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SUMMARY:Keynote lecture: The phi-function technique for packing problems: 
 mathematical modelling\, optimization and applications - Tetyana Romanova 
 (University of Leeds)
DTSTART:20230822T123000Z
DTEND:20230822T133000Z
UID:TALK204328@talks.cam.ac.uk
DESCRIPTION:Abstract&nbsp\;\nPacking problems are a class of problems that
  seek to optimise the arrangement of objects according to a given objectiv
 e while respecting a set of geometric constraints. These problems have man
 y and diverse applications. Packing problems are NP-hard\, and as a result
 \, solution methodologies generally employ heuristics.&nbsp\;The phi-funct
 ion technique is a powerful tool to help solve packing problems by providi
 ng an analytical description of the placement constraints. It deals with a
 rbitrary shaped 2D and 3D objects\, which can be continuously rotated and 
 translated. Using phi-functions reduces the packing problem to a Nonlinear
  Programming or Mixed Integer Nonlinear Programming model.&nbsp\;\nThe pap
 er will introduce the definition of a continuous and everywhere defined ph
 i-function as well as its basic features. It will explain the concept of q
 uasi phi-functions\, which generalizes the concept of phi-functions to inc
 lude auxiliary variables. This modification allows for the efficient model
 ling of relationships between objects that were not readily available with
  phi-functions. Mathematical models\, solution strategies and computationa
 l results are provided for some packing problems that arise in different a
 pplications\, in particular\, in material sciences and additive manufactur
 ing. The discussion will identify some future research areas.&nbsp\;\nAuth
 ors: &nbsp\;\nProf. Julia Bennell1 &nbsp\;\n1University of Leeds\, Leeds U
 niversity Business School &nbsp\;&nbsp\;\nJ.Bennell@leeds.ac.uk&nbsp\;\nPr
 of. Tetyana Romanova (speaker) 1\,2&nbsp\;\n1University of Leeds\, Leeds U
 niversity Business School &nbsp\;&nbsp\;\n&nbsp\;2Institute of Mechanical 
 Engineering Problems of the National Academy of Sciences of Ukraine&nbsp\;
 \nT.Romanova@leeds.ac.uk&nbsp\;
LOCATION:External
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