Using Branch-and-Price to Find High Quality Solutions Quickly

When integer programming (IP) models are used in operational situations there is a need to consider the tradeoff between the conflicting goals of solution quality and solution time, since for many problems solving realistic-size instances to a tight tolerance is still beyond the capability of state-of-the-art solvers. However, by appropriately defining small instances, good primal solutions frequently can be found quickly. This approach is taken, for example, within LP-based branch-and-bound algorithms using techniques such as local branching (Fischetti and Lodi (2003)) and RINS (Danna et al. (2005)). These techniques use information from the LP solution and incumbent solution to define a small IP, which is then optimized. These techniques can be applied to any integer program and are available in commercial solvers such as CPLEX. Another approach to defining small instances is to use problem structure. Hewitt et al. (2009) present an IP-based local search algorithm for the Multicommodity Fixed Charge Network Flow Problem (MCFCNF) where small IPs are chosen according to the attributes of previous solutions, such as the arcs used by various commodities. Combining exact and heuristic search techniques by solving small IPs has received quite a lot of attention recently, see, for example, De Franceschi et al. (2006), Schmid et al. (2008), Archetti et al. (2008), and Savelsbergh and Song (2008).