Multiobjective Aerodynamic Design Optimization of the NASA Common Research Model

TL;DR

The paper addresses the challenge of aerodynamic design optimization across varying cruise conditions by advocating direct multiobjective optimization rather than weighted multi-point scalarization. It introduces qPOTS, a batch Thompson-sampling-based MOBO method that uses Gaussian process surrogates and a Nyström-based scalability technique to efficiently generate Pareto-optimal design candidates in high dimensions. Through synthetic benchmarks and a 24D NASA CRM case, the method demonstrates superior or competitive performance in hypervolume improvement, particularly in batch settings, and provides open-source software. The work highlights the practical value of sampling Pareto-optimal paths to capture trade-offs between conflicting cruise-point objectives, offering a scalable, robust approach for complex aerospace design problems.

Abstract

Aircraft aerodynamic design optimization must account for the varying operating conditions along the cruise segment as opposed to designing at one fixed operating condition, to arrive at more realistic designs. Conventional approaches address this by performing a ``multi-point'' optimization that assumes a weighted average of the objectives at a set of sub-segments along the cruise segment. We argue that since such multi-point approaches are, inevitably, biased by the specification of the weights, they can lead to sub-optimal designs. Instead, we propose to optimize the aircraft design at multiple sub-segments simultaneously -- that is, via multiobjective optimization that leads to a set of Pareto optimal solutions. However, existing work in multiobjective optimization suffers from (i) lack of sample efficiency (that is, keeping the number of function evaluations to convergence minimal), (ii) scalability {in the absence of derivative information}, and (iii) the ability to generate a batch of iterates for synchronous parallel evaluations. To overcome these limitations, we {apply} a novel multiobjective Bayesian optimization methodology {for aerodynamic design optimization} that demonstrates improved sample efficiency and accuracy compared to the state of the art. Inspired by Thompson sampling, our approach leverages Gaussian process surrogates and Bayesian decision theory to generate a sequence of iterates according to the probability that they are Pareto optimal. Our approach, named batch Pareto optimal Thompson sampling (\qpots)\footnote{Here, $q$ stands for selecting a batch of $q$ iterates at every step.}, demonstrates superior empirical performance on a variety of synthetic experiments as well as a $24$ dimensional two-objective aerodynamic design optimization of the NASA common research model. We also provide open-source software of our methodology {and experiments}.

Figures (12)

• Figure 1: A simplified mission profile for a commercial aircraft that emphasizes the cruise segment. The change in aircraft weight during the cruise segment induces change in required lift and thrust, and hence the operating angle of attack, Mach and Reynolds numbers. We anticipate that designs optimized for any one point along the cruise segment will likely be sub-optimal for other points. Therefore, we argue that "multiobjective" optimization, that simultaneously considers multiple points along the cruise segment is necessary.
• Figure 2: Illustration of the differences between multi-point versus multiobjective (Pareto) optima on the two-objective ZDT3 test function. The turqouise circles are the objective pairs and the blue circles are the Pareto optimal objectives. The lines with inline labels represent the multi-point (scalarized) combination of the objectives: $w_1 f_1 + w_2 f_2$, for two different choices of weights $w_1,w_2$ on the left and right. The red circle is the multi-point optimum which is essentially the point where the lines intersect the Pareto frontier with the smallest scalarized objective. As can be seen, the choice of weights can drastically change the multi-point optimum. On the other hand, multiobjective optimization provides an ensemble of optimal designs that a practitioner can choose from.
• Figure 3: Plot shows aircraft drag for the NASA CRM evaluated at two different points along cruise segment for a variety of wing shapes. Notice that certain designs are nonconflicting, while others are not. Multiobjective optimization is necessary to properly account for design trade-offs and identify a set of optimal solutions for a practitioner to choose from.
• Figure 4: Hypervolume (higher the better) Vs. iterations for sequential ($q=1$) acquisition; plots show mean and $\pm 1$ standard deviation out of $10$ repetitions.
• Figure 5: Batch acquisition. Hypervolume Vs. iterations for batch ($q>1$) acquisition; plots show mean and $\pm 1$ standard deviation out of $10$ repetitions. $q\texttt{POTS}$ outperforms all competitors, but the benefit is more pronounced in the batch case.

Theorems & Definitions (4)

• Proposition 5.1
• proof
• Proposition 5.2: Converse under convexity
• proof : Sketch