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Reformulation and decomposition of integer programs

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  • VANDERBECK , François
  • WOLSEY , Laurence

    () (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.

Suggested Citation

  • VANDERBECK , François & WOLSEY , Laurence, 2009. "Reformulation and decomposition of integer programs," CORE Discussion Papers 2009016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2009016
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    File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2009_16.pdf
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    Keywords

    Integer program; Lagrangean relaxation; column generation; branch-and-price; extended formulation; Benders' algorithm;

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