Optimal Periodic Cruise Trajectories via a Two-Level Optimization Method

The determination of optimal periodic cruise trajectories that incorporate initial states as design variables is studied in this paper. A two-level optimization method that separately deals with initial states in the outer loop and control variables in the inner loop is introduced. The outer-loop parameter optimization problem uses tradespace visualization driven by a genetic algorithm and the inner-loop optimal control problem uses the direct shooting method. A multi-objective (fuel rate and heat load) optimal periodic cruise problem in the outer loop is investigated. It is shown that if the objective of the inner loop is heat load, the fuel performance is not desirable for all the initial states. Thus, only fuel rate is the inner-loop objective. The Pareto solutions that the path constraints have no impact on control variables and that the path constraints are activated on control variables are both identified by imposing the path constraints in the outer loop and inner loop, respectively. Approximation models, built through a response surface methodology, replace the inner-loop optimization model and generate the Pareto fronts during the process of tradespace visualization.