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A SCIP Constraint Handler for Piecewise Linear Functions

Please always quote using this URN: urn:nbn:de:0297-zib-49112
  • In this thesis, we study different modelling approaches for piecewise linear functions, in particular with respect to their occurrence in mathematical optimization problems. Reviewing the quality of the classical MIP models from the literature, we will see that all but the disaggregated convex combination method yield both sharp and locally ideal formulations. In the main part, we will present an alternative approach for modelling constraints involving piecewise linear functions, based on ideas of constraint programming and using a convex hull relaxation. For the purpose of developing a branch-and-bound procedure specifically adapted to our constraint formulation within SCIP, all required components such as propagation, branching and separation will be discussed. In particular, we will focus on adapting well-known MIP strategies for the selection of branching variables to our type of piecewise linear constraints.

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Author:Tom Walther
Document Type:Master's Thesis
Granting Institution:Technische Universität Berlin
Advisor:Benjamin Hiller
Year of first publication:2014
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