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Branch-And-Price: Column Generation for Solving Huge Integer Programs

Authors:

Cynthia Barnhart,

Ellis L. Johnson,

George L. Nemhauser,

Martin W. P. Savelsbergh,

Pamela H. VanceAuthors Info & Claims

Operations Research, Volume 46, Issue 3

Pages 316 - 329

https://doi.org/10.1287/opre.46.3.316

Published: 01 March 1998 Publication History

Abstract

We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-and-bound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.

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Branch-And-Price: Column Generation for Solving Huge Integer Programs
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Mixed discrete-continuous optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Mixed discrete-continuous optimization

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Published In

Operations Research Volume 46, Issue 3

March 1998

137 pages

ISSN:0030-364X

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Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 March 1998

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Numerical Experience with Lower Bounds for MIQP Branch-And-Bound

Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming

Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problem

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