Combining a Memetic Algorithm with Integer Programming to Solve the Prize-Collecting Steiner Tree Problem

The prize-collecting Steiner tree problem on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. For this well-known problem we develop a new algorithmic framework consisting of three main parts: (1) An extensive preprocessing phase reduces the given graph without changing the structure of the optimal solution. (2) The central part of our approach is a memetic algorithm (MA) based on a steady-state evolutionary algorithm and an exact subroutine for the problem on trees. (3) The solution population of the memetic algorithm provides an excellent starting point for post-optimization by solving a relaxation of an integer linear programming (ILP) model constructed from a model for finding the minimum Steiner arborescence in a directed graph. Extensive experiments on benchmark instances from the literature show that our combination of an MA with IL...

• Type: Conference
• Year: 2004
• Where: GECCO
• Authors: Gunnar W. Klau, Ivana Ljubic, Andreas Moser, Petra Mutzel, Philipp Neuner, Ulrich Pferschy, Günther R. Raidl, René Weiskircher
• Keywords: GECCO 2004, Memetic Algorithm, Steady-state Evolutionary Algorithm, Steiner Tree Problem