基于模糊理论的跳跃轨迹多目标优化设计

Fuzzy theory based multi-objective optimization of lunar return skip trajectories

针对探月返回跳跃轨迹的多目标优化设计问题,提出了一种基于模糊理论的优化设计方法,并对非线性隶属度函数对优化结果的影响进行了研究。首先,将连续的无限维优化问题进行离散化,转化为非线性规划问题;其次,用隶属度函数将各个子目标进行模糊化,将多目标优化问题转化为求模糊判决隶属度函数的最大值问题;最后,求解经过模糊化的非线性规划问题。分析了探月返回跳跃轨迹的特性,表明模糊多目标优化更能体现决策者的偏好。构造了具有不同凹凸性、不同形状的非线性隶属度函数,比较了它们对优化结果的影响,结果表明隶属度函数影响多目标模糊优化结果的首要因素是隶属度函数的凹凸性。

A fuzzy theory based multi-objective optimization method was proposed for the lunar return skip trajectory design and analysis,and the effect of nonlinear member functions of fuzzy sets on the optimization results was investigated. The optimization problem was converted to a nonlinear programming problem. Then each sub-objective was fuzzed to obtain the fuzzy decision set and its member function. Thus,the original multi-objective optimization problem was converted to a single-objective optimization problem which maximizes weighted sums of the member functions. The optimization results demonstrate that the proposed method can well show the preference of the decision maker. Nonlinear member functions with various shape and different concavity and convexity were constructed to investigate the main factor that affected the optimization results,and the results show that the concavity and convexity of member functions have much larger effect on the optimization than that of the shape.