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

• Published in: International journal for simulation and multidisciplinary design optimization Vol. 6; no. 1; p. A1
• Main Authors: Chocat, Rudy, Brevault, Loïc, Balesdent, Mathieu, Defoort, Sébastien
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 2015; EDP sciences/NPU (China)
• Subjects: Adaptation; CMA-ES; Complex systems; Computer Science; Constrained optimization; Constraints; Covariance matrix; Covariance Matrix Adaptation; Data Structures and Algorithms; Evolutionary algorithms; Evolutionary Strategy; Optimization; Optimization algorithms; Rocket design; Uncertainty; UNCERTAINTY; EVOLUTIONARY STRATEGY; CONSTRAINED OPTIMIZATION; ROCKET DESIGN; CMA-ES; COVARIANCE MATRIX ADAPTATION
• ISSN: 1779-627X; 1779-6288; 1779-6288
• DOI: 10.1051/smdo/2015001

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.