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# Finding the Best: Mathematical Optimization Based on Product and Process Requirements

## Abstract

The challenge of finding the best solution for a given problem plays a central role in many fields and disciplines. In mathematics, best solutions can be found by formulating and solving optimization problems. An optimization problem consists of an objective function, optimization variables, and optimization constraints, all of which define the solution space. Finding the optimal solution within this space means minimizing or maximizing the objective function by finding the optimal variables of the solution. Problems, such as geometry optimization of profiles (Hess and Ulbrich 2012), process control for stringer sheet forming (Bäcker et al. 2015) and optimization of the production sequence for branched sheet metal products (Günther and Martin 2006) are solved using mathematical optimization methods (Sects. 5.2 and 5.3). A variety of mathematical optimization methods is comprised within the field of engineering design optimization (EDO) (Roy et al. 2008).

Item Type: Book Section 2017 Groche, Peter and Bruder, Enrico and Gramlich, Sebastian Lüthen, Hendrik and Gramlich, Sebastian and Horn, Benjamin M. and Mattmann, Ilyas and Pfetsch, Marc E. and Roos, Michael and Ulbrich, Stefan and Wagner, Christian and Walter, Anna Finding the Best: Mathematical Optimization Based on Product and Process Requirements English The challenge of finding the best solution for a given problem plays a central role in many fields and disciplines. In mathematics, best solutions can be found by formulating and solving optimization problems. An optimization problem consists of an objective function, optimization variables, and optimization constraints, all of which define the solution space. Finding the optimal solution within this space means minimizing or maximizing the objective function by finding the optimal variables of the solution. Problems, such as geometry optimization of profiles (Hess and Ulbrich 2012), process control for stringer sheet forming (Bäcker et al. 2015) and optimization of the production sequence for branched sheet metal products (Günther and Martin 2006) are solved using mathematical optimization methods (Sects. 5.2 and 5.3). A variety of mathematical optimization methods is comprised within the field of engineering design optimization (EDO) (Roy et al. 2008). Manufacturing Integrated Design Cham Springer 978-3-319-52376-7 requirements, product properties, integration manufacturing-initiated solutions, shape optimization, optimization of deep drawing processes, partitioning optimization of unrollings 11 Department of Materials and Earth Sciences11 Department of Materials and Earth Sciences > Material Science11 Department of Materials and Earth Sciences > Material Science > Physical Metallurgy16 Department of Mechanical Engineering16 Department of Mechanical Engineering > Institute for Product Development and Machine Elements (pmd) 26 Jun 2017 05:45 https://link.springer.com/chapter/10.1007/978-3-319-52377-4_... BibTeXJSONHTML CitationDublin CoreASCII CitationSimple MetadataEndNoteRDF+XMLMultiline CSVAtomT2T_XMLMODSEP3 XMLReference Manager TUfind oder in Google
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