Abstract


Although Evolutionary Algorithrns (EAs) have become increasingly popular in aerodynamic 
design problems, the previous applications of EAs are restricted to more or less simplified problems 
involving not more than 10-30 design parameters. In contrast to that, in real-world design problems, a 
large number of design parameters must be handled -for example, a wing shape for a generic 
transonic aircraft usually parameterized by more than a hundred of design parameters. Since such 
problem has a highly multidimensional search space and extremely complicated objective function 
distribution, standard EAs would fail to find a globally optimum. This research develops a new, robust, 
and efficient numerical design method applicable to such real-world aerodynamic design problems.

One of the most important difficulties in real-world aerodynamic shape design problems is 
their highly multidimensional design space. To develop a robust and efficient EA applicable to such 
design problems, the real-coded ARGAs have been developed by incorporating the idea of the 
binary-coded ARGAs with the use of the floating-point representation. The performance of the 
proposed EAs was demonstrated by applying to a typical test function minimization problem and an 
aerodynamic airfoil shape optimization problem The real-coded ARGAs consistently found better
solutions than the conventional real-coded GAs do. 

Because the flow field is governed by a system of nonlinear partial differential equations, 
objective function landscape of an aerodynamic optimization is often multimodal and nonlinear. To 
improve EAs' capability of finding a global optimum in such a problem, a crossover operator based on 
the structured coding has been proposed. The coding structure of the design variables is constructed 
according to the interaction information among design parameters analyzed by the experimental 
design. Aerodynamic optimizations of a transonic wing demonstrated that the crossover based on the 
structured coding was more efficient than the traditional one.

To ensure the capability of the present EA in handling large-scale aerodynamic design 
optimizations, the real-coded ARGA coupled with the crossover based on the structured coding is 
applied to an aerodynamic design optimization of a transonic wing shape for generic transport aircraft. 
Aerodynamic performances of the design candidates are evaluated by using the three-dimensional 
compressive Navier-Stokes equations to guarantee an accurate model of the flow field. Structural 
constraint is introduced to avoid an apparent solution of zero thickness wing for low drag in high 
speeds. To overcome enormous computational time necessary for the optimization, the computation is 
parallelized on NWT. The designed wing had a good L/D value satisfying the given structural 
constraint on wing thickness.

Finally, an EA is applied to an aerodynamic wing shape design for a supersonic transport to 
examine the feasibility of the EA-based optimization in supersonic wing design optimizations. The 
optimum design obtained from the present approach yielded both the minimum induced drag and the 
minimum volume wave drag in the given design space. The design also indicated the most important 
features of supersonic wing design as compared with conventional transonic wing design as follows:

1) Warp geometry based on camber line and twist angle distributions plays a more important role 
than spanwise thickness distribution because the thickness becomes simply as thin as possible.
2) Because the wing thickness constraint comes from the wing structure, a practical structural 
constraint will be required.