Chebyshev center based column generation

The classical column generation approach often shows a very slow convergence. Many different acceleration techniques have been proposed recently to improve the convergence. Here, we briefly survey these methods and propose a novel algorithm based on the Chebyshev center of the dual polyhedron. The Chebyshev center can be obtained by solving a linear program; consequently, the proposed method can be applied with small modifications on the classical column generation procedure. We also show that the performance of our algorithm can be enhanced by introducing proximity parameters which enable the position of the Chebyshev center to be adjusted. Numerical experiments are conducted on the binpacking, vehicle routing problem with time windows, and the generalized assignment problem. The computational results of these experiments demonstrate the effectiveness of our proposed method.

► We propose a new column generation approach based on the Chebyshev center. ► The performance can be improved by a proximity adjusting scheme. ► Three well-known problems were used for computational experiments. ► The use of the Chebyshev center can accelerate the column generation.