Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

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In this paper, the ascent trajectory optimization of a lifting body Single- Stage To Orbit (SSTO) reusable launch vehicle is investigated. The work is carried out using a Direct Multiple Shooting method to solve the Optimal Control problem. The crucial initialisation of the optimisation process is performed by using a combination of two evolutionary algorithms, namely a Multi-Objective Parzen-based Estimation of Distribution (MOPED) algorithm and a Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA). MOPED belongs to the class of Estimation of Distribution Algorithms (EDAs) and it is used in the first phase of the initial guess research to explore the search space, then MP-AIDEA is used to refine the obtained results, and better fulfill the imposed constraints. The initial guesses obtained with this evolutionary framework were tested on different multiple shooting configurations. The importance of the continuity properties of the employed mathematical models was also quantitatively addressed.
Original languageEnglish
Number of pages26
JournalOptimization and Engineering
Early online date20 Nov 2021
Publication statusE-pub ahead of print - 20 Nov 2021


  • optimal control
  • reusable launch vehicle
  • direct multiple-shooting
  • trajectory optimization
  • evolutionary algorithm
  • initial guess research


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