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Presolving in linear programming

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Abstract

Most modern linear programming solvers analyze the LP problem before submitting it to optimization. Some examples are the solvers WHIZARD (Tomlin and Welch, 1983), OB1 (Lustig et al., 1994), OSL (Forrest and Tomlin, 1992), Sciconic (1990) and CPLEX (Bixby, 1994). The purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible.

In this paper we present a comprehensive survey of presolve methods. Moreover, we discuss the restoration procedure in detail, i.e., the procedure that undoes the presolve.

Computational results on the NETLIB problems (Gay, 1985) are reported to illustrate the efficiency of the presolve methods.

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Authors and Affiliations

  1. Department of Management, Odense University, Campusvej 55, DK-5230, Odense M, Denmark

    Erling D. Andersen

  2. Department of Mathematics and Computer Sciences, Odense University, Campusvej 55, DK-5230, Odense M, Denmark

    Knud D. Andersen

Authors
  1. Erling D. Andersen
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  2. Knud D. Andersen
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This author was supported by a Danish SNF Research studentship.

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Andersen, E.D., Andersen, K.D. Presolving in linear programming. Mathematical Programming 71, 221–245 (1995). https://doi.org/10.1007/BF01586000

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  • DOI: https://doi.org/10.1007/BF01586000

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