Complex system design problems, such as those involved in aerospace engineering, require the use of numerically costly simulation codes in order to predict the performance of the system to be designed. In this context, these codes are often embedded into an optimization process to provide the best design while satisfying the design constraints. Recently, new approaches, called Quality-Diversity, have been proposed in order to enhance the exploration of the design space and to provide a set of optimal diversified solutions with respect to some feature functions. These functions are interesting to assess trade-offs. Furthermore, complex design problems often involve mixed continuous, discrete, and categorical design variables allowing to take into account technological choices in the optimization problem. Existing Bayesian Quality-Diversity approaches suited for intensive high-fidelity simulations are not adapted to mixed variables constrained optimization problems. In order to overcome these limitations, a new Quality-Diversity methodology based on mixed variables Bayesian optimization strategy is proposed in the context of limited simulation budget. Using adapted covariance models and dedicated enrichment strategy for the Gaussian processes in Bayesian optimization, this approach allows to reduce the computational cost up to two orders of magnitude, with respect to classical Quality-Diversity approaches while dealing with discrete choices and the presence of constraints. The performance of the proposed method is assessed on a benchmark of analytical problems as well as on two aerospace system design problems highlighting its efficiency in terms of speed of convergence. The proposed approach provides valuable trade-offs for decision-markers for complex system design.

翻译：复杂系统设计问题（如航空航天工程中的问题）需利用高计算代价的仿真代码来预测待设计系统的性能。在此背景下，这些代码通常被嵌入优化流程中，以在满足设计约束的前提下提供最优设计方案。近年来，为增强设计空间探索能力并提供关于某些特征函数的最优多样化解集，一种称为质量-多样性的新方法被提出。这些特征函数对评估设计权衡至关重要。此外，复杂设计问题常涉及混合（连续、离散与分类）设计变量，可将技术选择纳入优化问题。现有适用于高保真密集仿真的贝叶斯质量-多样性方法无法处理含混合变量的约束优化问题。为克服这些局限，本文提出一种基于混合变量贝叶斯优化策略的新质量-多样性方法，适用于有限仿真预算场景。该方法通过采用适配的协方差模型及高斯过程贝叶斯优化中的专用采样策略，在应对离散选择与约束条件的同时，相较于传统质量-多样性方法可将计算成本降低两个数量级。通过基准解析问题及两个航天系统设计问题的测试，本文方法在收敛速度方面的有效性得到验证。所提方法为复杂系统设计的决策者提供了有价值的权衡方案。