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The aerodynamic performance characteristics of an unmanned aerial vehicle airfoil and wing are optimized in the low Reynolds number regime using a variable-fidelity Multi-Level Hierarchical Kriging (MHK) surrogate modeling framework. This methodology employs aerodynamic data obtained from computational grids of varying grid resolution. This approach results in an efficient framework for optimizing expensive aerodynamic functions with the aid of lower fidelity data. The MHK-based optimization framework is first applied to enhance the aerodynamic properties of an Eppler E214 airfoil. The endurance factor of the airfoil is improved by 28%. Next, the aerodynamic characteristics of a small unmanned aerial vehicle wing is optimized. The endurance factor of the optimal wing is improved by 12.5%, with a substantial 45 drag count reduction. The optimal wing is of a swept wing design with a leading edge sweep of 13.6°. The evolution of a swept wing as the optimal wing design is an interesting outcome of the present study. Though the effect of wing sweep is well studied in high-subsonic and supersonic flows, its effect in the incompressible low Reynolds number regime is quantified in the present study. The wing sweep increases the suction on the outboard portion of the wing leading to a higher lift coefficient of the optimal wing. Further, the drag coefficient of the optimal wing is also reduced compared to the baseline wing. Much of this drag reduction comes from the reduction in the pressure drag component. Thus the wing sweep not only increases the lift coefficient, but also decreases the drag coefficient. This leads to a significant increase in the lift-to-drag ratio and the endurance factor of the optimal wing design. The present results demonstrate the optimization efficiency of the MHK modeling approach in the sensitive low Reynolds number regime. [ABSTRACT FROM AUTHOR]

Boundary-layer ingestion and distributed propulsion are important concepts for future aircraft systems and technologies. Both concepts have the potential to increase aerodynamic efficiency and improve aircraft design in various other ways. The present study aims to address design implications and challenges of configuring a highly integrated and distributed propulsion system into wing sections within the compressible flow environment, which is the aerodynamic regime associated with large, commercial transport aircraft. To this end, a design and optimization framework was established to facilitate two-dimensional aeropropulsive optimization with strict, complex geometric constraints. A bi-objective, multipoint aeropropulsive shape optimization problem was solved using this package for an underwing-propulsor airfoil system to demonstrate the performance improvements achievable for a highly integrated aeropropulsive system. The results of this optimization indicate that an aerodynamic drag reduction of 11% and required mechanical flow power reduction of 35% are achievable relative to a baseline configuration. [ABSTRACT FROM AUTHOR]

The over-wing nacelle (OWN) configuration has the potential to improve on the conventional under-wing nacelle (UWN) configuration by enabling higher bypass ratios and increasing noise shielding. To explore this potential, we perform coupled aeropropulsive design optimization to study the coupled analysis and the design tradeoffs between aerodynamics and propulsion. We find that the variations in wing shape are not significant when the OWN configuration is optimized for different fan pressure ratios. Optimizing the OWN configuration using the proposed approach results in 3% less shaft power than optimizing the wing and propulsor separately. The OWN has marginally superior performance over the UWN for the same lower fan pressure ratio. However, this low fan pressure ratio may be unattainable for the UWN configuration because of ground clearance constraints, whereas the OWN configuration is not subject to such constraints. We study the optimal OWN placement and show that placing it aft of the trailing edge and away from the wing root results in lower required shaft power. In this study, we perform single-point optimizations to understand the fundamentals of the OWN configuration in terms of aerodynamics and propulsion. However, multiple operating conditions, structural integrity, and inclusion of the pylon geometry should be considered to assess the net benefit of the OWN configuration. Nevertheless, these advancements in aeropropulsive optimization are critical to OWN configuration design and more sustainable aircraft. [ABSTRACT FROM AUTHOR]

Airfoil design using numerical optimization has addressed the problem of minimizing drag for a given lift constraint for one or more flight conditions. However, designers often want to avoid separation at off-design conditions regardless of the drag. This paper develops a separation constraint formulation for airfoil shape optimization. We perform multipoint optimizations and demonstrate how a separation constraint yields practical airfoil shapes. We compare results from single-point optimizations with and without a leading-edge radius constraint, which is a simple approach used as a surrogate to avoid separation, to an optimization where separation is constrained at a low-speed high-lift off-design point. Constraining the leading-edge edge radius improves the high-lift performance of the airfoil but not as much as constraining separation at the off-design point. We also compare the results of separation-constrained optimizations with optimizations where the drag at an off-design point is included in the objective. The latter formulation also produces optimal designs that are separation-free at the off-design points. However, the separation-constrained formulation produces airfoils with better cruise performance. Finally, we demonstrate the separation constraint efficacy at the off-design point with multiple cruise points. The results help guide parameterization and constraint formulation for airfoil design optimization problems. [ABSTRACT FROM AUTHOR]

Many aerodynamic shape optimization methods often focus on utilizing the end-to-end relationship between design variables and aerodynamic performance to find the optimal design, while overlooking the exploration of geometric knowledge of the shape itself. To fully use geometric knowledge to improve optimization efficiency, this paper proposes an efficient method by exploring the potential correlation between geometric features and aerodynamic performance at a low cost. We use unsupervised isometric feature mapping in manifold learning to capture geometric features that can distinguish the aerodynamic performance of different airfoils without embedding any tags. Then a filter criterion is establish based on the geometric features. During the optimization process, airfoils that deliver poor aerodynamic performance can be filtered out with a high probability before being precisely evaluated through computational fluid dynamics simulations. This helps improve samples quality to enhance the optimization efficiency. We applied the proposed method to the unconstrained and constrained optimizations of the Royal Aircraft Establishment (RAE) 2822 airfoil to validate its performance. The results demonstrate that the proposed method can improve the efficiency of optimization by over 50% compared with the original evolutionary optimization algorithm. It performs well across various optimization problems, demonstrating high engineering practical value. [ABSTRACT FROM AUTHOR]

An on-the-fly unsteady adjoint-based aerodynamic and aeroacoustic optimization methodology is presented, aiming to achieve practical engineering applications to explore high-efficiency and low-noise design for aerodynamic shapes. Firstly, a novel on-the-fly hybrid CFD-CAA approach is developed with a close integration of unsteady Reynolds-averaged Navier-Stokes equations and a fully viscous time-domain FW-H formulation. Subsequently, an adjoint-based sensitivity analysis method is proposed for unsteady aerodynamic and aeroacoustic problems with either stationary or moving boundaries, wherein a unified architecture for discrete-adjoint sensitivity analysis of both aerodynamics and aeroacoustics is achieved by integrating the on-the-fly hybrid CFD-CAA approach. The on-the-fly approach facilitates direct evaluation of partial derivatives required for solving adjoint equations, eliminating the need for explicitly preprocessing flow and adjoint variables at all time levels in a standalone adjoint CAA solver and consequently substantially reducing memory consumption. The proposed optimization methodology is implemented within an open-source suite SU2. Results show that the proposed on-the-fly adjoint methodology is capable of achieving highly accurate sensitivity derivatives while significantly reducing memory requirements by an order of magnitude, and further demonstrations of single-objective and coupled aerodynamic and aeroacoustic optimizations highlight the potential of the proposed method in exploring high-efficiency and low-noise design for aerodynamic shapes. [ABSTRACT FROM AUTHOR]

The deployable aeroshell, a contemporary reentry system, utilizes a thin flexible membrane surface sustained by pressurized gas to efficiently decelerate a reentry vehicle at high altitudes while enabling low-ballistic-coefficient flight. When an in-flight aerodynamic force is applied, the membrane structure undergoes large deformation that may affect its performance. Hence, a coupled analysis that considers the feedback effect of structural deformation is essential for accurately predicting the behavior of such reentry vehicles. In this study, a numerical framework for coupled aeroelastic analysis was constructed in a partitioned manner using open-source software to elucidate the combined effect of structural deformation and compressible flow dynamics and characterize the aerodynamic performance of reentry vehicles with inflatable structures. The results revealed that the membrane surface was deformed elastically by the aerodynamic force owing to the large difference in pressure distribution between the front and back of the aeroshell. Fluctuating behavior was observed in the aerodynamic coefficients owing to the small-amplitude oscillation of the capsule. This oscillation was induced by the large wake behind the vehicle. Several wrinkles and concave-shaped depressions formed on the membrane surface, which exhibited a circumferential movement tendency with time. [ABSTRACT FROM AUTHOR]

The continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the γ−R˜eθt$$ \gamma -\tilde{R}{e}_{\theta t} $$ transition model (in three, non‐smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in‐house, vertex‐centered finite‐volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of "frozen transition" (assumption according to which the adjoint to the transition model equations are not solved) or "frozen turbulence" (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities. [ABSTRACT FROM AUTHOR]

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method's capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables. [ABSTRACT FROM AUTHOR]

In the early stages of aerospace design, reduced-order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multifidelity, parametric, and nonintrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction--employing proper orthogonal decomposition and model-based active subspace--with multifidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE 2822 airfoil and the 3D NASA CRM wing, assessing various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity principal component-active subspace (PCAS) method, our multifidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design. [ABSTRACT FROM AUTHOR]

• An efficient mid-range approximation method for large-scale problems is proposed. • The improved trust-region strategy has a flexible and controllable performance. • A metamodel assembly technique is developed to alleviate the efficiency issues. • Optimization problems of 512 and 232 design variables are considered respectively. • The method successfully obtains the optimum at a reasonable computational cost. This paper presents an efficient solution for high-fidelity large-scale aerodynamic shape optimization problems based on several developments in the mid-range approximation method within a trust region optimization framework. The mid-range approximation method is an iterative optimization technique that utilizes mid-range approximations to replace the physical experiments or simulations during the optimization based on the selected trust region strategy. It could transform the original optimization problem into a sequence of approximate sub-optimization problems. In this work, an improved trust region strategy is proposed to contain more optimization states with a flexible and controllable performance to suit different types of problems. A metamodel assembly technique and its gradient-enhanced version are developed to further relax the requirements of computational costs in the mid-range approximation method. Its performance is discussed through a detailed comparison of metamodel performance using a mathematical benchmark case named Vanderplaats scalable beam. The wing only of the Common Research Model is offered to the proposed method for aerodynamic shape optimization. The optimization has 1 design objective, 232 design variables, and 135 design constraints. With all constraints satisfied, the optimized configuration has a 4.85 % improvement in wing drag performance. The shock region is greatly reduced and the wing pressure distribution is smooth and nearly parallel. These results show that the proposed method could achieve the design goal successfully within a reasonable computational cost for large-scale problems. [ABSTRACT FROM AUTHOR]

The development of future novel aircraft concepts requires a holistic approach to vehicle design, analysis, and optimization. Aircraft designers can no longer consider components individually as systems become more interconnected and multidisciplinary. Hence, a new approach to aircraft design and a new way to measure the performance of aircraft are needed. A novel approach to aircraft design is the use of exergy methods that can evaluate typically disparate systems using a universal measure of performance mapped to global system performance. This paper introduces a new functional and its adjoint gradient in FUN3D to determine aerodynamic exergy destruction rates. The functional is verified using the Oswatitsch relationship by comparing it to native, surface-based drag coefficients. The adjoint gradient is verified using the FUN3D native complex step method, and discrete agreement is demonstrated for flowfields and geometric derivatives. The new functional is then used for aerodynamic exergy-based analysis and optimization of the generic hypersonic vehicle. An inverse design problem is conducted first to verify the design optimization framework. Finally, a planform and airfoil aerodynamic inviscid exergy optimization of the GHV is conducted, improving exergy destruction rates by 7.1% while making substantial improvements to the cruise trim characteristics of the vehicle. [ABSTRACT FROM AUTHOR]

The ultrahigh-aspect-ratio wing (UHARW) concept is a promising configuration to achieve future sustainable aviation goals. Twin-fuselage (TF) and strut-braced-wing (SBW) configurations are characterized by smaller structural bending moments and shear forces in the wing and are promising concepts for realizing UHARW designs. This paper addresses the aerostructural optimization problem of TF and SBW configurations with UHARW by using a coupled adjoint aerostructural optimization tool, which is composed of a geometrically nonlinear structural solver and a quasi-three-dimensional natural laminar flow (NLF) aerodynamic solver. The optimization results show significant improvements in fuel efficiency and performance for the TF and SBW aircraft, with fuel mass reductions of 13 and 10%, respectively, compared to the corresponding baseline aircraft designed in the conceptual design phase. In comparison to the original reference aircraft A320neo, the optimized TF and SBW have 48 and 31% lower fuel weights, respectively. The NLF range of both upper and lower wing surfaces is expanded during optimization. The optimized SBW configuration has a wing aspect ratio of 26.01, while the optimized TF has a wing aspect ratio of 20.74, indicating that the SBW concept is more conducive to realizing UHARW design compared with the TF configuration studied in this work. The optimized TF aircraft has a lighter fuel weight and gross weight compared to the optimized SBW aircraft, which is because the TF aircraft has a lighter operational empty weight, including a lighter fuselage structural weight, landing gear weight, etc., whereas the top-level aircraft requirements are the same for both aircraft, including range, payload, and cruise Mach. [ABSTRACT FROM AUTHOR]

Featured Application: The potential application of the work presented in this article lies in the preliminary airfoil and wing design and optimization. It is in this area that the strengths of this approach (negligible computation cost, robustness, ...) can be maximally exploited while the weaknesses that hinder it can be minimized. The code is ready to use for engineering practice. In the development of interactive aerodynamic optimization tools, the need to reduce the computational complexity of flow calculations has arisen. Computational complexity can be reduced by estimating the flow variables using machine learning, but that approach has a number of hindrances. Avoiding these hindrances through lowering the computational complexity by stating the assumptions of inviscid incompressible potential flow is the focus of this article. The assumptions used restrict the applicability of this approach to only specific cases, but in engineering practice, these cases are quite widespread. The assumptions allowed the coupling of the adjoint method with parsec parametrization and the panel method, yielding a highly computationally efficient and robust tool for optimizing an airfoil's lift coefficient ( C y ). The optimization of the NREL S809 airfoil was carried out, and the results were verified using the Xfoil 6.99 software. The Xfoil verification showed that by making minimal changes to the airfoil's shape, the C y and lift-to-drag ratios were significantly improved. The improvement magnitude was over 94% for a 0 deg angle of attack (AoA) and over 16% for 6.2 deg AoA. This indicates an improvement in performance that is similar to that of some genetic algorithms, but with computational costs that are many orders of magnitude lower. [ABSTRACT FROM AUTHOR]

The parametric design method is widely utilized in the preliminary design stage for hypersonic vehicles; it ensures the fast iteration of configuration, generation, and optimization. This study proposes a novel parametric method for a wide-range, wing-morphing glide vehicle. The whole configuration, including a waverider fuselage, a rotating wing, a blunt leading edge, rudders, etc., can be easily described using 27 key parameters. In contrast to the typical parametric method, the new method takes internal payloads into consideration during the shape optimization process. That is, the vehicle configuration can be flexibly adjusted depending on the internal payloads; these payloads may be of random amounts and have different shapes. The code for the new parametric design method is developed using the secondary development tools of UG (UG 10.0) commercial software. The lift and drag characteristics over a wide operational range (H = 6–25 km, M = 2.5–8.5, AOA = 0–10°) were numerically investigated, as was the influence of the retracting angle of the morphing wings. It was found that, for the mode of the fully deployed wings, the lift-to-drag ratio (L/D) remained at a high level (≥4.7) over a Mach range of 4.0–8.5 and an AOA range of 4–7°. For the mode of the fully retracted wings, the drag coefficient remained smaller than 0.02 over a Mach range of 4.0–8.5 and an AOA range of 0–5°. A wide L/D of 0.3–4.7 could be achieved by controlling the retracting angle of the wings, thus demonstrating a good potential for flight maneuverability. The flexible change in L/D proved to be a combined result of varying pressure distribution and edge-flow spillage. This will aid in the further optimization of lift/drag characteristics. [ABSTRACT FROM AUTHOR]

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

Deep-learning-based flow emulators are used to predict the flowfield around parametrically defined airfoils and then used in place of Reynolds-averaged Navier-Stokes solvers in design optimization. The flow emulators are based on a) decoder convolutional neural networks, which generate solution snapshots in the computational domain, and b) design-variable hypernetworks, which provide pointwise predictions in physical space. The flow emulators are used to predict parametric subsonic and transonic compressor flows in an industrial design use case with baseline geometry corresponding to the NASA rotor 37. Both methods are effective in representing unseen subsonic airfoil flowfields, with mean errors less than 1%. The hypernetwork-based method generalizes more effectively under transonic conditions and is used in place of computational fluid dynamics (CFD) to drive shape optimization at varying rotor speeds. Under transonic conditions and at nominal speed, the emulator-driven optimization achieves the same optimal design as CFD in a reduced number of iterations at a fraction of the online computational cost while providing similarly performing designs at off-nominal conditions. It is remarked that once the emulator is trained once offline, it can be used online to conduct many different design optimizations, e.g., with different objective functions, constraints, and tradeoffs. These results establish the utility of design-variable hypernetworks as a viable emulation and optimization tool in practical industrial design. [ABSTRACT FROM AUTHOR]

Most existing studies on aerodynamic shape optimization have not considered longitudinal trim under control surface deflection, typically achieving self-trim through a constraint of zero pitching moment or adjusting the optimized configuration for longitudinal trim. However, adjustments to the optimized configuration might introduce additional drag, reducing overall optimization benefits. In this paper, a novel approach of incorporating control surface deflection for longitudinal trim in aerodynamic optimization is proposed. Firstly, an aerodynamic computation program based on the high-order panel method was developed, introducing velocity perturbations on specific mesh surfaces to simulate actual control surface deflections. Subsequently, a comprehensive optimization framework was established, encompassing parametric modeling, aerodynamic computation, and variable-fidelity control surface deflection analysis. Finally, aerodynamic optimization analysis was conducted under both subsonic and supersonic conditions. Thirty-one design variables were selected with the trimmed lift-to-drag ratio in cruising condition as the objective function and the control surface deflection angle as the constraint. The results indicated an 8.52% increase in the trimmed lift-to-drag ratio compared to the baseline model under subsonic conditions and an 8.1% increase under supersonic conditions. [ABSTRACT FROM AUTHOR]

The improvement of existing turbines requires time-consuming computations that often limit the number of parameters that can be optimized. To address this challenge, this study uses through-flow code, which is about 200 times faster than 3D Computational Fluid Dynamics (CFD), to optimize a two-stage axial turbine with 112 geometrical parameters using a deep learning surrogate model. The surrogate model is a Convolutional Neural Network (CNN) that predicts the flow field and performance indicators of the turbine based on an input database generated by an airfoil generation method and an in-house through-flow code. The surrogate model has two components: a flow field prediction component and a performance prediction component. The network architecture is named conv2D-conv3D, as it employs 2D convolutional layers to map the geometry to the flow field and 3D convolutional layers to extract features from the flow field and output the performance indicators. The optimal hyperparameters of the network are determined by comparing different activation functions, batch sizes, and train-data sizes. The network achieves high accuracy ( R 2 > 0.93 ) even with a small fraction of the dataset (30% of data) and it is more than 10 5 times faster than the through-flow code. A vectorized genetic algorithm is applied to the surrogate model to maximize the efficiency and power of the turbine under a constant mass flow rate constraint. The optimization results are validated by through-flow and 3D CFD simulations of the baseline and optimized turbine. The efficiency and power are increased by 0.83% and 1.02%, respectively. [ABSTRACT FROM AUTHOR]

Handling a large number of geometric constraints brings a big challenge to the surrogate-based aerodynamic shape optimization (ASO) driven by computational fluid dynamics (CFD). It is not feasible to calculate the geometric constraint functions directly during the sub-optimization of a surrogate-based optimization, as the geometric constraint functions are to be evaluated thousands of times for each updating cycle and the total cost of a number of cycles can be prohibitive. This article proposes an efficient method of handling geometric constraints within the framework of a surrogate-based optimization to address this problem. The core idea is to use the Kreisselmeier- Steinhauser (KS) method to aggregate all geometric constraints into one that can be approximated by a cheap surrogate model, in order to avoid the large computational cost associated with tremendous calculation of geometric constraint values. The proposed method is verified by an analytical test case. Then, the proposed method is demonstrated and compared with the methods of building surrogate models of all geometric constraints and calculating all geometric constraints directly during each sub-optimization by drag minimizations of NACA0012 air foil and ONERA M6 wing in transonic flows. To investigate the ability of the proposed method for handling various geometric constraints, drag minimization of CRM wing in viscous transonic flow driven by CFD is performed. Results show that the proposed method can dramatically improve the optimization efficiency of ASO with the number of geometric constraints ranging from 15 to 1429 and the number of types of geometric constraints up to 3, which offers great potential for handling a larger number and more types of geometric constraints. [ABSTRACT FROM AUTHOR]

Aerodynamic shape optimization is frequently complicated and challenging due to the involvement of multiple objectives, large-scale decision variables, and expensive cost function evaluation. This paper presents a bilayer parallel hybrid algorithm framework coupling multi-objective local search and global evolution mechanism to improve the optimization efficiency and convergence accuracy in high-dimensional design space. Specifically, an efficient multi-objective hybrid algorithm (MOHA) and a gradient-based surrogate-assisted multi-objective hybrid algorithm (GS-MOHA) are developed under this framework. In MOHA, a novel multi-objective gradient operator is proposed to accelerate the exploration of the Pareto front, and it introduces new individuals to enhance the diversity of the population. Afterward, MOHA achieves a trade-off between exploitation and exploration by selecting elite individuals in the local search space during the evolutionary process. Furthermore, a surrogate-assisted hybrid algorithm based on the gradient-enhanced Kriging with the partial least squares(GEKPLS) approach is established to improve the engineering applicability of MOHA. The optimization results of benchmark functions demonstrate that MOHA is less constrained by dimensionality and can solve multi-objective optimization problems (MOPs) with up to 1000 decision variables. Compared to existing MOEAs, MOHA demonstrates notable enhancements in optimization efficiency and convergence accuracy, specifically achieving a remarkable 5–10 times increase in efficiency. In addition, the optimization efficiency of GS-MOHA is approximately five times that of MOEA/D-EGO and twice that of K-RVEA in the 30-dimensional test functions. Finally, the multi-objective optimization results of the airfoil shape design validate the effectiveness of the proposed algorithms and their potential for engineering applications. [ABSTRACT FROM AUTHOR]

This paper presents an assessment of the potential fuel burn savings offered by the transonic strut-braced-wing configuration within the single-aisle class of aircraft relative to a modern conventional tube-and-wing aircraft through aerodynamic shape optimization based on the Reynolds-averaged Navier-Stokes equations. A representative strut-braced-wing aircraft is first developed through conceptual multidisciplinary design optimization based on the Airbus A320neo, with current technology levels assumed. A concept for the conventional tube-and-wing configuration is also developed to represent the Airbus A320neo as a performance baseline. Single-point aerodynamic shape optimization is then performed on wing-body-tail models of each aircraft to address aerodynamic design challenges and to provide more accurate performance estimates. Results indicate that shock formation can be mitigated from the wing-strut junction of the strut-braced wing at Mach 0.78 and a relatively high design lift coefficient of 0.750, providing an 8.2% reduction in block fuel over a 1000 n mile nominal mission when compared to the conventional tube-and-wing aircraft. Multipoint aerodynamic shape optimization is then performed to build toward a more credible estimate of fuel burn performance, with results showing a reduction in the fuel burn savings to 7.8% at the nominal design point relative to the conventional tube-and-wing aircraft to maintain a 7.6-8.0% improvement over the envelope of operating conditions, which includes design points at even higher Mach numbers and lift coefficients. These results demonstrate the viability of the transonic strut-braced-wing configuration for transport aircraft within the single-aisle class and its potential for reducing commercial fleet fuel burn. [ABSTRACT FROM AUTHOR]

Most existing aerodynamic shape optimization (ASO) studies do not take the balanced pitching moment into account and thus the optimized configuration has to be trimmed to ensure zero pitching moment, which causes additional drag and reduces the benefit of ASO remarkably. This article proposes an efficient global ASO method that directly enforces a zero pitching moment constraint. A free-form deformation (FFD) parameterization combing Laplacian smoothing method is implemented to parameterize a full aircraft configuration and ensure sufficiently smooth aerodynamic shapes. Reynolds-averaged Navier–Stokes (RANS) equations are solved to simulate transonic viscous flows. A surrogate-based multi-round optimization strategy is used to drive ASO towards the global optimum. To verify the effectiveness of the proposed method, we adopt two design optimization strategies for the NASA Common Research Model (CRM) wing–body–tail configuration. The first strategy is to optimize the configuration without considering balance of pitching moment, and then manually trim the optimized configuration by deflecting the horizontal tail. The second one is to directly enforce the zero pitching moment constraint in the optimization model and take the deflection angle of the horizontal tail as an additional design variable. Results show that: (1) for the first strategy, about 4-count drag-reducing benefits would be lost when manually trimming the optimal configuration; (2) the second strategy can achieve 3.2-count more drag-reducing benefits than the first strategy; (3) compared with gradient-based optimization (GBO), surrogate-based optimization (SBO) is more efficient than GBO for ASO problems with around 80 design variables, and the benefit of ASO achieved by SBO is comparable to that obtained by GBO. [ABSTRACT FROM AUTHOR]

An airfoil shape parameterization that can generate a compact design space is highly desirable in practice. In this paper, a compact airfoil parameterization is proposed by incorporating deep learning into the PAERO parameterization method based on the thin-airfoil theory. Following the PAERO parameterization, the mean camber line is represented by a number of aerodynamic performance parameters, which can be used to narrow down the design space according to the thin-airfoil theory. In order to further reduce the design space, the airfoil thickness distribution is represented by data-driven generative models, which are trained by the thickness distributions of existing airfoils. The trained models can automatically filter out the physically unreasonable airfoil shapes, resulting in a highly compact design space. The test results show that the proposed method is significantly more efficient and more robust than the widely used CST parameterization method for airfoil optimization. [ABSTRACT FROM AUTHOR]

In the development of interactive aerodynamic optimization tools, the need to reduce the computational complexity of flow calculations has arisen. Computational complexity can be reduced by estimating the flow variables using machine learning, but that approach has a number of hindrances. Avoiding these hindrances through lowering the computational complexity by stating the assumptions of inviscid incompressible potential flow is the focus of this article. The assumptions used restrict the applicability of this approach to only specific cases, but in engineering practice, these cases are quite widespread. The assumptions allowed the coupling of the adjoint method with parsec parametrization and the panel method, yielding a highly computationally efficient and robust tool for optimizing an airfoil’s lift coefficient (Cy). The optimization of the NREL S809 airfoil was carried out, and the results were verified using the Xfoil 6.99 software. The Xfoil verification showed that by making minimal changes to the airfoil’s shape, the Cy and lift-to-drag ratios were significantly improved. The improvement magnitude was over 94% for a 0 deg angle of attack (AoA) and over 16% for 6.2 deg AoA. This indicates an improvement in performance that is similar to that of some genetic algorithms, but with computational costs that are many orders of magnitude lower.

System design is a complicated and iterative process. Accordingly, a robust optimization procedure should be involved during the design process to minimize complications and time consumed for the whole process. The present research proposes a new methodology to design missile fins that can lessen the gap between the conceptual and final phases during the missile design process. The proposed methodology is based on a new dynamic adaptive multi-objective optimization algorithm accompanied by a selection scheme to choose a single optimum design amongst a Pareto set of solutions. The adaptive normalization multi-objective evolutionary algorithm can be used in any system design. This algorithm is capable of predicting Pareto fronts for multi-objective optimization problems at very good dispersion. In addition, a selection scheme is provided to help decision-makers choose a single optimum amongst Pareto front points. The proposed algorithm is tested against several multi-objective test functions as well as the application of a selection scheme to the obtained Pareto fronts. The results showed the robustness of the proposed algorithm in the prediction of convex fronts. However, it still needs more improvement to deal with non-convex ones. An application for the considered algorithm is also provided as a case study to design tail fins for a conventional missile configuration. The output configuration of the designed fins has very reasonable dimensions when compared to similar configurations.

This paper presents an efficient aerodynamic shape optimization (ASO) method with the metric-based Proper orthogonal decomposition (POD) parameterization method. The efficiency of the ASO method is improved by reduced design variables and narrowed design space which both benefit from metric-based POD parameterization method. In addition, the parameterization method is also modified to be suitable to more types of objective functions by introducing data-based filtering strategy. Data-based filtering strategy filters superior data set for metric-based POD on the basis of labels of data which are related to the objective functions in the paper. The efficiency and effect of the optimization method are validated by two typical cases: inverse and direct design for airfoil. The results show that, only considering optimization process, the efficiency of the two cases is all improved with a little difference among the optimums; when it comes to the total process taking data-based filtering strategy into account, the efficiency of the direct design case is a little less than the reference, which means the efficiency of data-based filtering strategy should be improved on further study. [ABSTRACT FROM AUTHOR]

In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability and grid independent convergence is achieved via a combination of multigrid schemes for the simulation of the PDEs and quasi Newton methods on the optimization side. For this purpose a self-adapting, nonlinear extension operator is proposed within the framework of the method of mappings. This operator is demonstrated to identify critical regions in the reference configuration where geometric singularities have to arise or vanish. Thereby the set of admissible transformations is adapted to the underlying shape optimization situation. The performance of the proposed method is demonstrated for the example of drag minimization of an obstacle within a stationary, incompressible Navier–Stokes flow. [ABSTRACT FROM AUTHOR]

Novel aircraft concepts employing ultrahigh-aspect-ratio wings, such as the strut-braced wing (SBW) configuration, are promising ways to achieve the next-generation sustainable and fuel-efficient aviation goals. However, as the wing aspect ratio increases, the wing increasingly exhibits more flexibility, higher deformation, and geometrically nonlinear behavior that cannot be accurately simulated by conventional sizing methods and typical linear structural analysis models. This paper establishes a framework for SBW aircraft conceptual design, conceptual optimization, and aerostructural optimization. The presented aerostructural optimization method has medium-fidelity and physics-based features. A geometrically nonlinear structural analysis solver and a quasi-three-dimensional aerodynamic solver are coupled for the aerostructural optimization of composite natural-laminar-flow SBW aircraft. A medium-range (MR)-SBW aircraft is initially designed and optimized in the conceptual design stage. A gradient-based aerostructural optimization is performed using the proposed tool for minimizing the fuel mass of the initially sized and optimized MR-SBW aircraft. The optimization results in a more than 10% reduction in fuel mass, a more than 8% reduction in aircraft maximum takeoff mass, and a more than 30% reduction in wing and strut structural weight by optimizing the wing box structure, the wing planform, and the airfoil shape while satisfying the constraints on structural failure, wing loading, and aileron effectiveness. [ABSTRACT FROM AUTHOR]

Aerostructural optimization traditionally uses a single or small number of cruise conditions to estimate the mission fuel burn objective function. In reality, a mission includes other flight segments contributing to fuel burn, such as climbing and descent. We aim to quantify how much performance is sacrificed by optimizing the design for a fuel burn approximation that ignores these other flight segments and flight conditions. To do this, we compare traditional approaches to mission-based optimization, which uses an accurate fuel burn objective computed by numerically integrating fuel flow across the mission profile. We find that mission-based optimization offers only marginal benefits over traditional single-point and multipoint approaches for aerostructural optimization of a narrow-body aircraft--only 1-2% in the most extreme cases. Thus, the traditional aerostructural optimization is acceptable, especially in cases where most fuel is burned during cruise. For the cases where climb fuel burn is significant, we introduce a simple change to traditional fuel burn approximation methods that allows the optimizer to find nearly all the fuel burn reduction of mission-based optimization but at the computational cost of multipoint optimization. [ABSTRACT FROM AUTHOR]

Designing transonic laminar swept wing at high Reynolds numbers is challenging due to the premature flow transition from the prominent crossflow instabilities (CFIs). Hence, natural laminar flow (NLF) wings are limited to lower sweep angles. In this study, hybrid laminar flow control (HLFC) is used to extend this limit to design low-drag transonic infinite wing. A multi-objective genetic algorithm with competing drag components as objectives is used to design NLF and HLFC airfoils. Optimal design is a tradeoff between the drag reduction from skin friction drag, pressure drag, and suction drag, and does not resemble initial airfoils. Airfoil shape and suction distribution are coupled and optimized simultaneously. Euler flow solver with integral boundary-layer method is coupled with a higher-fidelity Linear Stability Analysis using 2.5D approximation for transition prediction. At wing sweep of 22.5°, Mach number of 0.78, and Reynolds number of 30 million, optimum NLF airfoil has 27% lower drag than an optimum turbulent airfoil. The optimum HLFC airfoil showed a 25% lower total drag than the NLF airfoil. A higher optimum sweep angle was observed for low-drag HLFC airfoil (20.5°) in comparison to the NLF airfoil (16.8°) and both favored an undercut on the lower surface to dampen CFI. [ABSTRACT FROM AUTHOR]

Robust optimization design is significant and urgently required for the fly wings, owing to its unique characteristics. However, there is a lack of efficient tools for performing shape optimization which considers multiple uncertainties. This is in part because implementing robust design in the widely used and very efficient adjoint-based optimization method is challenging. This paper addresses this need by developing an uncertainty-based optimization design framework where the gradient-enhanced polynomial chaos expansion and discrete, adjoint-based optimization framework are coupled to perform shape optimization under multiple uncertainties. The gradient information from adjoint equation is applied to improve the computation efficiency. The objective function is the statistic moment, consisting of mean and standard deviation. The gradients of the statistic moment are computed using the adjoint-based system and reconstructing a regression algorithm. A flying wing configuration with deterministic and two uncertainty-based optimizations is performed. The first uncertainty-based optimization considers flight conditions, Mach and angle of attack, and the second one added the planform uncertainty parameters, i.e., inner and outer wing sweep angle. The uncertainty-based optimizations gain reductions of statistic moments by 8.58% and 5.3%, respectively. Compared with the deterministic optimization, the uncertainty-based optimizations behave much better in robustness but sacrifice a small aerodynamic performance. The successful uncertainty-based optimization enables acceptable risks of fly wing design in the development process and indicates that our established framework can be applied for future aircraft robust optimization design. [ABSTRACT FROM AUTHOR]

Reducing fuel consumption and improving the economy by effectively reducing cruising drag is the main objective of the aerodynamic design of supersonic civil aircraft. In this paper, the aerodynamic optimization design system based on the Reynolds-Averaged Navier–Stokes (RANS) equation and discrete adjoint theory is applied to supersonic wing design. Based on this system, a single-point optimization design study of aerodynamic drag reduction in cruise conditions was carried out for two typical supersonic wing layouts, subsonic leading edge and supersonic leading edge, and the drag reduction reached 3.78% and 4.53%, respectively. The aerodynamic design characteristics of different types of supersonic wings were explored from the perspectives of wing load, twist angle distribution, pressure distribution, airfoil shape characteristics, and flow field characteristics. The optimization results show that the drag reduction of the subsonic leading edge configuration is dominated by the induced drag, while the optimizer mainly focuses on reducing the shock wave drag for the supersonic leading edge configuration. By comparing the sensitivity analysis of lift and drag coefficients to airfoil deformation with the optimization results, the optimized dominant directions of two types of supersonic wings are qualitatively analyzed. The derivatives obtained from discrete adjoint equations are useful to elaborate the design tendency and the reason for the trade-off generation of supersonic wings under specific layouts and engineering constraints, which provides a reference for the design of supersonic wings in the future. [ABSTRACT FROM AUTHOR]

The parametric design method is widely utilized in the preliminary design stage for hypersonic vehicles; it ensures the fast iteration of configuration, generation, and optimization. This study proposes a novel parametric method for a wide-range, wing-morphing glide vehicle. The whole configuration, including a waverider fuselage, a rotating wing, a blunt leading edge, rudders, etc., can be easily described using 27 key parameters. In contrast to the typical parametric method, the new method takes internal payloads into consideration during the shape optimization process. That is, the vehicle configuration can be flexibly adjusted depending on the internal payloads; these payloads may be of random amounts and have different shapes. The code for the new parametric design method is developed using the secondary development tools of UG (UG 10.0) commercial software. The lift and drag characteristics over a wide operational range (H = 6–25 km, M = 2.5–8.5, AOA = 0–10°) were numerically investigated, as was the influence of the retracting angle of the morphing wings. It was found that, for the mode of the fully deployed wings, the lift-to-drag ratio (L/D) remained at a high level (≥4.7) over a Mach range of 4.0–8.5 and an AOA range of 4–7°. For the mode of the fully retracted wings, the drag coefficient remained smaller than 0.02 over a Mach range of 4.0–8.5 and an AOA range of 0–5°. A wide L/D of 0.3–4.7 could be achieved by controlling the retracting angle of the wings, thus demonstrating a good potential for flight maneuverability. The flexible change in L/D proved to be a combined result of varying pressure distribution and edge-flow spillage. This will aid in the further optimization of lift/drag characteristics.

Most existing studies on aerodynamic shape optimization have not considered longitudinal trim under control surface deflection, typically achieving self-trim through a constraint of zero pitching moment or adjusting the optimized configuration for longitudinal trim. However, adjustments to the optimized configuration might introduce additional drag, reducing overall optimization benefits. In this paper, a novel approach of incorporating control surface deflection for longitudinal trim in aerodynamic optimization is proposed. Firstly, an aerodynamic computation program based on the high-order panel method was developed, introducing velocity perturbations on specific mesh surfaces to simulate actual control surface deflections. Subsequently, a comprehensive optimization framework was established, encompassing parametric modeling, aerodynamic computation, and variable-fidelity control surface deflection analysis. Finally, aerodynamic optimization analysis was conducted under both subsonic and supersonic conditions. Thirty-one design variables were selected with the trimmed lift-to-drag ratio in cruising condition as the objective function and the control surface deflection angle as the constraint. The results indicated an 8.52% increase in the trimmed lift-to-drag ratio compared to the baseline model under subsonic conditions and an 8.1% increase under supersonic conditions.

Efficient aerodynamic shape optimizations are realized in this research utilizing dimension reduction technologies. Several dimension reduction methods such as proper orthogonal decomposition, independent component analysis, kernel principal component regression and deep auto encoder, are investigated to reduce the dimensionality of design variables space. The number of design variables can be efficiently reduced by the proposed approach while obtained optimization results are comparable with that of a conventional optimization approach. The effect of each dominant mode is clarified in this study. A variable fidelity method is introduced by adopting a low-fidelity performance evaluation in the pre-process of the dimension reduction. By introducing the variable fidelity method, a multi objective aerodynamic shape optimization problem can be efficiently solved. Furthermore, design knowledge with respect to the tradeoff relationship between objective functions can be obtained from the results of dimension reduction.

In the conceptual design phase of conventional-configuration aircraft, calibrated low-fidelity methods provide sufficiently accurate estimates of aerodynamic coefficients. It has been observed, however, that for blended-wing-body aircraft, important flow effects are not captured adequately with low-fidelity aerodynamic tools. Consequently, high-fidelity methods become necessary to study blended-wing-body aerodynamics. Since repeated function calls are needed in an optimization loop, high-fidelity analysis is prohibitively expensive in the conceptual design phase, where several optimization scenarios are considered. In this paper, the integration of high-fidelity data for blended-wing-body aircraft for a mission calculation module is presented. A surrogate model based on Gaussian processes (GPs) with acceptably low prediction error is sought as an alternative to Reynolds-averaged Navier-Stokes computational fluid dynamics. Three adaptations are considered: sparse GPs, mixtures of GP approximators, and need-based filtering for GP. The results provide benchmark values for this case and show that the combination of subsonic and transonic behaviors in the training set is problematic and that, for the considered datasets, sparse GP models suffer from oversmoothing, while mixtures of GP models suffer from overfitting. From the error levels, it is observed that a GP with an infinitely differentiable squared exponential kernel based on reduced data pertinent to mission analysis is the most effective option. [ABSTRACT FROM AUTHOR]

Considering both supersonic and subsonic aerodynamic performances in aircraft design is challenging. This challenge can be alleviated through morphing design or plasma flow control. Therefore, if they are both considered in the aerodynamic optimization, the results can be undoubtedly improved. In this study, first, a new sliding shear variable sweep design scheme which can change both the plane shape (such as the span and sweep angle) and the wing profile (such as the chord length and the relative thickness) is proposed and some information about the elastomeric skin scheme is given. Second, an efficient global optimization framework based on surrogate-based optimization algorithm is established for the aerodynamic shape optimization of this morphing wing. Third, two optimizations are conducted, wherein one considers the effect of plasma actuation while the other does not. Due to the complexity and large calculations required, the effect of plasma actuation is not directly considered in computational fluid dynamics simulation but is indirectly considered by relaxing the subsonic lift constraint, which assumes that plasma actuation can offset the lift loss. Therefore, it is called "plasma constraint relaxation". In the two optimizations, three different configurations of the morphing wing which are 20°-, 30°- and 70°- sweep angle state, and three different flow conditions, which are subsonic (0.25 Ma), transonic (0.85 Ma) and supersonic (3 Ma) are considered. The results show that the comprehensive performance (objective function) improves by 12.6% with the effect of plasma actuation while it improves by 7.6% without the effect of plasma actuation after a two-round optimization. This suggests that the subsonic lift constraint, as an active constraint, significantly impacts the final optimization results. Finally, to verify whether plasma actuation can offset the lift loss, an experiment of nanosecond pulse dielectric barrier discharge plasma controlling flow separation is conducted to increase the subsonic lift of the optimization shape. The results show that the maximum lift increases by 18.1% when the actuation voltage is 8 kV and actuation frequency is 160 Hz and the lift loss caused by the constraint relaxation is 14.5%. [ABSTRACT FROM AUTHOR]

Creating a supersonic jet in the laboratory is both a challenging and an expensive task. The supersonic flow is sensitive to the shape of the wall bounding it because a shock could be developed at the sharp edges. Moreover, the growth of boundary layer, within and outside the nozzle, makes the design of a convergent-divergent nozzle a sophisticated work. The present work proposes an optimization algorithm that is believed to be efficient in constructing a nozzle contour to deliver a shock-free radially uniform flow at the exit plane. The steepest descent optimization technique is employed to obtain the shape with minimum radial velocity at the outlet, along with restriction on the inlet angle, i.e., the angle of divergence immediately downstream the throat. Three different ways of implementing the constraints are discussed and compared with the experimental results after fabricating the nozzle. The optimized nozzle shows a potential core of 7 throat diameters height at the nozzle exit and an axial extent of 28 throat diameters downstream the exit plane. Further, the nozzle appears to operate efficiently even after increasing the nominal total temperature by 25% or decreasing it by 50%. [ABSTRACT FROM AUTHOR]

The parametric representation and aerodynamic shape optimization of a three-dimensional circular-to-rectangular transition nozzle designed and built using control lines distributed along the circumferential direction were investigated in this study. A surrogate model based on class/shape transformation, principal component analysis and radial basis neural network was proposed with fewer design parameters for parametric representation and performance parameter prediction of the three-dimensional circular-to-rectangular transition nozzle. The surrogate model was combined with Non-dominated Sorting Genetic Algorithm-II to optimize the aerodynamic shape of the nozzle. The results showed that the surrogate model effectively achieved the parametric representation and aerodynamic shape optimization of the three-dimensional circular-to-rectangular transition nozzle. The geometric dimensions and performance parameters of the parametric reconstructed model were comparable to that of the initial model, implying that they can meet the needs of optimal design. The axial thrust coefficient and lift of the optimized nozzle were increased by approximately 0.742% and 15.707%, respectively. [ABSTRACT FROM AUTHOR]

System design is a complicated and iterative process. Accordingly, a robust optimization procedure should be involved during the design process to minimize complications and time consumed for the whole process. The present research proposes a new methodology to design missile fins that can lessen the gap between the conceptual and final phases during the missile design process. The proposed methodology is based on a new dynamic adaptive multi-objective optimization algorithm accompanied by a selection scheme to choose a single optimum design amongst a Pareto set of solutions. The adaptive normalization multi-objective evolutionary algorithm can be used in any system design. This algorithm is capable of predicting Pareto fronts for multi-objective optimization problems at very good dispersion. In addition, a selection scheme is provided to help decision-makers choose a single optimum amongst Pareto front points. The proposed algorithm is tested against several multi-objective test functions as well as the application of a selection scheme to the obtained Pareto fronts. The results showed the robustness of the proposed algorithm in the prediction of convex fronts. However, it still needs more improvement to deal with non-convex ones. An application for the considered algorithm is also provided as a case study to design tail fins for a conventional missile configuration. The output configuration of the designed fins has very reasonable dimensions when compared to similar configurations. [ABSTRACT FROM AUTHOR]

Corner modifications can reduce wind loads acting on supertall buildings and modify the corresponding flow structures. The present study investigated the aerodynamic shape optimization of the corner recession square cylinders with multiple geometric parameters in a large design space via the GA-GRNN surrogate model updating-based multi-objective optimization framework. Six typical optimal aerodynamic shape sections M1~M6 were selected from the Pareto optimal front, and the effects of multiple geometric parameters of these sections on the aerodynamic performance and flow field were analyzed. The results showed that the present multi-objective optimization framework can significantly reduce the computational load and time cost, and significantly improve the optimization efficiency in solving complex engineering problems. The optimal corner recession sections can obviously reduce the mean drag coefficient CD and root mean square lift coefficient CσL while significantly increasing the Strouhal number St of the square cylinder, and it is concluded that the aerodynamic shape optimization can significantly improve the aerodynamic performance of square-sectional supertall buildings. When compared with the benchmark section, the CD and CσL of the optimal section M1 can be reduced up to 45.7% and 84.5%, respectively. Based on the analysis of the flow structures around the optimal sections, the flow mechanism can be attributed to the fact that the corner recession modifications postpone the flow separation, and deflect the separated shear layer towards the side surfaces and suppress the development of vortex shedding in the wake, which leads to significant elongation of the wake length and reduction of the width of the recirculation region. The proposed multi-objective optimization framework in this study can provide an important reference for the aerodynamic shape optimization of building structures and relevant studies. [ABSTRACT FROM AUTHOR]