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

  • H. Lüthen
  • S. Gramlich
  • B. Horn
  • I. Mattmann
  • M. Pfetsch
  • M. Roos
  • S. Ulbrich
  • C. Wagner
  • A. Walter
Chapter

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).

Keywords

Requirements Product properties Integration Manufacturing-initiated solutions Shape optimization Optimization of deep drawing processes Partitioning Optimization of unrollings 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • H. Lüthen
    • 1
  • S. Gramlich
    • 2
  • B. Horn
    • 3
  • I. Mattmann
    • 2
  • M. Pfetsch
    • 1
  • M. Roos
    • 2
  • S. Ulbrich
    • 3
  • C. Wagner
    • 2
  • A. Walter
    • 3
  1. 1.Research Group Discrete Optimization (DOpt), Technische Universität DarmstadtDarmstadtGermany
  2. 2.Institute for Product Development and Machine Elements (pmd), Technische Universität DarmstadtDarmstadtGermany
  3. 3.Research Group Nonlinear Optimization (NOpt), Technische Universität DarmstadtDarmstadtGermany

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