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Valid Linear Programming Bounds for Exact Mixed-Integer Programming

Please always quote using this URN: urn:nbn:de:0297-zib-12332
  • Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound. Solutions are repaired by performing a projection and a shift to ensure all constraints are satisfied; bound computations are accelerated by reusing structural information through the branch-and-bound tree. We demonstrate this method to be widely applicable and faster than solving a sequence of exact LPs. Several variations of the algorithm are described and computationally evaluated in an exact branch-and-bound algorithm within the mixed-integer programming framework SCIP.

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Author:Daniel SteffyORCiD, Kati Wolter
Document Type:ZIB-Report
Tag:branch-and-bound; exact computation; linear programming bounds; mixed integer programming
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K05 Mathematical programming methods [See also 90Cxx]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C11 Mixed integer programming
Date of first Publication:2011/03/10
Series (Serial Number):ZIB-Report (11-08)
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