Bc - Opt : a Branch-and-cut Code for Mixed Integer Programs

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 gub 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 Optimisation 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. ∗This work has been supported in part by the Esprit projects 8755 (PAMIPS) and 20118(MEMIPS). †Cécile Cordier, CORE, Université Catholique de Louvain. ‡Hugues Marchand, CORE, Université Catholique de Louvain. Supported in part by a doctoral fellowship from Collège Interuniversitaire pour les Sciences du Management (CIM). §Richard Laundy, Dash Associates, Leamington Spa. ¶Laurence A. Wolsey, CORE and INMA, Université Catholique de Louvain.