A hybrid DE-SQP method for vertical trajectory optimization of continuous descent approach

Abstract

This paper mainly introduces a hybrid algorithm to solve vertical trajectory optimization problem during aircraft descent. According to the flap schedule of aircraft, the problem can be formulated as a multiple-phase optimal control problem. Pseudo-spectral method is used to discretize the continuous optimal control problem into nonlinear programming (NLP) problem. Then we adopt a hybrid method, namely DE-SQP, integrating differential evolution (DE) algorithm as global optimizer with sequential quadratic programming (SQP) for local search to solve the NLP problem. DE is a population-based heuristic algorithm with a strong capability of global search. However, multiple differential variables' path constraints constitute a heavy penalty term on objective function. Thereby, population searching process improbably converges to an acceptable fitness. In addition, SQP is efficient to solve NLP problems by gradient descent method which converges fast to global optimum with high accuracy. Simulation results indicate a better performance of hybrid algorithm than the other two.