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

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Manufacturing Integrated Design

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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).

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Authors and Affiliations

  1. Research Group Discrete Optimization (DOpt), Technische Universität Darmstadt, Darmstadt, Germany

    H. Lüthen & M. Pfetsch

  2. Institute for Product Development and Machine Elements (pmd), Technische Universität Darmstadt, Darmstadt, Germany

    S. Gramlich, I. Mattmann, M. Roos & C. Wagner

  3. Research Group Nonlinear Optimization (NOpt), Technische Universität Darmstadt, Darmstadt, Germany

    B. Horn, S. Ulbrich & A. Walter

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  1. H. Lüthen
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  2. S. Gramlich
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  4. I. Mattmann
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  7. S. Ulbrich
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Correspondence to H. Lüthen .

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Editors and Affiliations

  1. Institute for Production Engineering and Forming Machines (PtU), Technische Universität Darmstadt, Darmstadt, Germany

    Peter Groche

  2. Materials Science Department, Physical Metallurgy Division , Technische Universität Darmstadt, Darmstadt, Germany

    Enrico Bruder

  3. Institute for Product Development and Machine Elements (pmd), Technische Universität Darmstadt, Darmstadt, Germany

    Sebastian Gramlich

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Lüthen, H. et al. (2017). Finding the Best: Mathematical Optimization Based on Product and Process Requirements. In: Groche, P., Bruder, E., Gramlich, S. (eds) Manufacturing Integrated Design. Springer, Cham. https://doi.org/10.1007/978-3-319-52377-4_5

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