Flight Trajectory Optimization Using Genetic Algorithm Combined with Gradient Method

This paper considers the numerical method to solve trajectory optimization problems where efficient flight trajectories are searched to minimize a performance index with specified constrained. While a wide variety of numerical methods have been developed, the direct application of a nonlinear programming method is frequently used in the recent applications, which transforms the original problem into a nonlinear optimization problem. Although these methods can be applied to complicated applications, it is very difficult to find reasonable initial solutions since practical problems have high nonlinearlity. This paper tries to apply the Genetic Algorithm (GA) method. Sine the GA approach is one of the random search methods, the initial solutions are selected at random. As shown in numerical examples, the GA approach has slow convergence characteristics and the meaningless fluctuation in the solutions. Therefore, the gradient approach is utilized to refine the solutions. As the gradient method, the authors uses the BDH method which approximates the state and control variables using linear interpolation and the collocation method is used to satisfy the dynamic equations. The obtained Hessian matrix can be approximated in a Block Diagonal Form which is suitable for efficient computation. The proposed approach is applied to the optimal accent trajectory optimization of a spaceplane. The spaceplane is a future space transportation vehicle and its conceptual design is investigated.