Invited Session Wed.2.MA 415

Wednesday, 13:15 - 14:45 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Optimization applications in industry IV


Chair: Dietmar Hömberg



Wednesday, 13:15 - 13:40 h, Room: MA 415, Talk 1

Hans Josef Pesch
Direct versus indirect solution methods in real-life applications: Load changes of fuel cells

Coauthors: Kurt Chudej, Armin Rund, Kati Sternberg


When analyzing mathematical models for complex dynamical systems, their analysis and numerical simulation is often only a first step. Thereafter, one often wishes to complete these investigations by an optimization step to exploit inherent degrees of freedom. This generally leads to optimization problems of extremely high complexity if the underlying system is described by time dependent partial differential equations (PDEs) or, more generally, by a system of partial differential algebraic equations (PDAEs).
The driving example of this talk is concerned with the optimal control of a fuel cell system. The underlying mathematical model constitutes a high dimensional PDAE system describing the gas transport and the electro-chemical reactions within the fuel cells.
In this talk we will particularly discuss the pros and cons of direct versus indirect methods, resp. first discretize then optimize versus first optimize then discretize when applying these approaches
on real-life problems of extremely high complexity.



Wednesday, 13:45 - 14:10 h, Room: MA 415, Talk 2

Chantal Landry
Modeling of the optimal trajectory of industrial robots in the presence of obstacles

Coauthors: Matthias Gerdts, René Henrion, Dietmar Hömberg


In automotive industry robots work simultaneously on the same workpiece. They must accomplish their task as fast as possible and without colliding with surrounding obstacles. We model the search of the fastest collision-free trajectory of each robot as a time optimal control problem. The collision avoidance is based on linear programming and expressed as state constraints. The resulting optimal control problem is solved by a sequential quadratic programming method. In order to speed up the resolution an active set strategy based on back-face culling is added. Numerical examples illustrate the efficiency of this strategy.



Wednesday, 14:15 - 14:40 h, Room: MA 415, Talk 3

Jean-Antoine Désidéri
Multiple gradient descent algorithm (MGDA) for multi-objective optimization with application to compressible aerodynamics

Coauthors: Jean-Antoine Désidéri, Régis Duvigneau, Adrien Zerbinati


We focus on the development of numerical algorithms for multi-objective optimization, with application to physical systems governed by PDE’s. Indeed, concurrent engineering makes multi-objective optimization a particularly acute question in the design of complex systems. In several mature disciplines, modern simulation codes often provide along with the evaluation of the performance, or functional criterion, the calculation of the functional gradient. Assuming the gradients of different criteria are at hand, we propose and analyze systematic constructions of a descent direction common to all criteria. Based on this, MGDA generalizes to multi-objective optimization the classical steepest-descent method. We prove that it converges to Pareto stationary points, and demonstrate the efficiency of the method in several problems: aircraft wing design, shape optimization of an automobile cooling system duct.


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