Transforming Mathematical Models Using Declarative Reformulation Rules

  • Antonio Frangioni
  • Luis Perez Sanchez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6683)

Abstract

Reformulation is one of the most useful and widespread activities in mathematical modeling, in that finding a “good” formulation is a fundamental step in being able so solve a given problem. Currently, this is almost exclusively a human activity, with next to no support from modeling and solution tools. In this paper we show how the reformulation system defined in [13] allows to automatize the task of exploring the formulation space of a problem, using a specific example (the Hyperplane Clustering Problem). This nonlinear problem admits a large number of both linear and nonlinear formulations, which can all be generated by defining a relatively small set of general Atomic Reformulation Rules (ARR). These rules are not problem-specific, and could be used to reformulate many other problems, thus showing that a general-purpose reformulation system based on the ideas developed in [13] could be feasible.

Keywords

Column Generation Nonlinear Formulation Reformulation System Track Structure Discrete Apply Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Antonio Frangioni
    • 1
  • Luis Perez Sanchez
    • 2
  1. 1.Dipartimento di InformaticaUniversità di Pisa, Polo Universitario della SpeziaLa SpeziaItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaPisaItaly

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