中文摘要：

针对加权系数法求解弹道多目标优化问题时不能获取非凸Pareto非劣解，并且主观依赖性严重，难以选取合适的权值的问题，将物理规划引入弹道多目标优化中，建立了基于物理规划的弹道多目标优化模型，详细分析了基于物理规划的弹道多目标优化方法的求解流程，指出了该方法的优点．最后分别采用加权系数法、最优控制方法以及本文所提方法进行拉平段弹道多目标优化．优化结果对比研究表明，物理规划法效率更高，结果更好，对初值不敏感，鲁棒性更强，并且有利于获得非凸Pareto非劣解，从而体现了所提方法较强的工程实用价值．

英文摘要：

The weighted summary method （WSM） is widely adopted in the multi-objective trajectory optimization. However, it is rather difficult to obtain the non-convex Pareto non- inferior solutions by using WSM, and weights subjectively determined by users are usually inappropriate. To overcome the disadvantages above, the physical programming method is introduced and the model based on physical programming is presented for multi-objective trajectory optimization. The procedure of multi-objective trajectory optimization using physical programming was analyzed in detail and the advantages of proposed method were also pointed out. The pullout segment trajectory of a missile was optimized respectively by using three methods. WSM, optimal control theory method and the physical programming method. Through comparison of the optimization results, it is demonstrated that physical programming method has the advantages over other two methods. It is more efficient and robust, and is insensitive to initial value. It could achieve better optimization results. In addition, it has the ability of achieving the non-convex Pareto non-inferior solution. Thus, the physical programming method proposed in this article is proved to be quite practical in multi-objective trajectory optimization.