Path based column generation approach for the Steiner tree problem

Abstract

In this thesis, we solve the Steiner tree problem in graph using column generation technique. This algorithm is based on integer programming formulation for directed graph and based on path variables which can be generated in polynomial time. We improve the performance of the algorithm by adopting row-generation technique and stabilized column generation technique. We compare the performance of the algorithm with the branch-and-cut algorithm based on cut set constraint. The LP relaxations of our formulation and the cut-set based formulation provide the same lower bound on the optimal value. We compare the performance of both approaches in computation time, the number of generated cuts and columns. We use preprocessing for large test problems to reduce the problem size considerably. Test results on SteinLib benchmark problems are reported.