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On 31st January 2020, Pierre-Jean Barjhoux defended his thesis. Awarded by ISAE-SUPAERO, his work was realized both at Institut Clément Ader laboratory and IRT Saint Exupéry, under the supervision of Aéronautique-Astronautique doctoral school.
The high quality and the relevance of Pierre-Jean thesis contributed to get significant results as a part of MDA-MDO project.

Nowadays in the aircraft industry, structural optimization problems can be really complex and combine changes in choices of materials, stiffeners, or sizes/types of elements.

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.

Pierre DUYSINX	Rapporter	Professor at University of Liège
Michael KOKKOLARAS	Rapporter	Associate Professor at McGill University
Marco MONTEMURRO	Examiner	Associate Professor at ENSAM Bordeaux
Sonia CAFIERI	Examiner	Professor at ENAC
Joseph MORLIER	Thesis director	Professor at ISAE-SUPAERO
Youssef DIOUANE	Co-thesis director	Associate Professor at ISAE-SUPAERO
Dimitri BETTEBGHOR	Invited	Researcher at ONERA
Stéphane GRIHON	Invited	Expert at Airbus

• Mixed variable structural optimization: toward an efficient hybrid algorithm – P-J. Barjhoux, Y. Diouane, S. Grihon, D. Bettebghor and J. Morlier –  WCSMO 2017 (12th World Congress of Structural and Multidisciplinary Optimisation), Braunschweig, Germany – DOI
• A bilevel methodology for solving a structural optimization problem with both continuous and categorical variables – P-J. Barjhoux, Y. Diouane, S. Grihon, D. Bettebghor and J. Morlier – AIAA – ISSMO 2018 (19th Multidisciplinary Analysis and Optimization Conference), Atlanta, USA – DOI
• GEMS: a Python library for automation of multidisciplinary design optimization process generation – F. Gallard, C. Vanaret, D. Guenot, V. Gachelin, R. Lafage, B. Pauwels, P-J. Barjhoux and A. Gazaix – AIAA – ASCE/AHS/ASC Structures, Structural Dynamics, & Materials Conference, SciTech Forum – Kissimmee, USA – 2018 – DOI
• GEMS, a Generic Engine for MDO Scenarios : key features in application – F. Gallard, P-J. Barjhoux, R. Olivanti and A. Gazaix – AIAA 2019 (Aviation and Aeronautics Forum and Exposition), Dallas, USA – DOI