(A) branch-and-price algorithm for the Steiner tree packing problem

Abstract

In this thesis we consider the Steiner tree packing problem (STP). For a graph G = (V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets (nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. This problem arises in routing phase of VLSI design. We discuss several variants of practically relevant routing problems and give a short survey on the underlying technologies and design rules. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. To solve the linear programming relaxation that has exponentially many variables, we develop an efficient column generation procedure. Moreover, we devise a new primal-heuristic based on LP solution. Using the results, we develop a branch-and-price algorithm with column generation where a complete branching rule has been adopted. We test our algorithm on some standard test instances and compare the performances with the results using cutting plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grotschel et al. and can be used to solve practically sized problems.