Choosing the right system architecture for the problem at hand is challenging due to the large design space and high uncertainty in the early stage of the design process. Formulating the architecting process as an optimization problem may mitigate some of these challenges. This work investigates strategies for solving system architecture optimization (SAO) problems: expensive, black-box, hierarchical, mixed-discrete, constrained, multi-objective problems that may be subject to hidden constraints. Imputation ratio, correction ratio, correction fraction, and max rate diversity metrics are defined for characterizing hierarchical design spaces. This work considers two classes of optimization algorithms for SAO: multi-objective evolutionary algorithms such as NSGA-II, and Bayesian optimization (BO) algorithms. A new Gaussian process kernel is presented that enables modeling hierarchical categorical variables, extending previous work on modeling continuous and integer hierarchical variables. Next, a hierarchical sampling algorithm that uses design space hierarchy to group design vectors by active design variables is developed. Then, it is demonstrated that integrating more hierarchy information in the optimization algorithms yields better optimization results for BO algorithms. Several realistic single-objective and multi-objective test problems are used for investigations. Finally, the BO algorithm is applied to a jet engine architecture optimization problem. This work shows that the developed BO algorithm can effectively solve the problem with one order of magnitude less function evaluations than NSGA-II. The algorithms and problems used in this work are implemented in the open-source Python library SBArchOpt.

View Video Presentation: https://doi.org/10.2514/6.2022-4053.vid Bayesian optimization is an advanced tool to perform efficient global optimization. It consists on enriching iteratively surrogate Kriging models of the objective and the constraints (both supposed to be computationally expensive) of the targeted optimization problem. Nowadays, efficient extensions of Bayesian optimization to solve expensive multi-objective problems are of high interest. The proposed method, in this paper, extends the super efficient global optimization with mixture of experts (SEGOMOE) to solve constrained multi-objective problems. To cope with the ill-posedness of the multi-objective infill criteria, different enrichment procedures using regularization techniques are proposed. The merit of the proposed approaches are shown on known multi-objective benchmark problems with and without constraints. The proposed methods are then used to solve a bi-objective application related to conceptual aircraft design with five unknown design variables and three nonlinear inequality constraints. The prelimilnary results show a reduction of the total cost in terms of function evaluations by a factor of 20 compared to the evolutionary algorithm NSGA-II.

View Video Presentation: https://doi.org/10.2514/6.2022-0082.vid Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and categorical variables might arise during the optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.

View Video Presentation: https://doi.org/10.2514/6.2022-3870.vid Recently, there has been a growing interest for mixed categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies. Among the recently developed methods, we could cite: GP models built using continuous relaxation of the variables, Gower distance based models or GP models derived from direct estimation of the correlation matrix. In this paper, we present a kernel-based approach that extends continuous Gaussian kernels to handle mixed-categorical variables. The proposed kernel leads to a GP surrogate that generalizes continuous relaxation and Gower distance based GP models. The good potential of the proposed framework is shown on analytical mixed-categorical variables test cases. On different settings, our proposed GP models is as accurate as the state-of-the-art GP models.