On the optimal decomposition of high-dimensional solution spaces of complex systems

[+] Author and Article Information
Stefan Erschen

BMW Group Research and Innovation Center, Vehicle Dynamics, Preliminary Design, Knorrstrasse 147, 80788 Munich, Germany

Fabian Duddeck

Technical University of Munich, Associate Professorship of Computational Mechanics, Arcisstr. 21, 80333 Munich, Germany

Matthias Gerdts

Universität der Bundeswehr München, Institut für Mathematik and Rechneranwendung, Werner-Heisenberg-Weg 39, 85577 Neubiberg/Munich, Germany

Markus Zimmermann

BMW Group Research and Innovation Center, Vehicle Dynamics, Preliminary Design, Knorrstrasse 147, 80788 Munich, Germany

1Corresponding author.

ASME doi:10.1115/1.4037485 History: Received February 08, 2017; Revised July 09, 2017


In the early development phase of complex technical systems, uncertainties caused by unknown design restrictions must be considered. In order to avoid premature design decisions, sets of good designs are sought rather than one (possibly optimal) design that may later turn out to be infeasible. A set of good designs is called a solution space and serves as target region for design variables, including those that quantify properties of components or subsystems. Algorithms that approximate solution spaces as high-dimensional boxes are available, in which edges represent permissible intervals for single design variables. The box size is maximized to provide large target regions and facilitate design work. As a result of geometrical mismatch, however, boxes typically capture only a small portion of the complete solution space. To reduce this loss of solution space, this paper presents a new approach that optimizes a set of permissible two-dimensional regions for pairs of design variables, so- called 2D-spaces. Each 2D-space is confined by polygons. The Cartesian product of all 2D-spaces forms the solution space for all design variables, wherein all designs are good. An optimization problem is formulated that maximizes the size of the solution space, and is solved using an interior-point algorithm. The approach is applicable to arbitrary systems with performance measures that can be expressed or approximated as linear function of their design variables. Its effectiveness is demonstrated in a design problem of vehicle chassis development.

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