Graph Bisection Optimization: A Comparison Between GA, ILS and FF Metaheuristics

The aim of this paper is to compare different metaheuristics for the graph bisection problem. For this purpose, the Bui and Moon’s genetic algorithm adaptation for graph bisection is used. A second genetic algorithm adaptation for graph bisection is also presented. These algorithms are compared to an implementation of the iterated local search metaheuristic for graph bisection. All these metaheuristics used a very classical heuristic for graph partitioning, the Kernighan-Lin algorithm, as a local search heuristic. This heuristic is almost used for graph partitioning optimization and very efficient with the multilevel scheme. The multilevel scheme is based on the aggregation of the vertices of the graph to create a smallest graph. As opposed to classical and metaheuristics works on graph partitioning we used a metaheuristic called Fusion-Fission which works on parts of the partition and not on vertices of the graph. This algorithm is described, tested on several graphs and compared with the other algorithms. The test graphs are constructed such that their best partitions and their representations are known, thus graphical representations are shown. These results reveal the ability of ILS and Fusion-Fission algorithms to find the best bisections.