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Exponential irreducible neighborhoods for combinatorial optimization problems

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  • Robert T. Firla
  • Bianca Spille
  • Robert Weismantel

Abstract

This paper deals with irreducible augmentation vectors associated with three combinatorial optimization problems: the TSP, the ATSP, and the SOP. We study families of irreducible vectors of exponential size, derived from alternating cycles, where optimizing a linear function over each of these families can be done in polynomial time. A family of irreducible vectors induces an irreducible neighborhood; an algorithm for optimizing over this family is known as a local search heuristic. Irreducible neighborhoods do not only serve as a tool to improve feasible solutions, but do play an important role in an exact primal algorithm; such families are the primal counterpart of a families of facet inducing inequalities. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Robert T. Firla & Bianca Spille & Robert Weismantel, 2002. "Exponential irreducible neighborhoods for combinatorial optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(1), pages 29-44, August.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:1:p:29-44
    DOI: 10.1007/s001860200198
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