ISBN 978-3-8439-4621-6

978-3-8439-4621-6, Reihe Mathematik

Lisa Kusch
Robustness Measures and Optimization Strategies for Multi-Objective Robust Design

258 Seiten, Dissertation Technische Universität Kaiserslautern (2020), Hardcover, A5

Zusammenfassung / Abstract

A significant step to engineering design is to consider uncertainties and to find robust optimal designs. Furthermore, it is often of interest to optimize for different conflicting objective functions describing the quality of a design. In this context, generating methods for solving multi-objective optimization problems seek to find a representative set of solutions fulfilling the concept of Pareto optimality. When multiple uncertain objective functions are involved, it is essential to define suitable measures for robustness that account for a combined effect of uncertainties in objective space. Many tasks in engineering design include the solution of a partial differential equation that can be computationally expensive. Thus, it is of interest to use efficient optimization strategies. This research presents measures for robustness and optimization strategies in a multi-objective context.

This work introduces new ideas for robustness measures in the context of multi-objective robust design. Losses and expected losses based on distances in objective space are used to describe robustness. Different formulations based on expected losses are proposed for finding a set of robust optimal solutions.

Furthermore, suitable optimization strategies for solving the resulting multi-objective robust design problem are formulated and analyzed. The multi-objective optimization problem is solved with a constraint-based approach with a hybrid optimization strategy. The hybrid method combines a global search method on a surrogate model with adjoint-based optimization methods. In the context of optimization with an underlying partial differential equation, a one-shot approach is extended to handle additional constraints.

The developed concepts for multi-objective robust design and the proposed optimization strategies are applied to an aerodynamic shape optimization problem under the consideration of uncertain operational conditions and geometrical uncertainties.