The document presents a multi-objective evolutionary algorithm framework named airopt for optimizing aerodynamic shapes of two-dimensional airfoils, aimed at minimizing drag and maximizing lift-to-drag ratio. It utilizes a parameterization approach with Bézier curves, integrates a transition prediction model, and includes a robust method for estimating total drag by considering skin friction distribution. Preliminary results demonstrate the effectiveness of this approach, with future work planned on expanding the framework to three-dimensional wing designs.

1. *
Doctoral candidate, Centre for Hypersonics, UQ; formerly at Zeus Numerix Pvt. Ltd.
†
Founder, T-Cube Solutions Pvt. Limited; formerly at Zeus Numerix Pvt. Ltd.
‡
Head, Software Development.
AIROPT: A Multi-Objective Evolutionary Algorithm based Aerodynamic Shape Optimization Tool for
Airfoils
Sreekanth Raghunath*
The University of Queensland, Brisbane, Australia
Srinivethan Rangasamy†
T-Cube Solutions Pvt. Ltd., Chennai, India
Sandeep Somasekharan‡
Zeus Numerix Pvt. Ltd., Pune, India
Abstract
A multi-objective evolutionary algorithm based modular optimization framework available in OPT4J
has been used for aerodynamic shape optimization of two-dimensional airfoils in AIROPT. The primary
objectives of the optimization process taken up during the current study in AIROPT are: (i) to minimize the drag,
and, (ii) to maximize the lift-to-drag ratio at a given angle of attack. The airfoil geometry has been parametrized
using Bézier curves for generating the camber and thickness surfaces. The constraints imposed on the geometry
ensure a smooth leading edge and minimal, non-zero thickness at the trailing edge of the airfoils generated.
XFOIL has been used to estimate the pressure and boundary layer edge velocity distributions. Unlike most other
studies reported in literature, the γ-Reθ transition prediction model has been used to predict the location of onset
of transition in the current study. Another unique feature of AIROPT is that the distribution of skin friction
through the transition zone is taken into account in estimating the total drag, which ensures that optimization
process is more robust and only the best individuals are chosen by the optimization algorithm. These modules
are integrated within the optimization framework, which makes AIROPT a robust and reliable optimization tool.
Introduction
Viscous drag reduction in aerospace vehicles is one of the most challenging problems currently being
investigated by the aerospace research community. It is estimated that every 10% reduction in drag results in
about 8% reduction in fuel consumption [1], thus reducing CO2 and NOx emissions by a significantly large
amount [2]. With the discussion around the topic of climate change getting ever hotter, this problem has gained
more prominence.
[2, 3] provide an overview of the various techniques employed for viscous drag reduction. One of the
popular approaches adopted by researchers to reduce viscous drag is to extend the extent of laminar flow over
the wings either by shape optimization [4-8] or using one of laminar flow control techniques, such as, adding
riblets on the surface of the wing [9] or wall heating [10] or suction [11]. In the current work, an evolutionary
algorithm (EA) based multi-objective optimization framework in OPT4J [12] has been integrated with a generic
Bézier curve formulation, the XFOIL code [13] and a transition prediction module (for predicting the onset and
the extent of laminar-turbulent transition) to obtain the most optimal airfoil designs, with minimal drag and a
high lift-to-drag ratio at a given angle of attack.
Some of the major advantages of adopting this methodology will be presented in the full paper. It must
be pointed out here, however, that one of the unique features of the current approach is the inclusion of the
distribution of skin friction through the transition zone in estimating the total drag. Most of the other reported
optimization studies either assume that the flow would be fully turbulent downstream of the location of onset of
transition or do not include the effects of transition in their studies at all [14], which results in sub-optimal
designs. The next section provides a brief overview of the methodology adopted in the current work. The
following section provides preliminary results obtained during current work and a brief outline of the work that
will be presented in the full paper.

2. Methodology
The flowchart in Figure 1 provides an overview of the methodology adopted in AIROPT.
Figure 1: A flow-chart that provides an overview of the methodology of AIROPT
OPT4J adopts a modular approach, by which complex optimization tasks can be efficiently
decomposed into correlated sub-tasks that are optimized concurrently [12]. The NSGA-II multi-objective
evolutionary algorithm available within OPT4J is utilized in this work. OPT4J can be run in parallel, thus
speeding up the optimization process. The Creator module within OPT4J generates random genotypes, which
contain the genetic representation of an individual. In this case, 13 random integers within a specified range (0
to 40) are generated by the Creator module. The Decoder module converts the genotype into a phenotype, which
represents all observable characteristics and components of the individual. In this case, the Bézier control points

3. for generating the thickness and camber curves are computed by the Decoder module using the 13 random
integers from the earlier step.
These Bézier control points are used to generate the thickness and camber surfaces in AIROPT, which
are in turn used to generate the upper and lower surfaces of the airfoil. A check is performed to see if the
generated airfoils lie within the geometry constraints specified and only valid individuals are carried on to the
next step. The thickness range of the generated airfoils is limited to remain between 7% and 50% of the chord at
any given location. To ensure a smooth leading edge, the thickness is limited to 11% of the chord in the first 5%
of the chord near the leading edge. The maximum thickness is limited to 20% of the chord in the last 20% of the
chord and to 6% of the chord in the last 6% of the chord. The thickness at all locations is limited to above 2%,
ensuring no regions of non-zero thickness.
AIROPT calls XFOIL [13], which determines the velocity and pressure distributions over all the valid
airfoil geometries. The velocity distribution obtained from XFOIL is used in the transition prediction module.
The correlation-based γ-Reθ transition prediction model of Langtry and Menter [15], which takes into account
the effects of free-stream turbulence intensity and pressure gradient to predict the location of onset of transition,
has been used in the current study. To model the intermittent transition zone, the intermittency factor of
Narasimha [16] has been used in conjunction with the Linear Combination Model approach of Narasimha and
Dey [17]. An accurate estimation of the total drag is obtained from this process, which is used in estimating the
fitness value.
The desired objectives of the optimization process are to be specified in the Evaluator module of OPT4J.
For the cases reported in this paper, the following objectives are considered in evaluating the fitness value of
each individual:
• To maximize the lift-to-drag ratio at a given angle of attack.
• To minimize the drag experienced by the airfoil by maximizing the surface of the airfoil covered by
laminar flow. In the optimization process, this was achieved by maximizing the distance from the
leading edge to the location of onset of transition on both the pressure and suction surfaces of the
airfoil separately. Evaluating the total drag taking into account the skin friction distribution through the
transition zone ensured that the estimated value of total drag was more accurate than otherwise.
The Evaluator module estimates the fitness values of all individuals within a particular generation, and
stores the best individuals that meet the specified objectives. Depending on the specified cross-over rate and
mutation rate, a certain number of these “best individuals” are archived and carried over to the next generation.
Either upon completion of the specified number of generations or once the specified objectives are met, OPT4J
is halted and the most optimal airfoil shapes generated during the optimization process are obtained.
Preliminary Results
Preliminary results for a few test cases are presented in this section. The flight conditions considered
during the current optimization process are: a Reynolds number of 3x106
and Mach number of 0.14. A
convergence plot and Pareto plot corresponding to this optimization run are presented in Figure 2 and Figure 3.
As seen in Figure 2, the optimization run is heading towards convergence, with the maximum, minimum and
mean values of objective 2 (in this case, the transition location on the upper surface) plateauing out. In the
Pareto plot in Figure 3, objective 1 is plotted as a function of objective 2 at a certain time during the
optimization run. The red dots represent individuals that have been archived and are to be considered with the
next generation, while the grey dots are non-optimal solutions and get eliminated. As the optimization run
converges, the Pareto plot generally contains mostly red dots, indicating that the most optimal airfoil shapes
have been obtained. As seen in Figure 3, an evolutionary algorithm based optimization framework does not
provide a single optimal design but a set of optimal designs with the most desirable characteristics. Depending
on the purpose for which the optimization process has been undertaken, the user chooses the individual that
most suits their requirement over a range of design and off-design conditions.

4. Figure 2: A convergence plot depicting the maximum, minimum and the mean values of Objective 2, as a function of
the number of iterations for which the optimizer has been run.
Figure 3: A Pareto plot of objective 1 (lift-to-drag ratio) as a function of objective 2 (transition location on upper
surface), depicting individuals of the populations that have been archived in red.
Future Work
The full paper will include a detailed review of existing body of literature related to airfoil optimization
and describe some of the major advantages of the current approach in more detail. Further details about the
methodology adopted during the current study will also be included in the full paper. Results, including airfoil
geometries and corresponding aerodynamic characteristics at a few flow conditions will be provided in the full
paper, along with the corresponding Pareto and Convergence plots.
Although not considered in this particular study, this code has provisions to include other relevant
objectives related to structural, electro-magnetic, acoustic and other disciplines, to make AIROPT a multi-
objective, multi-disciplinary optimization tool. Developing AIROPT to include three-dimensional wing design
will be considered as part of the future work.

5. References
1. Leschziner, M.A., Choi, H., Choi, K. S., Flow-control approaches to drag reduction in
aerodynamics: progress and prospects. Philos Trans A Math Phys Eng Sci, 2011. 369(1940):
p. 1349-51.
2. Jahanmiri, M., Aircraft Drag Reduction: An Overview. Division of Mechanics, Research
Report, Chalmers University of Technology, 2011.
3. Bushnell, D.M., Aircraft drag reduction—a review. Proceedings of the Institution of
Mechanical Engineers, Part G: Journal of Aerospace Engineering,, 2003. 217(1): p. 1-18.
4. Jameson, A. and S. Kim, Reduction of the Adjoint Gradient Formula for Aerodynamic Shape
Optimization Problems. AIAA Journal, 2003. 41(11): p. 2114-2129.
5. Amoignon, O.G., Pralits, Jan O., Hanifi, Ardeshir, Berggren, Martin, Henningson, Dan S.,
Shape Optimization for Delay of Laminar-Turbulent Transition. AIAA Journal, 2006. 44(5):
p. 1009-1024.
6. Gardner, B.A., & Selig, M. S., Airfoil design using a genetic algorithm and an inverse method.
41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2003-43), 2003.
7. Nadarajah, S.K. and C. Tatossian, Multi-objective aerodynamic shape optimization
for unsteady viscous flows. Optimization and Engineering, 2008. 11(1): p. 67-106.
8. Chen, X. and R.K. Agarwal, Shape optimization of airfoils in transonic flow using a multi-
objective genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part G:
Journal of Aerospace Engineering, 2013. 228(9): p. 1654-1667.
9. Viswanth, P.R., Aircraft viscous drag reduction using riblets. Progress in Aerospace Sciences,
2002. 38(6): p. 571-600.
10. Dovgal, A.V., Levchenko, V. Y., & Timopeev, V. A., Boundary layer control by a local
heating of the wall. In Laminar-Turbulent Transition (Springer Berlin Heidelberg), 1990: p.
113-121.
11. Hanifi, A., Pralits, J., Amoignon, O., & Chevalier, M., Laminar Flow Control and
Aerodynamic Shape Optimization. 2009.
12. Lukasiewycz, M., Glaß, M., Reimann, F., & Teich, J., Opt4J: a modular framework for meta-
heuristic optimization. In Proceedings of the 13th annual conference on Genetic and
evolutionary computation, 2011: p. 1723-1730.
13. Drela, M., XFOIL: An analysis and design system for low Reynolds number airfoils. In Low
Reynolds number aerodynamics, Springer Berlin Heidelberg, 1989: p. 1-12.
14. Wauquiez, C., Shape optimization of low speed airfoils using Matlab and Automatic
Differentiation. Licentiate’s Thesis, Royal Institute of Technology, Stockholm, 2000.
15. Langtry, R.B., & Menter, F. R., Correlation-based transition modeling for unstructured
parallelized computational fluid dynamics codes. AIAA Journal, 2009. 47(12): p. 2894-2906.
16. Narasimha, R., On the distribution of intermittency in the transition region of a boundary
layer. Journal of the Aeronautical Sciences, 1957. 24(9): p. 711-712.
17. Narasimha, R., & Dey, J. , Transition-zone models for 2-dimensional boundary layers: A
review. Sadhana, 1989. 14(2): p. 93-120.