SAMURAI: A New Asynchronous Bayesian Optimization Technique for Optimization-Under-Uncertainty

In this work, optimization-under-uncertainty (OUU) is treated by simultaneously minimizing the mean of the objective and its variance due to variability of design variables and/or parameters in a multi-objective setting, while simultaneously ensuring that the minimal probability of constraint failure is met. This allows the designer to choose its robustness level without the need to repeat the optimization as typically encountered when formulated as a single objective and ensuring that the system will not fail with a prescribed probability. To account for the computational cost that is often encountered in OUU problems, the problem is fitted in a Bayesian optimization framework. The use of surrogate modeling techniques to efficiently solve problems under uncertainty has effectively found its way in the optimization community leading to surrogate-assisted OUU schemes. The surrogates are often considered cheap-to-sample black-boxes and are sampled to obtain the desired quantities of interest. However, since the analytical formulation of the surrogates is known, the mean square predictive error of the quantities of interest can be derived. To obtain these quantities without sampling, an analytical uncertainty propagation and reliability analysis through the surrogate is presented. The multi-objective Bayesian optimization framework and the analytical uncertainty propagation and reliability analysis are linked together through the formulation of the reliability-based robust expected improvement. To further enhance the efficiency of the approach, the Bayesian optimization method is solved in an asynchronous manner. In doing so the novel Surrogate-assisted Asynchronous Multi-objective optimization under Uncertainty framework for Robust and reliable solutions to Applications in Industry (SAMURAI) scheme is defined. The method is applied to a number of case studies and the design of a low-Re airfoil for blended-wing-bodies, which proves the effectiveness of the novel methodology.