Improvement of efficient global optimization with mixture of experts: methodology developments and preliminary results in aircraft wing design

摘要

For decades, numerical tool improvements enabled the optimization of complex processes occurring during the conceptual phase. Nowadays simulators can determine numerous coupled physical effects with high accuracy and allow cheap and fast virtual testing. However, high fidelity tools require long computation times (several days of computation using High Performance Computing solutions) and thus optimization based on these high fidelity tools is often done at higher computational cost (gradient based). This work aims at optimizing a complex design using costly simulation codes given a fixed computational budget. In aeronautical engineering these codes can be coupled in space (such as Fluid Structure Interaction) and/or in time (for transient analysis). The fixed budget implies the use of surrogate-based method with adaptive sampling in order to promote a trade-off between exploration and exploitation. The proposed optimization is based on a sequential enrichment approach (typically Efficient Global Optimization), using an adaptive mixture of kriging-based models. The strategy relies on an improvement of the kriging model that enables the handling of a large number of design variables whilst maintaining rapidity and accuracy. A key feature is the use of mixture of experts technique to combine local surrogate models to approximate both the objective function and the constraints. Our strategy will be introduced through mathematical methods and detailed algorithms presentation. Finally, we produce several validations on analytical test cases (supervised) and two extensions such as the well-known MOPTA test case from automotive industry and aircraft wing structural optimization. The experiments confirm that the proposed global optimization approach minimizes the number of black box evaluations and in this sense it is well suited for high-dimensional problems with a large number of constraints.