A column generation / simplicial decomposition algorithm

Abstract

The solution strategy known as the column generation principle—and its dual counterpart, constraint generation—is one of the standard tools of mathematical programming. Since the pioneering work on the maximum multi-commodity network flow problem by Ford and Fulkerson [FoF58, FoF62] in the late 50’s, column generation methods have been developed and applied in a variety of contexts. With no doubt, the most famous column generation method is the Dantzig-Wolfe decomposition method for specially structured linear programs ([DaW60, DaW61]), in which the column generation is based on the pricingout mechanism of the simplex method. [Another famous column generation technique is the one for cutting stock problems, where the column generation is based on the solution of knapsack problems ([GiG61, GiG63, GiG65]).]