Research Article

Modified Covariance Matrix Adaptation – Evolution Strategy algorithm for constrained optimization under uncertainty, application to rocket design

¹ IFMA, EA3867, Laboratoires de Mécanique et Ingénieries, Clermont Université, CP 104488, 63000 Clermont-Ferrand, France
² Onera – The French Aerospace Lab, BP 80100, 91123 Palaiseau Cedex, France
³ CNES – Launchers Directorate, 52 rue Jacques Hillairet, 75612 Paris, France

^* e-mail: mathieu.balesdent@onera.fr

Received: 9 October 2014
Accepted: 3 March 2015

Abstract

The design of complex systems often induces a constrained optimization problem under uncertainty. An adaptation of CMA-ES(λ, μ) optimization algorithm is proposed in order to efficiently handle the constraints in the presence of noise. The update mechanisms of the parametrized distribution used to generate the candidate solutions are modified. The constraint handling method allows to reduce the semi-principal axes of the probable research ellipsoid in the directions violating the constraints. The proposed approach is compared to existing approaches on three analytic optimization problems to highlight the efficiency and the robustness of the algorithm. The proposed method is used to design a two stage solid propulsion launch vehicle.