Start date :31/01/2020
End date :31/01/2020
Location : salle des thèses de l'ISAE-SUPAERO - 10 avenue Edouard Belin, 31000, Toulouse
Doctoral School: Aéronautique-Astronautique
In this work, we propose to solve large scale structural weight minimization problems with both categorical and continuous variables, subject to stress and displacements constraints. Three original algorithms have been proposed.
As a first attempt, an algorithm based on the branch and bound methodology has been implemented. A specific formulation to compute lower bounds has been proposed. According to the test case results, the proposed algorithm returned the exact optima. However, the exponential scalability of the computational cost with respect to the number of structural elements is a strong limit to apply directly the methodology in industry.
The second algorithm relies on a bi-level formulation of the mixed categorical problem. The master full categorical problem consists of minimizing a first order like approximation of the slave problem with respect to the categorical design variables. The method offers a quasi-linear scaling of the computational cost with respect to the number of elements and categorical values.
Finally, in the third approach the optimization problem is formulated as a bi-level mixed integer non-linear program with relaxable design variables. It relies on efficiently computed linearizations of the slave problem optimum. Numerical tests include an optimization case with more than one hundred structural elements. Also, the computational cost scaling is quasi-independent from the number of available categorical values per element.