Genetic Algorithms And Their Applications To Aerodynamic Optimization Problems

The goal of this dissertation is to apply the Genetic Algorithms to aerodynamic optimization problems based on the CFD-Solver and to develop a new gradient free optimization method for aerodynamic problems.Genetic Algorithms, as a good optimization method, have features of robustness and global convergence. However, the traditional Genetic Algorithms will expend too much time to estimate the fitness values when applied to the aerodynamic optimizations. The way to remedy this problem in this dissertation is by improving the efficiency of the optimizer and the solver. Firstly, a small population evolutionary algorithm is developed by using the following techniques: A) A new kind of real coding without limitation of accuracy is studied systemically in order to keep the diversity of the genes. B) Three operators, elitist determined reproduction, adaptive mutation and average crossover are newly constructed. These operators can avoid inbreeding between individuals of the population, decrease the reproduction error and tap the potentialities of the limited size of population. C) The adaptive fitness scaling is developed and the suitable fitness function is designed for the specific optimization problem. Secondly, two kinds of CFD-Solvers, as fitness evaluators in GAs search, have been developed using the finite volume methods in the dissertation. One is developed by time-marching method based on the unsteady Euler equations for subsonic, transonic and supersonic flow simulations in two/three dimensions. The measures for acceleration in convergence are used by means of local tune stepping, enthalpy damping and implicit smoothing. The other is developed by space-marching method based on the steady Euler equations, which has been proved to have fast convergence for supersonic flows over 3-D bodies.As all known, the representation of the parameters to be optimized is an important factor when the Genetic Algorithms are used for solving engineering problems. The representation itself doesn't change the nature of the problem, but effects the searching efficiency of the algorithm. It is verified though our research that the representation using Spline curves can reduce the searching scope and hence accelerate the convergence of the Gas, for it only needs a few of control points to describe an aerodynamic shape. While the point by point representation is suitable for minor modification of aerodynamic shapes.The implicit scheme of the Euler solver, as evaluator, is used in the GAs for airfoil optimizations. The airfoils are optimized based on the minimization of the drag and the maximization of the ratio of the lift to drag after the success of the reconstruction design of the airfoils. Then, the GAs are extended to the three dimensional aerodynamic optimizations. The 3-D unsteady Euler solver is accelerated by reducing the computational domain to four mesh layers in circumference when the GAs are used to the dragminimization of the revolution body at zero angle. We found that the optimized revolution body has the lower drag as compared with the well-known Karman-body that the drag is constant according to the linearized theory while the drag of the optimized body varies with the Mach number of the far field. The steady Euler solver is applied to the optimization of the canopy-fuselage. The optimized results show that the droop of the fuselage and the geometry of the windshield are the main elements to effect the drag at the supersonic conditions.Multi-objective optimization problem is always interested to the engineering field. Theoretically, the solution of this problem is the set of Pareto solution. A Pareto Genetic Algorithm (Pareto-GAs) is developed through constructing a set of operators and strategies based on the definition of the Pareto solution. It is remind that the Pareto-GAs is a cooperative multi-objective optimization method. In the searching process, the Pareto-GAs is speeded up by presenting a ranking method which can identify accurately the individuals who are closer to the Pareto front. As for...