Design strategies for multi-objective optimization of aerodynamic surfaces

Abstract

Purpose This paper aims to investigates several design strategies to solve multi-objective aerodynamic optimization problems using high-fidelity simulations. The purpose is to find strategies which reduce the overall optimization time while still maintaining accuracy at the high-fidelity level. Design/methodology/approach Design strategies are proposed that use an algorithmic framework composed of search space reduction, fast surrogate models constructed using a combination of physics-based surrogates and kriging and global refinement of the Pareto front with co-kriging. The strategies either search the full or reduced design space with a low-fidelity model or a physics-based surrogate. Findings Numerical investigations of airfoil shapes in two-dimensional transonic flow are used to characterize and compare the strategies. The results show that searching a reduced design space produces the same Pareto front as when searching the full space. Moreover, as the reduced space is two orders of magnitude smaller (volume-wise), the number of required samples to setup the surrogates can be reduced by an order of magnitude. Consequently, the computational time is reduced from over three days to less than half a day. Originality/value The proposed design strategies are novel and holistic. The strategies render multi-objective design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces computationally tractable.

Applications of surrogate-assisted and multi-fidelity multi-objective optimization algorithms to simulation-based aerodynamic design

“…The SA-MOEA (Amrit et al , 2017a) utilizes the two ends of the Pareto front as its starting point and is obtained using space-mapping-based single-objective optimizations. To expedite the optimization procedure, the algorithm involves utilization of surrogate models constructed from fast low-fidelity model, c , based on coarse-discretization CFD simulations.…”

“…The steps of the SA-MOEA (Amrit et al , 2017a) are as follows: Setup a physics-based surrogate s 0 ; Perform design space reduction using s 0 ; Sample the design space and acquire the surrogate model data with s 0 ; Construct a kriging surrogate s KR based on the data from Step 3; Obtain an approximate Pareto set representation by optimizing s KR using MOEA (Fonseca, 1995); Evaluate the high-fidelity model f along the Pareto front; Construct/update the co-kriging surrogate s CO ; Update Pareto set by optimizing s CO using MOEA (Fonseca, 1995); and If termination condition is not satisfied go to Step 6; else END. …”

“…Hence, in Step 2, the design space is reduced (in terms of design variable ranges, as well as dimensionality) within which, kriging (Step 4) and co-kriging (Step 7) models are setup using a limited number of model evaluations. The design space reduction methodology is described (Amrit et al , 2017a). In Step 3, Latin Hypercube Sampling (Beachkofski and Grandhi, 2002) (LHS) is used to select the shapes within the reduced design space and the corresponding low-fidelity model values for each sample is collected.…”

“…Leifsson et al (2016) used multi-fidelity models and local response surface surrogate models for multi-objective design exploration of transonic airfoil shapes. Amrit et al (2017a) developed design strategies for multi-objective aerodynamic design exploration using design space reduction, evolutionary algorithms, cokriging (Laurenceau and Sagaut, 2008; Keane, 2012) and multi-fidelity models. In our recent work (Amrit et al , 2017b), we developed a multi-objective aerodynamic design optimization algorithm using multi-fidelity models and the point-by-point Pareto set identification technique, originally developed for microwave antenna design (Koziel and Bekasiewicz, 2016).…”

“…This paper presents new applications and comparisons of three recently developed surrogate-assisted and multi-fidelity MOO algorithms. In particular, the algorithms are: The surrogate-assisted MOEA (SA-MOEA) developed by Amrit et al (2017a). The multi-fidelity multi-objective aerodynamic design exploration using point-by-point Pareto set identification (Amrit et al , 2017b), and The multi-fidelity sequential domain patching (SDP) algorithm, originally developed by Koziel and Bekasiewicz (2018), for the design of microwave antennas. …”