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Branch-and-Bound Algorithm

Statistical and Numerical Computing

  1. David Whitaker

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vab031

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Whitaker, D. 2006. Branch-and-Bound Algorithm. Encyclopedia of Environmetrics. 1.

Author Information

  1. University of Waikato, New Zealand

Publication History

  1. Published Online: 15 SEP 2006

Abstract

The branch and bound algorithm is mostly used to solve global optimization problems with integer variables (unknowns), linear objective and linear constraints (integer linear programming (LP) problems). The recent increase in the speed of computation on desktop computers has meant that the algorithm can be applied to large problems with several hundred integer variables, which only a decade ago were intractable to any true optimization algorithms. Although a number of algorithms have been proposed for the integer LP problem, the branch and bound technique is used in almost all of the available computer software. This technique has proven to be reasonably efficient for practical problems because it has the embedded advantage of solving continuous linear programmes as subproblems. Furthermore, in some situations the embedded subproblem is a special case of a LP problem (such as assignment and transportation problems), which have more efficient algorithms than the general LP algorithm. Branch and bound methods are also easy to implement on parallel processors. An increasing number of applications are currently forthcoming in this area.