Optimization of nose shape of Launch Vehicle using genetic algorithm and response surface methods

Abstract

In this study, to reduce the drag force, the nose shape of Launch Vehicle with determined flight conditions, is optimized. Two optimization methods are considered: binary genetic algorithm and response surface method. Since the value of drag coefficient is proportional to dynamic pressure, the objective function is based on minimization of drag coefficient in flight conditions which is corresponding to the maximum dynamic pressure. In order to evaluation of objective function, the aerodynamic prediction engineering code is used. The results of aerodynamic prediction code directly entered to binary genetic algorithm code and with common parameters of this algorithm like crossover, mutation and elitism, the optimization process is done. Moreover, the sensibility analysis of this algorithm respect to mutation parameter and size of population is analyzed and optimum values of them are obtained. Also, response Surface Method with quadratic model is considered. Some special points from domain of design variables are selected and corresponding drag coefficients for these points are calculated by aerodynamic prediction engineering code. Then, the appropriate second order surface is fitted to these points regarding to least square method. The results show that with optimum values of genetic algorithm parameters (rate of mutation and size of population); the algorithm converges rapidly with a few generations. In this case, the genetic algorithm only searches the 1.4% of solution space and then converged. Generally, the results show good agreement between two methods.