Hybrid genetic algorithm within branch-and-cut for the minimum graph bisection problem

Authors:
Michael Armbruster;Marzena Fügenschuh;Christoph Helmberg;Nikolay Jetchev;Alexander Martin
Affiliations:
Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany;Department of Mathematics, Darmstadt University of Technology, Darmstadt, Germany;Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany;Department of Mathematics, Darmstadt University of Technology, Darmstadt, Germany;Department of Mathematics, Darmstadt University of Technology, Darmstadt, Germany
Venue:
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
Year:
2006

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Abstract

We develop a primal heuristic based on a genetic algorithm for the minimum graph bisection problem and incorporate it in a branch-and-cut framework. The problem concerns partitioning the nodes of a weighted graph into two subsets such that the total weight of each set is within some lower and upper bounds. The objective is to minimize the total cost of the edges between both subsets of the partition. We formulate the problem as an integer program. In the genetic algorithm the LP-relaxation of the IP-formulation is exploited. We present several ways of using LP information and demonstrate the computational success.