Modified genetic algorithm for constrained trajectory optimization

Although direct methods using sequential quadratic programming, such as direct collocation, have been widely applied to trajectory optimization problems, optimization results for these methods are sensitive to initial solutions in some cases. For the purpose of finding an appropriate initial solution to gradient-based direct trajectory optimization, a numerical trajectory optimization method using a real-coded genetic algorithm (GA) is considered. Because a typical GA solves unconstrained optimization problems, the penalty function has usually been used as the selection criterion of surviving individuals. However, the convergence properties of this conventional method are sensitive to the penalty parameter. Therefore, a new method that robustly achieves global optimization of the objective function and the feasibility search even with a large penalty parameter is proposed. The proposed method is applied to the constrained brachistochrone problem and a space plane reentry problem. Results indicate promising performance of the proposed method in providing appropriate initial solutions for gradient-based trajectory optimization.