Covariance matrix adaptation evolution strategy for multidisciplinary optimization of expendable launcher family

After 30 years of success of Ariane launches, Astrium Space Transportation as prime contractor is preparing the future of launch vehicles with research and development activities. This paper describes the results of the collaboration between INRIA and Astrium to solve the typical multidisciplinary problem of expendable launch vehicle design thanks to the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The different disciplines integrated in the Multidisciplinary platform are propulsion system, aerodynamics, mass budget, trajectory integration, control. CMA-ES was tested on a two-liquid-staged launcher with solid boosters. The algorithm produced conclusive results on an optimization problem that proved to be very ill-conditioned. The comparison with Non-Dominated Sorting Genetic Algorithm NSGA-II gave equivalent results on a bi-level optimization, the trajectory subproblem being solved separately by a reduced gradient method. The good performance of CMA-ES on a single launcher case allowed us to extend the tests on a launcher family. A launcher family is composed of several launcher configurations sharing common characteristics with different payload targets and optimized together. In these last cases, CMA-ES surpasses NSGA-II in terms of performance and was able to handle multiple error cases during the search of optimum.