Isomorphism, Normalization, And A Genetic Algorithm For Sorting Network Optimization

In this paper, we de ne sorting network isomorphism and examine its relationship to graph-theoretic problems. We devise the normalization technique that exploits the functional similarities of sorting networks, which in turn helps genetic algorithms avoid too much perturbation. The sorting network isomorphism provides the basis for the normalization. In addition, we developed an e ective local search heuristic for the problem. Combining the local heuristic with a genetic algorithm, we found 60-comparator sorting networks in the 16-bus problem without xing any comparators on a single-CPU PC. This result is signi cantly faster and more stable than the previous study conducted with a supercomputer.