Study of multi-objective trajectory optimization based on physical programming

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.