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We propose a new gene reordering scheme for the graph bisection problem. Our gene reordering starts with two or more vertices to capture the clustering structure of graphs effectively. We devised a chromosome repairing method for hybrid genetic search, which helps exploit clusters when combined with gene reordering. Experimental tests showed that the suggested reordering scheme significantly improves the performance of genetic algorithms over previous reordering methods.

Most memetic algorithms (MAs) for graph partitioning reduce the cut size of partitions using iterative improvement. But this local process considers one vertex at a time and fails to move clusters between subsets when the movement of any single vertex increases cut size, even though moving the whole cluster would reduce it. A new heuristic identifies clusters from the population of locally optimized random partitions that must anyway be created to seed the MA, and as the MA runs it makes beneficial cluster moves. Results on standard benchmark graphs show significant reductions in cut size, in some cases improving on the best result in the literature.

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