization approach that couples Efficient Global Optimization (EGO) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in the Topology Optimization (TO) of mechanical structures. Both of these methods are regarded as good optimization strategies for continuous global optimization of expensive and multimodal problems, e.g. associated with vehicle crashworthiness. CMA-ES is flexible and robust to changing circumstances. Moreover, by taking advantage of a low-dimensional parametrization introduced by the Evolutionary Level Set Method (EA-LSM) for structural Topology Optimization, such Evolution Strategy allows for dealing with costly problems even more efficiently. However, it is characterized by high computational costs, which can be mitigated by using the EGO algorithm at the early stages of the optimization process. By means of surrogate models, EGO allows for the construction of cheap-to-evaluate approximations of the objective functions, leading to an initial fast convergence towards the optimum in opposition to a poor exploitive behavior. The approach presented here – the Hybrid Kriging-assisted Level Set Method (HKG-LSM) – first uses the Kriging-based method for Level Set Topology Optimization (KG-LSM) to converge fast at the beginning of the optimization process and explore the design space to find promising regions. Afterwards, the algorithm switches to the EA-LSM using CMA-ES, whose parameters are initialized based on the previous model. A static benchmark test case is used to assess the proposed methodology in terms of convergence speed. The obtained results show that the HKG-LSM represents a valuable option for speeding up the optimization process in real-world applications with limited computational resources. As such, the proposed methodology exhibits a much more general potential, e.g. when dealing with high-fidelity crash simulations.

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