A Piecewise Linear Dual Procedure in Mixed Integer Programming

  • István Maros
Part of the Applied Optimization book series (APOP, volume 13)

Abstract

Most solution methods for Mixed Integer Programming (MIP) problems require repeated solution of continuous linear programming (LP) problems. It is typical that subsequent LP problems differ just slightly. In most cases it is practically the right-hand-side that changes. For such a situation the dual simplex algorithm (DSA) appears to be the best solution method.

The LP relaxation of a MIP problem contains many bounded variables. This necessitates such an implementation of the DSA where variables of arbitrary type are allowed. The paper presents an algorithm called BSD for the efficient handling of bounded variables. This leads to a “mini” nonlinear optimization in each step of the DSA. Interestingly, this technique enables several cheap iterations per selection making the whole algorithm very attractive. The implementational implications and some computational experiences on large scale MIP problems are also reported. BSD is included in FortMP optimization system of Brunel University.

Keywords

Linear Programming Problem Mixed Integer Programming Linear Programming Relaxation Dual Objective Dual Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • István Maros
    • 1
    • 2
  1. 1.Imperial CollegeLondonUK
  2. 2.Computer and Automation InstituteBudapestHungary

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