Reduce-and-Split Cuts: Improving the Performance of Mixed Integer Gomory Cuts

Abstract

Mixed integer Gomory cuts have become an integral part of state-of-the-art software for solving mixed integer linear programming problems. Therefore, improvements in the performance of these cutting planes can be of great practical value. In this paper we present a simple and fast heuristic for improving the coefficients on the continuous variables in the mixed integer Gomory cuts. This is motivated by the fact that, in a mixed integer Gomory cut, the coefficient of an integer variable lies between 0 and 1, whereas for a continuous variable, there is no upper bound. The heuristic tries to reduce the coefficients of the continuous variables. We call the resulting cuts reduce-and-split cuts. We found that, on several test problems, reduce-and-split cuts can substantially enhance the performance of a branch-and-bound algorithm.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2005
Accession Number
AD1021103

Entities

People

  • Gérard Cornuéjols
  • Kent Andersen
  • Yanjun Li

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computer Programming
  • Electric Power Production
  • Engineering
  • Equations
  • Evolutionary Algorithms
  • Generators
  • Inequalities
  • Integer Programming
  • Iterations
  • Linear Programming
  • Management Planning And Control
  • Scheduling (Production)
  • Systems Engineering
  • Trees (Data Structures)

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Electrical Engineering
  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design