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Mathematical Problems in Engineering
Volume 2015, Article ID 949480, 13 pages
Research Article

Spacecraft Multiple-Impulse Trajectory Optimization Using Differential Evolution Algorithm with Combined Mutation Strategies and Boundary-Handling Schemes

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China

Received 25 January 2015; Revised 7 April 2015; Accepted 14 April 2015

Academic Editor: Yakov Strelniker

Copyright © 2015 Yuehe Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.