Cooperation and Competition in Multi-Disciplinary Approaches

The seminar aims at presenting an algorithmic approach to PDE-constrained multidisciplinary shape optimization problems.
In the first part, a number of optimum-shape design in compressible aerodynamics will be briefly presented. The classical approaches to treat multiobjective optimization problems, their merits and weaknesses will be reviewed. Then, the difficult exercise of an aircraft wing-shape optimization w.r.t. criteria originating from both aerodynamics and structural design will be treated by an approach in which aerodynamics is considered as a preponderant and/or fragile discipline. This prototype problem will serve to support a theoretical construction, valid for disciplines in competition based on a Nash game relying on a split of territory in adequate supplementary subspaces.

In the second part, a result on convex analysis will serve to define a complementary cooperative-optimization phase. As a result, it is proposed to rely on competitive Nash game formulations only at completion of the cooperative phase, when the set of Pareto-stationary points has been reached.