Direct Solution of Multi-Objective Optimal Control Problems Applied to Spaceplane Mission Design

Abstract

This paper presents a novel approach to the solution of multiphase 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 nonlinear programming (MONLP) problem with a memetic strategy that extends the Multi Agent Collaborative Search algorithm. The MONLP problem is reformulated as two nonlinear programming problems: a bilevel and a single-level problem. The bilevel formulation is used to globally explore the search space and generate a well spread set of nondominated decision vectors, whereas the single-level formulation is used to locally converge to Pareto efficient solutions. Within the bilevel formulation, the outer level selects trial decision vectors that satisfy an improvement condition based on Chebyshev weighted norm, whereas the inner level restores the feasibility of the trial vectors generated by the outer level. The single-level refinement implements a Pascoletti-Serafini scalarization of the MONLP problem to optimize the objectives while satisfying the constraints. The approach is applied to the solution of three test cases of increasing complexity: an atmospheric reentry problem, an ascent and abort trajectory scenario, and a three-objective system and trajectory optimization problem for spaceplanes.