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A relaxation approach for hybrid multi-objective optimal control : application to multiple debris removal mission

Ricciardi, Lorenzo A. and Vasile, Massimiliano (2019) A relaxation approach for hybrid multi-objective optimal control : application to multiple debris removal mission. In: 29th AAS/AIAA Space Flight Mechanics Meeting, 2019-01-13 - 2019-01-17, Sheraton Maui Resort & Spa.

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This paper presents a novel approach to the solution of multi-phase multi-objective hybrid optimal control problems. The proposed solution strategy extends previous work which integrated the Direct Finite Elements Transcription (DFET) method to transcribe dynamics and objectives, with a memetic strategy called Multi Agent Collaborative Search (MACS). The problem is reformulated as two non-linear programming problems: a bi-level and a single level one. In the bi-level formulation the outer level, handled by MACS, generates trial control vectors that are then passed to the inner level, which enforces the feasibility of the solution. Feasible control vectors are then returned to the outer level to evaluate the corresponding objective functions. The single level formulation is also run periodically to ensure local convergence to the Pareto front. In order to treat mixed integer problems, the heuristics of MACS have been modified in order to preserve the discrete nature of integer variables. For the single level refinement and the inner level of the bi-level approach, discrete variables are relaxed and treated as continuous. Once a solution to the relaxed problem has been found, a smooth constraint is added to systematically force the relaxed variables to assume integer values. The approach is first tested on a simple motorised travelling salesmen problem and then applied to the mission design of a multiple debris removal mission.