bc-opt: A branch-and-cut code for mixed integer programs

bc-opt: A branch-and-cut code for mixed integer programs

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Article ID: iaor20003725
Country: Germany
Volume: 50
Issue: 2
Start Page Number: 335
End Page Number: 353
Publication Date: Jan 1999
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: , , ,
Keywords: programming: integer
Abstract:

A branch-and-cut mixed integer programming system, called bc-opt, is described, incorporating most of the valid inequalities that have been used or suggested for such systems, namely lifted 0–1 knapsack inequalities, 0–1 greatest upper bound knapsack and integer knapsack inequalities, flowcover and continuous knapsack inequalities, path inequalities for fixed charge network flow structure and Gomory mixed integer cuts. The principal development is a set of interface routines allowing these cut routines to generate cuts for new subsets or aggregations of constraints. The system is built using the XPRESS Optimization Subroutine Library (XOSL) which includes a cut manager that handles the tree and cut management, so that the user only essentially needs to develop the cut separation routines. Results for the MIPLIB3.0 library are presented – 37 of the instances are solved very easily, optimal or near optimal solution are produced for 18 other instances, and of the 4 remaining instances, 3 have 0, +1, –1 matrices for which bc-opt contains no special features.

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