基于NSGA-II算法的RLV多目标再入轨迹优化设计

传统的再入轨迹优化设计通常只考虑单目标优化问题,例如最小热流、最小大航程、最小控制能量等。随着人们对降低费用和提高性能的期望越来越高,多目标再入轨迹优化问题也引起了注意。以往人们通过加权因子等方法将多目标问题转化为单目标问题,避免了复杂的多目标优化算法的应用。但也引入了新的参数,且每次优化只能获得与该参数相关的1个解。N SGA-II算法是最近发展起来的具有优良性能的多目标遗传算法,它引入了快速分类、约束支配和精英策略,1次运行可以获得多个Pareto最优解。文中利用N SGA-II算法来求解具有最小热载和最大横程的2个目标的再入轨迹优化问题。算例表明N SGA-II算法能够有效地搜索到优化轨迹的Pareto前沿,是RLV初步设计的有力工具。

Implementing a Multi-Objective Optimization Design of RLV Reentry Trajectory

Purpose.The majority of past optimization designs of RLV(Reusable Launch Vehicle) chose single objective optimization or what is equivalent to a single objective optimization.Such a way is,in our opinion,increasingly unsatisfactory to meet the increasingly high demands on RLV.We apply NSGA-II algorithm, first proposed by Indian engineers~([2]),to implementing a two-objective optimization design of RLV reentry trajectory.Multi-objective reentry trajectory optimization is often necessary such as minimum heat load and maximum maneuverable range.These types of optimization problems have traditionally been solved by averaging each objective with a weighting factor,and then combine the objectives into a single scalar objective.Such reduction techniques eliminate the need for a more complex multi-objective,but introduce new parameters in the form of weighting factors;it is really equivalent to only a single objective optimization.Each run of the algorithm can produce only one optimal trajectory.NSGAII algorithm is a good multi-objective genetic optimization algorithm based on Pareto-optimal front with low computational requirements,elitist approach,parameter-less niche approach and simple constraint-handling strategy.Pareto-optimal front is a series of optimal solutions,from which the designers can choose the best one.Finally we give a numerical example,whose demonstration model is the same as that of Indian engineers~([4]),and it uses the three-dimensional reentry dynamic equations based on rotational spherical Earth model.The chromosome is designed by Chebeshev polynominals.The population has 100 individuals and NSGAII algorithm gives 51 Pareto-optimal solutions in less than 10 minutes on a 3.2 GHz PC.The results indicate that NSGA-II algorithm performs well in multi-objective reentry trajectory design.The control curve of one of the trajectories plotted is smooth and is easy to implement.The designers can choose what they want in RLV preliminary design.