Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.
To study the efficiency of genetic algorithms (GAs) in the
optimization of aerodynamic shapes, the shape of an airfoil
was optimized by a genetic algorithm to obtain maximum lift
to drag ratio and maximum lift. The flow field is assumed to
be two dimensional, Invicsid, transonic and is analyzed
numerically. The camber line and thickness distribution of the
airfoil were modeled by a fourth order polynomial. The airfoil
chord length was assumed constant. Also, proper boundary
conditions were applied. A finite volume method using the
first order Roe’s flux approximation and time marching
(explicit) method was used for the flow analysis. The simple
genetic algorithm (SGA) was used for optimization. This
algorithm could find the optimum point of this problem in an
acceptable time frame. Results show that the GA could find
the optimum point by examining only less than 0.1% of the
total possible cases. Meanwhile, effects of parameters of GA
such as population size in each generation, mutation
probability and crossover probability on accuracy and speed of
convergence of this SGA were studied. These parameters have
very small effects on the accuracy of the genetic algorithm,
but they have a sensible effect on speed of convergence. The
parameters of this genetic algorithm were improved to obtain
the minimum run time of optimization procedure and to
maximize the speed of convergence of this genetic algorithm.
Robustness and efficiency of this algorithm in optimizing the
shape of the airfoils were shown. Also, by finding the
optimum values of its parameters, maximum speed and
minimum run time was obtained. It is shown that for
engineering purposes, the speed of GAs is incredibly high, and
acceptable results are sought by a fairly low number of
generations of computations.
