.png){kind=icon}
.png){kind=icon}
Return
Fixing variables and generating classical cutting planes when using an interior point branch and cut method to solve integer programming problems
.png){kind=icon}
PRE
AI
DOI：10.1016/0377-2217(95)00373-8.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Branch and cut methods for integer programming problems solve a sequence of linear programming problems. Traditionally, these linear programming relaxations have been solved using the simplex method. The reduced costs available at the optimal solution to a relaxation may make it possible to fix variables at zero or one. If the solution to a relaxation is fractional, additional constraints can be generated which cut off the solution to the relaxation, but do not cut off any feasible integer points. Gomory cutting planes and other classes of cutting planes are generated from the final tableau. In this paper, we consider using an interior point method to solve the linear programming relaxations. We show that it is still possible to generate Gomory cuts and other cuts without having to recreate a tableau, and we also show how variables can be fixed without using the optimal reduced costs. The procedures we develop do not require that the current relaxation be solved to optimality; this is useful for an interior point method because early termination of the current relaxation results in an improved starting point for the next relaxation.
Keywords:
integer programming
interior point methods
cutting
linear programming
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
6
Papers:
2.2W
Citations:
6.4W
Organization
No organization information available