Direct solution of multi-objective optimal control problems applied to spaceplane mission design

This paper presents a novel approach to the solution of multi-phase multi-objective optimal control problems. The proposed solution strategy is based on the transcription of the optimal control problem with Finite Elements in Time and the solution of the resulting Multi-Objective Non-Linear Programming (MONLP) problem with a memetic strategy that extends the Multi Agent Collaborative Search algorithm. The MONLP problem is reformulated as two non-linear programming problems: a bi-level and a single level problem. The bi-level formulation is used to globally explore the search space and generate a well spread set of non-dominated decision vectors while the single level formulation is used to locally converge to Pareto efficient solutions. Within the bi-level formulation, the outer level selects trial decision vectors that satisfy an improvement condition based on Chebyshev weighted norm, while the inner level restores the feasibility of the trial vectors generated by the outer level. The single level refinement implements a Pascoletti-Serafini scalarisation of the MONLP problem to optimise the objectives while satisfying the constraints. The approach is applied to the solution of three test cases of increasing complexity: an atmospheric re-entry problem, an ascent and abort trajectory scenario and a three-objective system and trajectory optimisation problem for spaceplanes.