Approximate and Exact Approaches for the Optimization of Hybrid-Rocket Upper Stage

摘要

Different strategies have been successfully introduced in order to reduce the computational time required for the optimization of a hybrid rocket upper stage. A recently developed nested evolutionary/ indirect procedure, which optimizes the overall ascent trajectory, has been improved. A multiple-shooting approach allowed for reducing by 15-20% the computational time and increasing robustness of the optimizer. The computing time is further reduced to about one-fifth if the trajectory integration is limited to the hybrid rocket upper stage only. The achieved solution is very close to the optimal one in this case. Finally, an approximated control law for the thrust angles has been adopted and a pure cooperative evolutionary algorithm has been used to further reduce computational time. The present pure evolutionary algorithm is not so efficient as the nested procedure. Nevertheless, it has shown capabilities to deal with complex problems. The performance of the evolutionary algorithm can be increased with a better formulation of the fitness function (i.e., the value of W_0) and computational time can be decreased by introducing checks of the individual before the integration. The pure evolutionary algorithm can be used as a powerful tool when detailed information about the problem is not available. It can deal with discrete variable (e.g., choice of the propellant combinations) and it is able to give a first tentative solution for an accurate optimization of the trajectory or to be used to find a guess for the nested strategy. It is therefore extremely useful for exploring large solution spaces in the early stages of conceptual design.