Particle Swarm Optimization for Solving a Shooting Point

A shooting method is based on the solution of the ordinary differential equation for optimality that is obtained from Pontryagin´s maximum principle. A shooting point must be approaching the perfect solution in order to assure algorithm´s convergence. A particle swarm optimization is used to decide a shooting point by neural network´s mapping ordinary differential equation initial states to final states and by defining sufficiency form as final states majorized function. To make up normal algorithm´s deficiency secondary search of changing search level is introduced which can largely avoid trapping in local extremum and increase hitting global maximum´s rate. The method´s validity was proved by an illustration