The Impact of Filtering in a Branch-and-Cut Algorithm for Multicommodity Capacitated Fixed Charge Network Design

In this paper, we present a state-of-the-art branch-and-cut (B&C) algorithm for the multicommodity capacitated fixed charge network design problem (MCND). This algorithm combines bounding and branching procedures inspired by the latest developments in mixed-integer programming (MIP) software tools. Several filtering methods that exploit the structure of the MCND are also developed and embedded within the B&C algorithm. These filtering methods apply inference techniques to forbid combinations of values for some variables. This can take the form of adding cuts, reducing the domains of the variables, or fixing the values of the variables. Our experiments on a large set of randomly generated instances show that an appropriate selection of filtering techniques allows the B&C algorithm to perform significantly better than the variant of the algorithm without filtering. These experiments also show that the B&C algorithm, with or without filtering, is competitive with a state-of-the-art MIP solver.