Subgradient Optimization Prior to Column Generation --- A Means for Predicting Optimal Columns

Abstract

We propose a two-phase combination of two optimization techniques, Lagrangian relaxation and column generation, with the aim of overcoming their respective drawbacks. In a prediction phase, subgradient optimization is used and the Lagrangian relaxed solutions found are used to initialize a master problem. In a solution phase, column generation is performed. We provide a validation of this two-phase method through an asymptotic result for the prediction phase and give guidelines for its truncated usage.The two-phase method is assessed on a multicommodity network flow problem, for which it performs significantly better than a pure column generation method. We conclude that the subgradient optimization prediction phase can accelerate a column generation method considerably.