Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm

• John E. Mitchell
• Brian Borchers
Chapter
Part of the Applied Optimization book series (APOP, volume 33)

Abstract

We describe a cutting plane algorithm for solving linear ordering problems. The algorithm uses a primal-dual interior point method to solve the first few relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We solve integer programming problems with as many as 31125 binary variables. Computational results show that the combined approach can dramatically outperform the other two methods.

Keywords

Interior Point Simplex Method Interior Point Method Cutting Plane Current Relaxation
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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