For a given graph G with vertex and edge weights, we partition the vertices into subsets to minimize the total weights for edges crossing the subsets (weighted cut size) under the constraint that the vertex weights are evenly distributed among the subsets. We propose two new effective graph partition algorithms based on simulated annealing and tabu search, and compare their performance with that of the LPK algorithm reported in Ref. 12. Extensive experimental study shows that both of our new algorithms produce significantly better solutions than the LPK algorithm (maximal and minimal improvements on average weighted cut size are roughly 51.8% and 10.5% respectively) with longer running time, and this advantage in solution quality would not change even if we run the LPK algorithm repeatedly with random initial solutions in the same time frame as required by our algorithms.
