Multi-Objective Optimization and Surrogate Modeling of Composite Morphing Airfoils: Trends, Bottlenecks, and Research Priorities

Morphing airfoil technologies have recently attracted considerable interest and have emerged as a way to achieve adaptive and fuel-efficient aerodynamic systems for future aircraft. Morphing airfoil technologies improve the lift/drag ratio, handling characteristics, stall extension, and reduce fuel burn through geometric control during flight operations for commercial aircraft, military aircraft, and unmanned aerial vehicles (UAVs). The improvements achieved are reduced fuel consumption for commercial aircraft and over 20% performance enhancement for UAVs, confirming the importance of morphing technologies for the future of sustainable aviation [1-3]. These aerodynamic benefits are inherently governed by the mechanical behavior and deformation capability of advanced composite materials and compliant structural skins used in morphing airfoil systems [4, 5].

The computational formulation of morphing airfoil shapes necessarily involves the complexity of multi-objective compromises concerning aero performance, structural robustness, kinematic constraints, and fluid-dynamic stability. The complexity of the discipline has led to the widespread adoption of Multi-Objective Optimization (MOO) algorithms, specifically evolutionary algorithms such as Genetic Algorithms (GA) [6, 7], NSGA-II, Artificial Bee Colony algorithms [8], and modern hybrid and metaheuristic approaches such as Black Widow Optimization and Particle Swarm Optimization [9, 10].

These compromises become more critical in composite-based morphing airfoils, where material anisotropy, stiffness tailoring, and deformation limits strongly influence feasible design solutions. particularly in composite laminates, elastomeric skins, and smart material–based morphing concepts [11, 12].

These metaheuristics are typically applied for robust global searches of complex and large-scale, nonlinear spaces. At the same time, gradient-based methods using the Adjoint Sensitivity formulation and implemented within high-fidelity computational fluid dynamics (CFD) have emerged and been widely characterized by the capability of efficiently computing the gradient of the objective using the Adjoint Jacobian [13, 14], thus used for the refined optimization of morphing leading and trailing edges during both transonic and cruise flight [15].

However, the effectiveness of adjoint-based optimization remains strongly dependent on the accurate representation of composite material deformation and structural response during morphing.

Figure 1 illustrates that morphing capability is primarily enabled by the interaction between compliant composite skins and internal load-bearing structures, emphasizing the material-driven nature of morphing airfoil design.

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The importance of high-fidelity simulations using CFD cannot be overemphasized for morphing airfoil models using Reynolds-averaged Navier Stokes (RANS) simulations and models such as Spalart Allmaras and SST k-ω [10, 17] Nevertheless, the accurate simulation of separation, transition, and transient phenomena in morphing models is challenging [18], and various authors [1, 19, 20] have used multi-point optimization and simulation of transitional turbulence together with experiments.

These modeling challenges are further amplified when composite skins undergo large deformations, where material nonlinearity and structural flexibility interact with unsteady flow phenomena.

Because of the high computational intensity involved with completely coupled CFD optimization, the field has gradually shifted towards the use of surrogate models and multi-fidelity modeling. In composite-based morphing structures, surrogate models also serve as a practical tool to incorporate material behavior, structural deformation, and aero-structural coupling within optimization frameworks.

Kriging models, radial basis function (RBF) models, artificial neural networks, and deep surrogates such as deep neural operators [21], convolutional neural network (CNN) multi-fidelity models [22], transfer-learning frameworks [23], and gradient-enhanced deep surrogates [24] have proven capable of accurately modeling high-fidelity aerodynamic predictions with errors typically below the 6% level. These technologies greatly accelerate the optimization task while allowing for the examination of very large design spaces. Recent advancements include the combination of physics and machine learning (ML) [25], latent diffusion models for inverse modeling [26], and geometric deep learning (DL), reflecting the ever-growing interest in the direct coupling of aerodynamics knowledge and data models. This shift is particularly relevant for composite morphing structures, where repeated high-fidelity simulations are required to capture material-driven deformation behavior.

From a materials and structural perspective, morphing airfoils represent a class of advanced composite structures subjected to controlled large deformations.

Parallel to aerodynamic simulation models, modern and robust multifaceted/multidisciplinary design optimization (MDO) tools are currently being enhanced with analysis of structures, compliant mechanism designs, and fluid-structure interactions. Finite element analysis (FEA) and explicit nonlinear solution strategies of the structure have been widely used for validating morphing skin structures and internal dynamics [27-29]. Multi-fidelity models of aeroelastic systems [30, 31], mesh morphing strategies for structurally optimized models [32, 33], and coordinated aerodynamic and control concepts for adaptive mission tasks [33, 34] also reflect the emerging demands for integrated a Nonetheless, several challenges still exist within the literature.

The surrogate models experience challenges of generalizing morphing layouts that are novel [35]. There are also challenges related to the modeling of turbulence within morphing shapes that are dynamically changing [36]. The models are mostly treated within two-dimensional morphing airfoil layouts and not completely within morphing wings [37]. The tests are mostly not within the scope of validating UAV morphing shapes [1, 15]. The models are not well developed within aspects of constrained morphing actions, real-time morphing control strategies, and uncertainty.

This review is unprecedented because of the extensive incorporation of Multiple Objective Optimization Techniques and the modern frameworks of Surrogate Models for morphing airfoil shapes that are being used currently [38-40]. This review provides a thorough and interdisciplinary examination that brings together aerodynamic optimization and structural simulation and data-driven solutions, and also includes the broader aspects of the aforementioned topics such as Evolutionary Optimization Techniques, Adjoint Optimization Techniques, High-Fidelity Computational Fluid Dynamics Simulations, Multi-Fidelity Simulation Models, Deep Surrogate Models, Mesh Morphing Methods, Fluid Structure Interaction Models, and ML-Based Inverse Simulation that were considered separately and individually within the earlier reviews related to aerodynamics and morphing airfoils. This review brings together the various technologies and determines the computational implications of the aforementioned challenges related to the morphing airfoil technologies.

Unlike previous reviews that primarily focused on aerodynamic optimization, this review explicitly highlights the role of advanced composite materials, compliant structures, and material-driven constraints in shaping modern morphing airfoil optimization frameworks.

While considerable advancements have been made in the development of optimization algorithms and surrogate modeling approaches, the review highlights the fundamental limitation that currently restricts the practical implementation of morphing airfoil optimization methodologies. In particular, the nonlinear, anisotropic, and coupled nature of composite material deformation physics is identified as the major limitation, hindering the effective translation of numerical optimization outcomes into morphing airfoil hardware. It is proposed that future optimization methodologies should take into consideration material modeling approaches in order to effectively capture composite material deformation physics and enable the development of morphing airfoil optimization methodologies.

This work is a specific attempt at the synthesis of modern MOO methodologies used within morphing airfoil shape optimization, including both evolutionary algorithms and various other hybrid strategies.

3.1 Descriptive overview of the included studies

A total of 50 rigorously selected peer-reviewed studies have been identified and included in the final dataset to investigate composite-based morphing airfoil optimization, surrogate modeling, and aero-structural integration. The selection process is described in Figure 2, where the PRISMA flow diagram illustrates the selection process from 521 to 50 studies. These studies are the state-of-the-art in multi-objective aerodynamic optimization, composite structural modeling, and data-driven surrogate modeling approaches. The thematic distribution of the selected studies is provided in Table 1. Optimization algorithms are identified as the predominant research focus, appearing in 29 out of 50 studies. This is followed by multidisciplinary aero-structural integration and multi-fidelity modeling approaches, each appearing in 23 studies. The fact that morphing airfoil design is indeed a multidisciplinary optimization problem where aerodynamics, structural behavior, and material-induced deformation constraints are to be addressed simultaneously. Composite materials and structural behavior are addressed in 18 studies, which is a significant increase in recent literature to address material behavior as a design variable. Surrogate modeling approaches are identified in 15 studies, indicating their growing importance in aerodynamic and aero-structural optimization. Likewise, the topic of high-fidelity CFD and turbulence modeling is discussed in 14 studies for simulating realistic aerodynamics. Experimental validation is discussed in only 8 studies, again due to the emphasis on computational methods and the lack of experimentally validated morphing airfoil-based optimization methods.

In terms of the application of the methods, a significant bias towards UAV-based platforms. This review shows that it can be used for various morphing concepts due to the reduced structural loads, reduced regulatory requirements, and the ability for experimental prototyping of the concepts, as suggested in [2, 20]. By contrast, commercial aircraft and transportation-scale morphing applications are underrepresented, which may be attributed to higher structural complexities, certification requirements, and actuation difficulties associated with larger-scale morphing applications.

Table 1. Thematic classification of the 50 studies

Note: Individual studies may belong to multiple thematic categories; therefore, the total count exceeds the number of reviewed studies (n = 50)

3.2 Optimization algorithms and multi-objective design strategies

The analysis reveals that evolutionary MOO algorithms dominate the selection of optimization algorithms for morphing airfoil designs. Specifically, GA, NSGA-II, and other meta-heuristic algorithms were used in over half of the analyzed studies (see Table 1), and their potential for addressing nonlinear multi-objective problems associated with morphing airfoil designs.

The studies presented in Table 2 show the efficiency of evolutionary optimization algorithms for the improvement of aerodynamic characteristics. For instance, Longtin Martel et al. [7] showed the improvement of the lift-to-drag ratio by up to 65% using the NSGA-II algorithm for optimizing a morphing trailing-edge airfoil. In this regard, the authors of the study demonstrate the efficiency of evolutionary algorithms for solving multi-objective problems and finding the optimal solution for conflicting requirements. A similar trend can be observed from Ullah et al. [41], where an improvement in stall characteristics and drag reduction is presented by applying a Black Widow algorithm for optimizing a flexible droop nose morphing airfoil.

The general scheme of the typical actuation layout for morphing airfoils is presented in Figure 3, where composite skins, internal linkages, and shape memory alloy (SMA) actuators play a crucial role as enabling mechanisms for controlled aerodynamic shape deformation [16]. These structural parts will introduce new constraints for the distribution of stiffness, deformation, and force requirements.

Adjoint-based gradient optimization methods are also popular methods, especially for high-fidelity aerodynamic optimizations that include transonic flight or cruise flight conditions. The efficiency of the drag minimization problem using an adjoint-based gradient optimization method for the design of the morphing leading and trailing edges of an aircraft has been successfully demonstrated in the research work presented by Zhang et al. [13]. The efficiency of the adjoint sensitivity analysis in the optimization of the morphing trailing-edge wing was also effectively demonstrated in the research by Lyu and Martins [14].

Table 2. Summary of key influential studies

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However, from the results, it is evident that the effectiveness of these optimization algorithms is also dependent on the composite material properties, deformation limits, and aero-structural coupling effects. The anisotropic properties, non-linear deformation, and actuator-material interactions also impose additional constraints on the design space, which affect the design solutions [11, 28, 29].

Hybrid optimization techniques, which include evolutionary algorithms, have also been proposed in recent studies on morphing wing design optimization [23, 24, 30].

3.3 Computational fluid dynamics modeling fidelity and surrogate-assisted optimization

The aerodynamic performance of the morphing airfoils is mainly computed using RANS-based CFD models coupled with turbulence models such as the SST k-ω and Spalart-Allmaras model in the studies reviewed. The RANS model is widely used in aerodynamic optimizations due to its efficiency in computing the aerodynamic performance in an iterative manner.

Table 2 shows that many studies have successfully incorporated the results of CFD simulations into the framework of surrogate modeling techniques for reducing computation costs while maintaining prediction accuracy. For example, Wang et al. [1] have successfully demonstrated that Kriging-based surrogate modeling techniques are capable of producing prediction errors of less than 6% for the efficient MOO of transonic morphing airfoils. Similarly, Shukla et al. [21] have successfully demonstrated that deep neural operator-based surrogate modeling techniques are capable of producing highly accurate aerodynamic shape predictions with significantly reduced computation costs.

The surrogate modeling techniques that have been successfully incorporated into the framework of morphing airfoil optimization, based on the results of the literature review, are Kriging models, RBF models, artificial neural networks, deep neural operators, and multi-fidelity surrogate models [21-27]. These surrogate modeling techniques enable efficient exploration of high-dimensional morphing airfoil design spaces while significantly reducing computational cost. Moreover, the incorporation of advanced actuation mechanisms and smart material systems in optimization algorithms for morphing airfoil design emphasizes the necessity of using a combination of surrogate optimization and physical models of morphing systems [42].

From the results of the literature review, however, it is evident that the predictive reliability of the results of surrogate modeling techniques is highly dependent on the quality of the training data and the composite structural deformation. For example, there are many studies that have reported limitations of the generalization capability of surrogate modeling techniques for morphing airfoils that are different from the training dataset or have different deformation conditions [35, 43].

Furthermore, turbulence modeling and transition prediction are significant limitations of the results of CFD simulations for morphing airfoil analysis, particularly under large deformation conditions. The limitations of the results of CFD simulations have a direct influence on the accuracy of the results of optimization techniques.

3.4 Multidisciplinary aero-structural integration and composite material influence

A significant portion of the studies that have been incorporated into the results of the literature review have successfully incorporated multidisciplinary aero-structural optimization techniques for integrating the results of CFD simulations with structural analysis techniques such as the finite element method (FEM). The multidisciplinary aero-structural analysis techniques have been successfully incorporated into the framework of morphing airfoil analysis for efficiently evaluating the aerodynamic performance of morphing airfoils.

Composite materials are recognized as the main facilitators for the implementation of morphing airfoils, given their anisotropic stiffness, fatigue, and high elastic deformation capabilities [4, 10, 44, 45]. Advanced material systems, such as flexible composite skins and morphing structures, have been identified to play a crucial role in enabling the aerodynamic adaptation of airfoils. Numerical and experimental validation of the structural and aerodynamic performance of composite morphing airfoils has been achieved in previous studies. Liu et al. [10] analyzed the deformation and failure characteristics of flexible composite skins, while De Gaspari et al. [46] experimentally validated the aerodynamic performance and structural viability of a full-scale composite morphing droop nose airfoil.

Figure 4 shows the multi-segment configuration of the morphing airfoil, focusing on the position of the actuators, the segmentation of the structure, and the deformation of the structure for the improvement of aerodynamic performance. These structural configurations for the morphing airfoil show the importance of the material's stiffness properties, the actuators, and the aero-structural coupling behavior for the improvement of aerodynamic performance.

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Even though the aerodynamic benefits of the morphing airfoil are significant, the findings of the present study reveal the limitations of the optimization studies, where the behavior of the composite material is considered a constraint instead of a design variable for the improvement of aerodynamic performance.

3.5 Thematic and chronological trends

Thematic classification of the 50 studies reveals several main themes:

1. Evolutionary and adjoint-based algorithms for multi-objective morphing of airfoils.
2. Multidisciplinary and multi-fidelity methodologies: coupled CFD–FEM methods, hierarchically mixed models.
3. Surrogate modeling and ML: Deep SURROGATES, multi-fidelity neural networks, physics-informed models.
4. CFD and turbulence modeling: high-fidelity RANS and transitional models for morphing flows
5. Structural and material-based modeling and parameterization methods: FEM-based parameterization, mesh morphing, geometric DL.
6. Applications: UAV, commercial aircraft, and tiltrotor morphing concepts.
7. Composite materials and compliant structural concepts for morphing applications.

Chronologically, the literature evolves from foundational GA + CFD optimization and basic parameterization (2006–2010) to multidisciplinary and multi-fidelity frameworks (2012–2018), and, more recently, to deep-learning-based surrogates, advanced multi-fidelity modeling, and automated parameterization (2019–2025). This trajectory indicates a clear shift from single-discipline, high-cost CFD optimization to data-driven, integrated, and computationally efficient design workflows.

This review aims to provide a comprehensive overview of numerical methods applied to morphing airfoil optimization, with special focus on MOO strategies, high-fidelity CFD methods, and surrogate model techniques. From analyzing the 50 peer-reviewed articles, it can be noted that evolutionary algorithms are preferred methods for exploring the design space, whereas adjoint-based gradient methods are precise methods when applied with high-fidelity methods. The promising results from notable advancements include Kriging methods, DL methods, and multi-fidelity surrogate models. The morphing airfoil concept has now transformed into an interdisciplinary area where aerodynamics, structural response, and material response are strongly interconnected. This can be noted from UAV applications, where morphing airfoils have shown significant improvements in lift-drag ratio, range, and maneuverability when compared to conventional airfoils. However, morphing airfoils have not yet been applied to commercial and military aircraft due to difficulties in integrating morphing structures, durability, and certification of morphing composite materials. Although notable advancements have been made, many limitations need to be overcome before morphing airfoils can be applied to real-world applications. Notable limitations include turbulence and transition models for morphed wings, insufficient experimental validations, and optimization problems being restricted to two-dimensional wing models. Surrogate models have shown difficulties in generalization due to material nonlinearity, large deformations of composite materials, and insufficient training data. The focus areas for future work include material-aware surrogate models, aero-structural control-oriented optimization methods, and three-dimensional morphing composite wings. The morphing airfoil concept must be validated at the wind tunnel and flight scale to ensure reliable performance. The morphing airfoil concept must be transformed from a numerical model to a real-world application.