Distributed optimization based column generation

Abstract

The simplex based column generation is a well-known method for solving large-sized mathematical programming problems. However, it has a major drawback that it often shows slow convergence. Recently, many acceleration schemes for column generation have been proposed in response to the aforementioned weakness. The stabilized column generation (Du Merle, et al., 1999) and Chebyshev center based column generation (Lee and Park, 2011) are representative accelerations. Both can result in faster convergence, on the other hand, they largely depend on the problems. In particular, the algorithms do not work well for problems where the master problem is relatively hard to solve. This research proposes a column generation technique based on distributed optimization and develops an efficient algorithm using the latest technologies including parallelism. Numerical comparisons are conducted for two applications: bin-packing problem and generalized assignment problem. Computational experiments show that our algorithm outperforms the existing accelerated column generation algorithms in large size problems.