Branch‐and‐Price Guided Search for Integer Programs with an Application to the Multicommodity Fixed‐Charge Network Flow Problem

We develop an exact algorithm for integer programs that uses restrictions of the problem to produce high‐quality solutions quickly. Column generation is used both for generating these problem restrictions and for producing bounds on the value of the optimal solution. The performance of the algorithm is greatly enhanced by using structure, such as arises in network flow type applications, to help define the restrictions that are solved. In addition, local search around the current best solution is incorporated to enhance overall performance. The approach is parallelized and computational experiments on a classical problem in network design demonstrate its efficacy.