Innovative multilevel techniques for structural optimization

Porcelli M., Colson B., Toint P. L.

Linear algebra  Optimization  J.2 PHYSICAL SCIENCES AND ENGINEERING 

We address the structural optimization problem of sizing an aircraft fuselage. The problem consists in computing the dimensions of the dierent elements constituting a fuselage mini- mizing the total mass subject to some mechanical constraints. Mathematically, the problem may be formulated as a very large nonlinear optimization problem subjected to several non- linear inequality constraints. We show that this problem possesses a natural hierarchical structure that can be exploited by a multilevel approach. This approach is innovative in the industrial sector and represents a promising alternative to the commonly employed decom- position strategies. Hence, we propose a multilevel procedure which embeds the Recursive Multilevel Trust Region method [1] into an Augmented Lagrangian framework. Some results on both academic and industrial test cases are presented.

Source: Congresso Biennale SIMAI MiniSimposio: MSP - Large-Scale Numerical Linear Algebra And Optimization, Torino, 25-28 June 2012